the basics of structural equation modeling

The Basics of FEA Procedure有限元分析程序的基本知识2.1IntroductionThis chapter discusses the spring element,especially for the purpose of introducing various concepts involved in use of the FEA technique.本章讨论了弹簧元件，特别是用于引入使用的有限元分析技术的各种概念的目的A spring element is not very useful in the analysis of real engineering structures;however,it represents a structure in an ideal form for an FEA analysis.Spring element doesn’t require discretization(division into smaller elements)and follows the basic equation F=ku.在分析实际工程结构时弹簧元件不是很有用的;然而,它代表了一个有限元分析结构在一个理想的形式分析。

弹簧元件不需要离散化(分裂成更小的元素)只遵循的基本方程F=ku We will use it solely for the purpose of developing an understanding of FEA concepts and procedure.我们将使用它的目的仅仅是为了对开发有限元分析的概念和过程的理解。

2.2Overview概述Finite Element Analysis(FEA),also known as finite element method(FEM)is based on the concept that a structure can be simulated by the mechanical behavior of a spring in which the applied force is proportional to the displacement of the spring and the relationship F=ku is satisfied.有限元分析(FEA),也称为有限元法(FEM)，是基于一个结构可以由一个弹簧的力学行为模拟的应用力弹簧的位移成正比,F=ku切合的关系。

幼儿建构游戏中的steam学习读后感(中英文实用版)After delving into the concept of integrating STEAM learning into toddlers" constructive play, I was thoroughly impressed by the potential it holds in nurturing young minds.The fusion of science, technology, engineering, arts, and mathematics in playtime activities not only sparks curiosity but also cultivates essential skills for the future.在深入探讨了将STEAM学习融入幼儿建构游戏的概念之后，我对其在培养幼儿心智方面的潜力深感震撼。

将科学、技术、工程、艺术和数学融合到游戏活动中，不仅激发了孩子们的好奇心，同时也培养了他们未来所需的必备技能。

It"s fascinating to observe how, through building blocks or Lego, for instance, children learn about shapes, sizes, and the basics of structural integrity, all while exercising their creativity.The process subtly introduces them to the wonders of engineering and the beauty of artistic design.观察孩子们如何通过积木或乐高等游戏学习形状、大小以及结构完整性的基础，同时锻炼他们的创造力，这简直太神奇了。

财务管理论⽂英⽂⽂献 参考⽂献的引⽤应当实事求是、科学合理，不可以为了凑数随便引⽤。

下⽂是店铺为⼤家整理的关于财务管理论⽂英⽂⽂献的内容，欢迎⼤家阅读参考! 财务管理论⽂英⽂⽂献篇1： [1]Allport, G. W. Personality: A psychological interpretation. New York: Holt,Rinehart & Winston, 1937. [2]DeVellis, R. Scale development: Theory and application. London: Sage. 1991. [3]Anderson,J. R. Methodologies for studying human knowledge. Behavioural and Brain Sciences,1987,10(3)，467-505 [4]Aragon-Comea, J. A. Strategic proactivity and firm approach to the natural environment. Academy of Management Journal,1998,41(5)，556-567. [5]Bandura, A. Social cognitive theory: An agentic perspective. Annual Review of Psychology, 2001,52,1-26. [6]Barr, P. S,Stimpert,J. L,& Huff,A. S. Cognitive change,strategic action and organizational renewal. Strategic Management Journal, 1992,13(S1)，15-36. [7]Bourgeois, L. J. On the measurement of organizational slack. Academy of Management Review, 1981,6(1)，29-39. [8]Belkin, N. J. Anomalous state of knowledge for information retrieval. Canadian Journal of Information Science, 1980,5(5)，133-143. [9]Bentler,P. M,& Chou C. P. Practical issues in structural equation modeling.Sociological Methods and Research,1987,16(1)，78-117 [10]Atkin, C. K. Instrumental utilities and information seeking. New models for mass communication research, Oxford,England: Sage,1973. [11]Adams, M. and Hardwick, P. An Analysis of Corporate Donations: UnitedKingdom Evidence [J], Journal of Management Studies, 1998,35 (5)： 641-654. [12]Aronoff,C.,and J Ward. Family-owned Businesses: A Thing of the Past or Model of the Future. [J]. Family Business Review, 1995,8(2); 121-130. [13]Beckhard,R“Dyer Jr.,W.G. Managing continuity in the family owned business [J]. Organizational Dynamics, 1983,12 (1)： 5-12. [14Casson, M. The economics of family firms [J]. Scandinavian Economic History Review, 1999' 47(1)：10 - 23. [15]Alchian,A.,Demsetz, H. Production, information costs, and economic organization. American Economic Review [J]. 1972,62(5)： 777-795. [16]Allen, F,J, Qian and M, J. Qian. Law,Finance and Economic Growth in China [J], Journal of Financial Economics, 2005,77: pp.57-116. [17]Amato,L. H.,& Amato,C. H. The effects of firm size and industry on corporate giving [J]. Journal of Business Ethics,2007,72(3)： 229-241. [18]Chrisman, J.J., Chua,J.H., and Steier, L. P. An introduction to theories of family business [J]. Journal of Business Venturing, 2003b, 18(4)： 441-448 财务管理论⽂英⽂⽂献篇2： [1]Antelo,M. Licensing a non-drastic innovation under double informational asymmetry. Rese arch Policy,2003,32(3)， 367-390. [2]Arora, A. Patents,licensing, and market structure in the chemical industry.Research Policy, 1997,26(4-5)， 391-403. [3]Aoki,R.,& Tauman,Y. Patent licensing with spillovers. Economics Letters,2001,73(1)，125-130. [4]Agarwal, S,& Hauswald, R. Distance and private information in lending.Review of Financial Studies,2010,23(7)，2757-2788. [5]Brouthers, K.D.,& Hennart, J.F. Boundaries of the firm: insights from international entry mode research. Journal of Management, 2007,33,395-425. [6]Anderson, J. E. A theoretical foundation for the gravity equation. American Economic Review, 1997,69(1)，106-116. [7]Barkema,H. G.,Bell,J. H. J.,& Pennings, J. M. Foreign entry,cultural barriers,and learning. Strategic Management Journal, 1996, 17(2)，151-166. [8]Bass, B.,& Granke, R. Societal influences on student perceptions of how to succeed in organizations. Journal of Applied Psychology, 1972,56(4)，312-318. [9]Bresman, H.,Birkinshaw, J.,& Nobel, R. Knowledge transfer in international acquisitions. Journal of International Business Studies,1999,30(3)，439-462. [10]Chesbrough, H. W.,& Appleyard,M, M. Open innovation and strategy.California Management Review, 2007,50(1)，57-76.。

Mathematics Course DescriptionMathematics course in middle school has two parts: compulsory courses and optional courses. Compulsory courses content lots of modern mathematical knowledge and conceptions, such as calculus,statistics, analytic geometry, algorithm and vector. Optional courses are chosen by students which is according their interests.Compulsory Courses:Set TheoryCourse content:This course introduces a new vocabulary and set of rules that is foundational to the mathematical discussions. Learning the basics of this all-important branch of mathematics so that students are prepared to tackle and understand the concept of mathematical functions. Students learn about how entities are grouped into sets and how to conduct various operations of sets such as unions and intersections(i.e. the algebra of sets). We conclude with a brief introduction to the relationship between functions and sets to set the stage for the next stepKey Topics:The language of set theorySet membershipSubsets, supersets, and equalitySet theory and functionsFunctionsCourse content:This lesson begins with talking about the role of functions and look at the concept of mapping values between domain and range. From there student spend a good deal of time looking at how to visualize various kinds of functions using graphs. This course will begin with the absolute value function and then move on to discuss both exponential and logarithmic functions. Students get an opportunity to see how these functions can be used to model various kinds of phenomena.Key Topics:Single-variable functionsTwo –variable functionsExponential functionLogarithmic functionPower- functionCalculusCourse content:In the first step, the course introduces the conception of limit, derivative and differential. Then students can fully understand what is limit of number sequence and what is limit of function through some specific practices. Moreover, the method to calculate derivative is also introduced to students.Key Topics:Limit theoryDerivativeDifferentialAlgorithmCourse content:Introduce the conception of algorithm and the method to design algorithm. Then the figures of flow charts and the conception of logical structure, like sequential structure, contracture of condition and cycle structure are introduced to students. Next step students can use the knowledge of algorithm to make simple programming language, during this procedure, student also approach to grammatical rules and statements which is as similar as BASIC language.Key Topics:AlgorithmLogical structure of flow chart and algorithmOutput statementInput statementAssignment statementStatisticsCourse content:The course starts with basic knowledge of statistics, such as systematic sampling and group sampling. During the lesson students acquire the knowledge like how to estimate collectivity distribution according frequency distribution of samples, and how to compute numerical characteristics of collectivity by looking at numerical characteristics of samples. Finally, the relationship and the interdependency of two variables is introduced to make sure that students mastered in how to make scatterplot, how to calculate regression line, and what is Method of Square.Key Topics:Systematic samplingGroup samplingRelationship between two variablesInterdependency of two variablesBasic Trigonometry ICourse content:This course talks about the properties of triangles and looks at the relationship that exists between their internal angles and lengths of their sides. This leads to discussion of the most commonly used trigonometric functions that relate triangle properties to unit circles. This includes the sine, cosine and tangent functions. Students can use these properties and functions to solve a number of issues.Key Topics:Common AnglesThe polar coordinate systemTriangles propertiesRight trianglesThe trigonometric functionsApplications of basic trigonometryBasic Trigonometry IICourse content:This course will look at the very important inverse trig functions such as arcsin, arcos, and arctan, and see how they can be used to determine angle values. Students also learn core trig identities such as the reduction and double angle identities and use them as a means for deriving proofs. Key Topics:Derivative trigonometric functionsInverse trig functionsIdentities●Pythagorean identities●Reduction identities●Angle sum/Difference identities●Double-angle identitiesAnalytic Geometry ICourse content:This course introduces analytic geometry as the means for using functions and polynomials to mathematically represent points, lines, planes and ellipses. All of these concepts are vital in student’s mathematical development since they are used in rendering and optimization, collision detection, response and other critical areas. Students look at intersection formulas and distance formulas with respect to lines, points, planes and also briefly talk about ellipsoidal intersections. Key Topics:Parametric representationParallel and perpendicular linesIntersection of two linesDistance from a point to a lineAngles between linesAnalytic Geometry IICourse content:Students look at how analytic geometry plays an important role in a number of different areas of class design. Students continue intersection discussion by looking at a way to detect collision between two convex polygons. Then students can wrap things up with a look at the Lambertian Diffuse Lighting model to see how vector dot products can be used to determine the lighting and shading of points across a surface.Key Topics:ReflectionsPolygon/polygon intersectionLightingSequence of NumberCourse content:This course begin with introducing several conceptions of sequence of number, such as, term, finite sequence of number, infinite sequence of number, formula of general term and recurrence formula.Then, the conception of geometric sequence and arithmetic sequence is introduced to students. Through practices and mathematical games, students gradually understand and utilizethe knowledge of sequence of number, eventually students are able to solve mathematical questions.Key Topics:Sequence of numberGeometric sequenceArithmetic sequenceInequalityThis course introduces conception of inequality as well as its properties. In the following lessons students learn the solutions and arithmetic of one-variable quadratic inequality, two variables inequality, fundamental inequality as well how to solve simple linear programming problems. Key Topics:Unequal relationship and InequalityOne-variable quadratic inequality and its solutionTwo-variable inequality and linear programmingFundamental inequalityVector MathematicsCourse content:After an introduction to the concept of vectors, students look at how to perform various important mathematical operations on them. This includes addition and subtraction, scalar multiplication, and the all-important dot and cross products. After laying this computational foundation, students engage in games and talk about their relationship with planes and the plane representation, revisit distance calculations using vectors and see how to rotate and scale geometry using vector representations of mesh vertices.Key Topics:Linear combinationsVector representationsAddition/ subtractionScalar multiplication/ divisionThe dot productVector projectionThe cross productOptional CoursesMatrix ICourse content:In this course, students are introduced to the concept of a matrix like vectors, matrices and so on. In the first two lessons, student look at matrices from a purely mathematical perspective. The course talks about what matrices are and what problems they are intended to solve and then looks at various operations that can be performed using them. This includes topics like matrix addition and subtraction and multiplication by scalars or by other matrices. At the end, students can conclude this course with an overview of the concept of using matrices to solve system of linear equations.Key Topics:Matrix relationsMatrix operations●Addition/subtraction●Scalar multiplication●Matrix Multiplication●Transpose●Determinant●InversePolynomialsCourse content:This course begins with an examination of the algebra of polynomials and then move on to look at the graphs for various kinds of polynomial functions. The course starts with linear interpolation using polynomials that is commonly used to draw polygons on display. From there students are asked to look at how to take complex functions that would be too costly to compute in a relatively relaxed studying environment and use polynomials to approximate the behavior of the function to produce similar results. Students can wrap things up by looking at how polynomials can be used as means for predicting the future values of variables.Key Topics:Polynomial algebra ( single variable)●addition/subtraction●multiplication/divisionQuadratic equationsGraphing polynomialsLogical Terms in MathematicsCourse content:This course introduces the relationships of four kinds of statements, necessary and sufficient conditions, basic logical conjunctions, existing quantifier and universal quantifier. By learning mathematical logic terms, students can be mastered in the usage of common logical terms and can self-correct logical mistakes. At the end of this course, students can deeply understand the mathematical expression is not only accurate but also concise.Key Topics:Statement and its relationshipNecessary and sufficient conditionsBasic logical conjunctionsExisting quantifier and universal quantifierConic Sections and EquationCourse content:By using the knowledge of coordinate method which have been taught in the lesson of linear and circle, in this lesson students learn how to set an equation according the character of conic sections. Students is able to find out the property of conic sections during establishing equations. The aim of this course is to make students understand the idea of combination of number and shape by using the method of coordinate to solve simple geometrical problems which are related to conic sections.Key Topics:Curve and equation OvalHyperbolaParabola。

School of chemical engineering and pharmaceuticaltest tubes 试管test tube holder试管夹test tube brush 试管刷test tube rack试管架beaker烧杯stirring搅拌棒thermometer温度计boiling flask长颈烧瓶Florence flask平底烧瓶flask,round bottom,two-neck boiling flask,three-neck conical flask锥形瓶wide-mouth bottle广口瓶graduated cylinder量筒gas measuring tube气体检测管volumetric flask容量瓶transfer pipette移液管Geiser burette(stopcock)酸式滴定管funnel漏斗Mohr burette(with pinchcock)碱式滴定管watch glass表面皿evaporating dish蒸发皿ground joint磨口连接Petri dish有盖培养皿desiccators干燥皿long-stem funnel长颈漏斗filter funnel过滤漏斗Büchner funnel瓷漏斗separatory funnel分液漏斗Hirsh funnel赫尔什漏斗filter flask 吸滤瓶Thiele melting point tube蒂勒熔点管plastic squeez e bottle塑料洗瓶 medicine dropper药用滴管rubber pipette bulb 吸球microspatula微型压舌板pipet吸量管mortar and pestle研体及研钵filter paper滤纸Bunsen burner煤气灯burette stand滴定管架support ring支撑环ring stand环架distilling head蒸馏头side-arm distillation flask侧臂蒸馏烧瓶air condenser空气冷凝器centrifuge tube离心管fractionating column精(分)馏管Graham condenser蛇形冷凝器crucible坩埚crucible tongs坩埚钳beaker tong烧杯钳economy extension clamp经济扩展夹extension clamp牵引夹utility clamp铁试管夹hose clamp软管夹 burette clamp pinchcock;pinch clamp弹簧夹 screw clamp 螺丝钳ring clamp 环形夹goggles护目镜stopcock活塞wire gauze铁丝网analytical balance分析天平分析化学absolute error绝对误差accuracy准确度assay化验analyte(被)分析物calibration校准constituent成分coefficient of variation变异系数confidence level置信水平detection limit检出限determination测定estimation 估算equivalent point等当点gross error总误差impurity杂质indicator指示剂interference干扰internal standard内标level of significance显着性水平 limit of quantitation定量限masking掩蔽matrix基体precision精确度primary standard原始标准物purity纯度qualitative analysis定性分析 quantitative analysis定量分析random error偶然误差reagent试剂relative error相对误差robustness耐用性sample样品relative standard deviation相对标准偏差 selectivity选择性sensitivity灵敏度specificity专属性titration滴定significant figure有效数字solubility product溶度积standard addition标准加入法standard deviation标准偏差standardization标定法stoichiometric point化学计量点systematic error系统误差有机化学acid anhydride 酸酐acyl halide 酰卤alcohol 醇aldehyde 醛aliphatic 脂肪族的alkene 烯烃alkyne炔allyl烯丙基amide氨基化合物amino acid 氨基酸aromatic compound 芳香烃化合物amine胺butyl 丁基aromatic ring芳环,苯环 branched-chain支链chain链carbonyl羰基carboxyl羧基chelate螯合chiral center手性中心conformers构象copolymer共聚物derivative 衍生物dextrorotatary右旋性的diazotization重氮化作用dichloromethane二氯甲烷ester酯ethyl乙基fatty acid脂肪酸functional group 官能团general formula 通式glycerol 甘油，丙三醇heptyl 庚基heterocyclie 杂环的hexyl 己基homolog 同系物hydrocarbon 烃,碳氢化合物hydrophilic 亲水的hydrophobic 疏水的hydroxide 烃基ketone 酮levorotatory左旋性的methyl 甲基molecular formula分子式monomer单体octyl辛基open chain开链optical activity旋光性（度）organic 有机的organic chemistry 有机化学organic compounds有机化合物pentyl戊基phenol苯酚phenyl苯基polymer 聚合物，聚合体propyl丙基ring-shaped环状结构 zwitterion兼性离子saturated compound饱和化合物side chain侧链straight chain 直链tautomer互变（异构）体structural formula结构式triglyceride甘油三酸脂unsaturated compound不饱和化合物物理化学activation energy活化能adiabat绝热线amplitude振幅collision theory碰撞理论empirical temperature假定温度enthalpy焓enthalpy of combustion燃烧焓enthalpy of fusion熔化热enthalpy of hydration水合热enthalpy of reaction反应热enthalpy o f sublimation升华热enthalpy of vaporization汽化热entropy熵first law热力学第一定律first order reaction一级反应free energy自由能Hess’s law盖斯定律Gibbs free energy offormation吉布斯生成能heat capacity热容internal energy内能isobar等压线isochore等容线isotherm等温线kinetic energy动能latent heat潜能Planck’s constant普朗克常数potential energy势能quantum量子quantum mechanics量子力学rate law速率定律specific heat比热spontaneous自发的standard enthalpy change标准焓变standard entropy of reaction标准反应熵standard molar entropy标准摩尔熵standard pressure标压state function状态函数thermal energy热能thermochemical equation热化学方程式thermodynamic equilibrium热力学平衡uncertainty principle测不准定理zero order reaction零级反应 zero point energy零点能课文词汇实验安全及记录：eye wash眼药水first-aid kit急救箱gas line输气管safety shower紧急冲淋房water faucet水龙头flow chart流程图loose leaf活页单元操作分类：heat transfer传热Liquid-liquid extraction液液萃取liquid-solid leaching过滤vapor pressure蒸气压membrane separation薄膜分离空气污染：carbon dioxide 二氧化碳carbon monoxide一氧化碳particulate matter颗粒物质photochemical smog光化烟雾primary pollutants一次污染物secondary pollutants二次污染物 stratospheric ozone depletion平流层臭氧消耗sulfur dioxide二氧化硫volcanic eruption火山爆发食品化学：amino acid氨基酸,胺amino group氨基empirical formula实验式,经验式fatty acid脂肪酸peptide bonds肽键polyphenol oxidase 多酚氧化酶salivary amylase唾液淀粉酶 steroid hormone甾类激素table sugar蔗糖triacylglycerol三酰甘油,甘油三酯食品添加剂：acesulfame-K乙酰磺胺酸钾,一种甜味剂adrenal gland肾上腺ionizing radiation致电离辐射food additives食品添加剂monosodium glutamate味精,谷氨酸一钠（味精的化学成分）natural flavors天然食用香料,天然食用调料nutrasweet天冬甜素potassium bromide 溴化钾propyl gallate没食子酸丙酯sodium chloride氯化钠sodium nitraten硝酸钠sodium nitrite亚硝酸钠trans fats反式脂肪genetic food转基因食品food poisoning 食物中毒hazard analysis and critical control points (HACCP)危害分析关键控制点技术maternal and child health care妇幼保健护理national patriotic health campaign committee(NPHCC) 全国爱国卫生运动委员会rural health农村卫生管理the state food and drug administration (SFDA)国家食品药品监督管理局光谱：Astronomical Spectroscopy天文光谱学Laser Spectroscopy激光光谱学 Mass Spectrometry质谱Atomic Absorption Spectroscopy原子吸收光谱Attenuated T otal Reflectance Spectroscopy衰减全反射光谱Electron Paramagnetic Spectroscopy电子顺磁谱Electron Spectroscopy电子光谱Infrared Spectroscopy红外光谱Fourier Transform Spectrosopy傅里叶变换光谱Gamma-ray Spectroscopy伽玛射线光谱Multiplex or Frequency-Modulated Spectroscopy复用或频率调制光谱X-ray SpectroscopyX射线光谱色谱：Gas Chromatography气相色谱High Performance Liquid Chromatography高效液相色谱Thin-Layer Chromatography薄层色谱magnesium silicate gel硅酸镁凝胶retention time保留时间mobile phase流动相stationary phase固定相反应类型：agitated tank搅拌槽catalytic reactor催化反应器batch stirred tank reactor间歇搅拌反应釜continuous stirred tank 连续搅拌釜exothermic reactions放热反应pilot plant试验工厂fluidized bed Reactor流动床反应釜multiphase chemical reactions 多相化学反应packed bed reactor填充床反应器redox reaction氧化还原反应reductant-oxidant氧化还原剂acid base reaction酸碱反应additionreaction加成反应chemical equation化学方程式valence electron价电子combination reaction化合反应hybrid orbital 杂化轨道decomposition reaction分解反应substitution reaction取代(置换)反应Lesson5 Classification of Unit Operations单元操作Fluid flow流体流动它涉及的原理是确定任一流体从一个点到另一个点的流动和输送。

‘Structural Chemistry ’Course SyllabusCourse Code：09040001Course Category：Major BasicMajors：ChemistrySemester：SpringTotal Hours：54 Hours Credit：3Lecture Hours：54 HoursTextbooks：《Structural Chemistry》孙墨珑编著，东北林业大学出版社。

I.Introduction to Structural ChemistryThe major targets this course includes the followings: (1) to introduce the material structure of the basic concepts, basic theory, and basic methods for learning “Structural Chemistry”; (2) to explore the relationship between the microstructures and properties of atoms, molecules, and crystals; (3) to systematically clarify the essence of the periodic law of elements; (4) to deeply and qualitatively clarify the essence of the chemical bonds. This course introduces the basic principles of quantum mechanics and their applications in simple systems, structure of atoms, molecules, and crystals, symmetry of molecular orbitals, molecular orbital theory, and ligand field theory, etc. After learning this course, the students should be able to analyze and solve the basic chemistry problems from the point of view of quantum mechanics.II.Table of contentsSection I (Chapter 1) Basic knowledge of quantum mechanics1.1 Failures of classical mechanics1）Black-body radiation & Planck’s solution;2）Ph otoelectric effect & Einstein’s theory;3）Hydrogen spectrum & Bohr’s model.1.2Characteristics of the motion of microscopic particles1)Wave-particle duality;2)Uncertainty principle.1.3The basic postulates of quantum mechanics1)Postulate 1: wavefunction;2)Postulate 2: Hermitian operators;3)Postulate 3: Schrödinger equation;4)Postulate 4: linearity and superposition;5)Postulate 5: Pauli exclusion principle.1.4Applications of quantum mechanics in simple cases1)Free particle in one-dimensional (1D) box;2)Applications of the 1D-box model in simple chemical systems;3)Free particle in two-dimensional (2D) & three-dimensional (3D) box;4)Tunneling & scanning tunneling microscopy (STM).Section II (Chapter 2) Structures and properties of atoms2.1 One-electron atom: H atom1)The Schrödinger equation of H atoms;2)Solution of the Schrödinger equation of H atom.2.2Quantum numbers1)Principle quantum number, n;2)Angular momentum quantum number, l;3)Magnetic quantum number, m;4)Zeeman effect.2.3Wavefunction and electron cloud1)Radial distribution;2)Angular distribution;3)Spatial distribution.2.4 Structure of multi-electron atoms1)The Schrödinger equation of multi-electron atoms•Self-consistent field method;•Central field approximation.2)The building-up principles and electron configuration of multi-electron atoms•Pauli exclusion principle;•Principle of minimum energy;Hund’s rule.2.5Electron spin and Pauli exclusion principle2.6Atomic spectroscopy1)Orbital-spin coupling;2)Spectroscopic terms & term symbol;3)Derivation of atomic term.4)Hund’s rule on the spectroscopic terms;2.7Atomic properties1)Energy of ionization;2)Electron affinity;3)Electronegativity.Section III (Chapters 3-6) Structures and properties of molecules Chapter 3 Geometric structure of molecules─Molecular symmetry & symmetry point group3.1Symmetry elements and symmetry operations1)Symmetry elements and symmetry operations;2)Combination rules of symmetry elements;3.2Point groups & symmetry classification of molecules3.3Point groups & groups multiplication3.4Applications of molecular symmetry1)Chirality & optical activity;2)Polarity & dipole moment.Chapter 4 S tructure of biatomic molecules (X2 & XY)4.1 Linear variation method and structure of H2+ ion1) Shrödinger equation of H2+ ion;2) Linear variation method;3) Treatment of H2+ ion using linear variation method;4) Solutions of H2+ ion.4.2 Molecular orbital theory and diatomic molecules1) Molecular orbital theory;2) Structure of homonuclear diatomic molecules (X2);3) Structure of heteronuclear diatomic molecules (XY).4.3 Valence bond (VB) theory and H2 moleculeChapter 5 Structure of polyatomic molecules (A)5.1 Structure of Methane (CH4)1) Delocalized molecular orbitals of methane (CH4);2) Localized molecular orbitals of methane (CH4).5.2 Molecular orbital hybridization1) Theory of molecular orbital hybridization;2) Construction of hybrid orbitals;3) Structure of AB n molecules;4) Molecular stereochemistry: valence shell electron-pair repulsion (VSEPR)model.5.3 Delocalized molecular orbital theory─Hückel molecular orbital (HMO) theory1) HMO method & conjugated systems;2) HMO treatment for butadiene;3) HMO treatment for cyclic conjugated polyene (C n H n);4) Molecular diagrams;5) Delocalized π bonds.5.4 Structure of electron deficient molecules5.5 Symmetry of molecular orbitals and symmetry rules for molecular reactions5.6 Molecular spectroscopy1)Infrared absorption spectroscopy: molecular vibrations;2)Raman scattering spectroscopy: molecular vibrations;3)Fluorescence spectroscopy: electronic transitions;4)NMR spectroscopy: nuclear magnetic resonances.Chapter 6 Structure of polyatomic molecules (B), coordination compounds 6.1 Crystal field theory6.2 CO and N2 coordination complexes6.3 Organic metal complexes1) Zeise’s salts;2) Sandwich complexes.6.4 Clusters1) Transition-metal cluster compounds2) Carbon clusters and nanotubesSection IV (Chapters 7-9) Structure of crystalsChapter 7 Basics of crystallography7.1 Periodicity and lattices of crystal structure1) Characteristics of crystal structure;2) Lattices and unit cells;3) Bravais lattices and unit cells of crystals;4) Real crystals & crystal defects.7.2 Symmetry in crystal structure1) Symmetry elements and symmetry operations;2) Point groups (32) and space groups (230).7.3 X-Ray diffraction of crystals1) X-ray diffraction of crystals•Laue equation;•Bragg’s law;•Reciprocal lattice.2) Instrumentation of X-ray diffraction;3) Applications of X-Ray diffraction•Single crystal diffraction: crystal structure determination;•Powder diffraction: qualitative & quantitative analysis of crystalline materialsChapter 8 Crystalline solids, I: metals and alloys8.1 Close Packing of Spheres1) Close packing of identical spheres;2) Packing density;3) Interstices.8.2 Structures and Properties of Pure Metals8.3 Structures and Properties of AlloyChapter 9 Crystalline solids, II: ionic crystals9.1 Packing of Ions;9.2 Crystal Structure of Some Typical Ionic Compounds9.3 Trend of Variation of Ionic Radii9.4 Pauling Rule of Ionic Crystal Structure9.5 Crystals of Functional Materials1) Nonlinear optical materials;2) Magnetic materials;3) Conductive polymers;4) Semiconductors: band gap and photocatalysisIII.Table of ScheduleReferences[1] 王荣顺主编，东北师范大学等，《结构化学》，高等教育出版社，2003年。

结构方程模型英语Structural Equation ModelingStructural equation modeling (SEM) is a powerful and versatile type of statistical modeling used to examine relationships among observed and latent variables. It is a multivariate method of analysis that is particularly useful when examining complex systems. Structural equation modeling examines the relationships between variables to determine the causal effect of one variable on another, or the degree of correlation between two variables. The model is often used to make predictions about relationships and can be used to evaluate the accuracy of a hypothesis or to explore the validity of a theory.Structural equation modeling consists of a set of equations that represent a system of relationships between observed and latent variables. The equations are derived from a model, which is a graphical representation of the relationships between variables. Each equation is a mathematical representation of the relationships between a set of observed and latent variables. The equations are usually derived from a path analysis of the relationships between variables. The equations are used to estimate the parameters of the model, which are thenused to make predictions about relationships and to evaluate the accuracy of the model.Structural equation modelling is a powerful tool that can be used to understand the relationships between variables in various ways. It can be used to evaluate the validity of a hypothesis, to explore the structure of a data set, and to make predictions about relationships between variables. It is also a useful tool for studying the causal effect of one variable on another, or the degree of correlation between variables. SEM has become increasingly popular in recent years, in part due to its ability to analyze data from a variety of sources, including self-report surveys, observational studies, and databases. Structural equation modeling has become a valuable tool for researchers and scholars in a variety of fields, including psychology, sociology, economics, and public health.。

摘要机械手是在自动化生产过程中使用的一种具有抓取和移动工件功能的自动化装置，由其控制系统执行预定的程序实现对工件的定位夹持。

完全取代了人力，节省了劳动资源，提高了生产效率。

本设计以实现铣床自动上下料为目的，设计了个水平伸缩距为200mm，垂直伸缩距为200mm具有三个自由度的铣床上下料机械手。

机械手三个自由度分别是机身的旋转，手臂的升降，以及机身的升降。

在设计过程中，确定了铣床上下料机械手的总体方案，并对铣床上下料机械手的总体结构进行了设计，对一些部件进行了参数确定以及对主要的零部件进行了计算和校核。

以单片机为控制手段，设计了机械手的自动控制系统，实现了对铣床上下料机械手的准确控制。

关键词：机械手；三自由度；上下料；单片机AbstractManipulator , an automation equipment with function of grabbing and moving the workpiece ,is used in an automated production process.It perform scheduled program by the control system to realize the function of the positioning of the workpiece clamping. It completely replace the human, saving labor resources, and improve production efficiency.This design is to achieve milling automatic loading and unloading .Design a manipulator with three degrees of freedom and 200mm horizontal stretching distance, 120mm vertical telescopic distance. Three degrees of freedom of the manipulator is body rotation, arm movements, as well as the movements of the body. In the design process, determine the overall scheme of the milling machine loading and unloading manipulator and milling machine loading and unloading manipulator, the overall structure of the design parameters of some components as well as the main components of the calculation and verification. In the means of Single-chip microcomputer for controlling, design the automatic control system of the manipulator and achieve accurate control of the milling machine loading and unloading.Key words: Manipulator; Three Degrees of Freedom; Loading and unloading; single chip microcomputer目录摘要．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．I第1章绪论．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．11.1选题背景．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． (1)1.2设计目的．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．11.3国内外研究现状和趋势．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．21.4设计原则．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．2第2章设计方案的论证．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．32.1 机械手的总体设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．32.1.1机械手总体结构的类型．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．32.1.2 设计具体采用方案．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．42.2 机械手腰座结构设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．52.2.1 机械手腰座结构设计要求．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．52.2.2 具体设计采用方案．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．52.3 机械手手臂的结构设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．62.3.1机械手手臂的设计要求．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．62.3.2 设计具体采用方案．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．72.4 设计机械手手部连接方式．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．72.5 机械手末端执行器（手部）的结构设计．．．．．．．．．．．．．．．．．．．．．．．．．．．82.5.1 机械手末端执行器的设计要求．．．．．．．．．．．．．．．．．．．．．．．．．．．．．82.5.2 机械手夹持器的运动和驱动方式．．．．．．．．．．．．．．．．．．．．．．．．．．92.5.3 机械手夹持器的典型结构．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．92.6 机械手的机械传动机构的设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．102.6.1 工业机械手传动机构设计应注意的问题．．．．．．．．．．．．．．．．．．．102.6.2 工业机械手传动机构常用的机构形式．．．．．．．．．．．．．．．．．．．．．102.6.3 设计具体采用方案．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．122.7 机械手驱动系统的设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．122.7.1 机械手各类驱动系统的特点．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．122.7.2 机械手液压驱动系统．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．132.7.3机身摆动驱动元件的选取．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．132.7.4 设计具体采用方案．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．142.8 机械手手臂的平衡机构设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．14第3章理论分析和设计计算．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．163.1 液压传动系统设计计算．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．163.1.1 确定液压传动系统基本方案．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．163.1.2 拟定液压执行元件运动控制回路．．．．．．．．．．．．．．．．．．．．．．．．．．．173.1.3 液压源系统的设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．173.1.4 确定液压系统的主要参数．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．173.1.5 计算和选择液压元件．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．243.1.6机械手爪各结构尺寸的计算．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．26 第4章机械手控制系统的设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．284.1 系统总体方案．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．284.2 各芯片工作原理．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．284.2.1 串口转换芯片．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．284.2.2 单片机．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．294.2.3 8279芯片．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．304.2.4 译码器．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．314.2.5 放大芯片．．．．．．．．．．．．．．．．．．．．．．．.．．．．．．．．．．．．．．．．．．．．．．．．324.3 电路设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．334.3.1 显示电路设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．334.3.2 键盘电路设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．334.4 复位电路设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．334.5 晶体振荡电路设计．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．344.6 传感器的选择．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．34结论．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．36致谢．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．37参考文献．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．38CONTENTS Abstract (I)Chapter 1 Introduction (1)1.1 background (1)1.2 design purpose (1)1.3 domestic and foreign research present situation and trends (2)1.4 design principles (2)Chapter 2 Design of the demonstration (3)2.1manipulator overall design (3)2.1.1 manipulator overall structure type (3)2.1.2 design adopts the scheme (4)2.2 lumbar base structure design of mechanical hand (5)2.2.1 manipulator lumbar base structure design requirements (5)2.2.2specific design schemes (5)2.3mechanical arm structure design (6)2.3.1 manipulator arm design requirements (6)2.3.2 design adopts the scheme (7)2.4 design of mechanical hand connection mode (7)2.5 the manipulator end-effector structure design (8)2.5.1 manipulator end-effector design requirements (8)2.5.2 manipulator gripper motion and driving method (9)2.5.3 manipulator gripper structure (9)2.6 robot mechanical transmission design (10)2.6.1 industry for transmission mechanism of manipulator design shouldpay attention question (10)2.6.2 industrial machinery hand transmission mechanism commonlyused form of institution (10)2.6.3 design adopts the scheme (12)2.7 mechanical arm drive system design (12)2.7.1 manipulator of various characteristics of the drive system (12)2.7.2 hydraulic drive system for a manipulator (13)2.7.3 Body swing the selection of drive components (13)2.7.4 Design the specific use of the program (14)2.8 mechanical arm balance mechanism design (14)Chapter 3 Theoretical analysis and design calculation (16)3.1 hydraulic system design and calculation (16)3.1.1 the basic scheme of hydrauic transmission system (16)3.1.2 formulation of the hydraulic actuator control circuit (17)3.1.3 hydraulic source system design (17)3.1.4 determine the main parameters of the hydraulic system (17)3.1.5 calculation and selection of hydraulic components (24)3.1.6 Manipulator calculation of the structural dimensions (26)Chapter 4 The robot control system design (28)4.1 Overall scheme (28)4.2 Chip works (28)4.2.1 serial conversion chip (28)4.2.2 MCU (29)4.2.3 8279 chip (30)4.2 .4 decoder (31)4.2.5 amplifier chip (32)4.3 Circuit design (33)4.3.1 show the circuit design (33)4.3.2 The keyboard circuit design (33)4.4 Reset circuit design (33)4.5 crystal oscillation circuit design (34)4.6 sensor selection (34)Conclusion (36)Acknowledgements (37)References (38)第1章绪论1.1选题背景机械手是在自动化生产过程中使用的一种具有抓取和移动工件功能的自动化装置，它是在机械化、自动化生产过程中发展起来的一种新型装置。

The Fundamentals of Modal TestingApplication Note 243 - 3Η(ω) = Σnr =1φφi j /m(n - )+ (2n )ωωξωω22 2 2PrefaceModal analysis is defined as the study of the dynamic characteristics of a mechanical structure. This applica-tion note emphasizes experimental modal techniques, specifically the method known as frequency response function testing. Other areas are treated in a general sense to intro-duce their elementary concepts and relationships to one another. Although modal techniques are math-ematical in nature, the discussion is inclined toward practical application. Theory is presented as needed to enhance the logical development of ideas. The reader will gain a sound physical understanding of modal analysis and be able to carry outan effective modal survey with confidence.Chapter 1 provides a brief overview of structural dynamics theory. Chapter 2 and 3 which is the bulkof the note – describes the measure-ment process for acquiring frequency response data. Chapter 4 describes the parameter estimation methods for extracting modal properties. Chapter 5 provides an overviewof analytical techniques of structural analysis and their relation to experimental modal testing.2Table of ContentsPreface2Chapter 1 — Structural Dynamics Background4Introduction4Structural Dynamics of a Single Degree of Freedom (SDOF) System5Presentation and Characteristics of Frequency Response Functions6Structural Dynamics for a Multiple Degree of Freedom (MDOF) System9Damping Mechanism and Damping Model11Frequency Response Function and Transfer Function Relationship12System Assumptions13Chapter 2 — Frequency Response Measurements14Introduction14General Test System Configurations15Supporting the Structure16Exciting the Structure18Shaker Testing19Impact Testing22Transduction25Measurement Interpretation29Chapter 3 — Improving Measurement Accuracy30Measurement Averaging30Windowing Time Data31Increasing Measurement Resolution32Complete Survey34Chapter 4 — Modal Parameter Estimation38Introduction38Modal Parameters39Curve Fitting Methods40Single Mode Methods41Concept of Residual Terms43Multiple Mode-Methods45Concept of Real and Complex Modes47Chapter 5 — Structural Analysis Methods48Introduction48Structural Modification49Finite Element Correlation50Substructure Coupling Analysis52Forced Response Simulation53Bibliography543IntroductionA basic understanding of structural dynamics is necessary for successful modal testing. Specifically, it is important to have a good grasp of the relationships between frequency response functions and their individ-ual modal parameters illustrated in Figure 1.1. This understanding is of value in both the measurement and analysis phases of the survey. Know-ing the various forms and trends of frequency response functions will lead to more accuracy during the measurement phase. During the analysis phase, knowing how equa-tions relate to frequency responses leads to more accurate estimation of modal parameters.The basic equations and their various forms will be presented conceptually to give insight into the relationships between the dynamic characteristics of the structure and the correspond-ing frequency response function measurements. Although practical systems are multiple degree of free-dom (MDOF) and have some degree of nonlinearity, they can generally be represented as a superpositionof single degree of freedom (SDOF) linear models and will be developed in this manner.First, the basics of an SDOF linear dynamic system are presented to gain insight into the single mode concepts that are the basis of some parameter estimation techniques. Second, the presentation and properties of vari-ous forms of the frequency response function are examined to understand the trends and their usefulness in themeasurement process. Finally, theseconcepts are extended into MDOFsystems, since this is the type ofbehavior most physical structuresexhibit. Also, useful conceptsassociated with damping mechanismsand linear system assumptionsare discussed.Figure 1.1Phases of amodal testModal ParametersCurve Fit RepresentationΗ(ω) = Σijnr=1φ φir jrmr (r-+ j2r)ωωζωω22ωζφ—Frequency—Damping{}—Mode ShapeChapter 1Structural Dynamics Background45Structural Dynamics of a Single Degree of Freedom (SDOF) SystemAlthough most physical structures are continuous, their behavior can usual-ly be represented by a discrete parameter model as illustrated in Figure 1.2. The idealized elements are called mass, spring, damper and excitation. The first three elements describe the physical system. Energy is stored by the system in the mass and the spring in the form of kinetic and potential energy, respectively. Energy enters the system through excitation and is dissipated through damping.The idealized elements of the physi-cal system can be described by the equation of motion shown in Figure 1.3. This equation relates the effects of the mass, stiffness and damping in a way that leads to the calculation of natural frequency and damping factor of the system. This computation is often facilitated by the use of the def-initions shown in Figure 1.3 that lead directly to the natural frequency and damping factor.The natural frequency, ω, is in units of radians per second (rad/s). The typical units displayed on a digital signal analyzer, however, are in Hertz (Hz). The damping factor can also be represented as a percent of critical damping – the damping level at which the system experiences no oscillation.This is the more common understand-ing of modal damping. Although there are three distinct damping cases, only the underdamped case (ζ< 1) is important for structural dynamics applications.Figure 1.2SDOF discrete parameter modelFigure 1.3Equation of motion —modal definitionsFigure 1.4Complex roots of SDOF equationFigure 1.5SDOF impulse response/free decayResponsemx + cx + kx = f(t)...ω2n = ,k m2n =ζωc m or =ζc2km s = -+ j d1,2σωσωζ— Damping Rate— Damped Natural FrequencyWhen there is no excitation, the roots of the equation are as shown in Figure 1.4. Each root has two parts: the real part or decay rate, which defines damping in the system and the imaginary part, or oscillatory rate, which defines the damped natural frequency, wd. This free vibration response is illustratedin Figure 1.5.When excitation is applied, the equa-tion of motion leads to the frequency response of the system. The frequen-cy response is a complex quantity and contains both real and imaginary parts (rectangular coordinates). It can be presented in polar coordinates as magnitude and phase, as well. Presentation and Characteristics of Frequency Response FunctionsBecause it is a complex quantity, the frequency response function cannot be fully displayed on a single two-dimensional plot. It can, however, be presented in several formats, each of which has its own uses. Although the response variable for the previous discussion was displacement, it could also be velocity or acceleration. Acceleration is currently the accepted method of measuring modal response.One method of presenting the datais to plot the polar coordinates, mag-nitude and phase versus frequency as illustrated in Figure 1.6. At reso-nance, when ω= ωn, the magnitude is a maximum and is limited only by the amount of damping in the system. The phase ranges from 0° to 180° and the response lags the input by 90° at resonance.Figure 1.6Frequencyresponse —polarcoordinatesMagnitudePhaseωdωdH() =ωθω() = tan-11/m(n- )+ (2n)ωωζωω22 2 22nn-ξωωωω226Another method of presentingthe data is to plot the rectangular coordinates, the real part and the imaginary part versus frequency.For a proportionally damped system, the imaginary part is maximum at resonance and the real part is 0, as shown in Figure 1.7.A third method of presenting the frequency response is to plot the real part versus the imaginary part. This is often called a Nyquist plot or a vector response plot. This display empha-sizes the area of frequency response at resonance and traces out a circle, as shown in Figure 1.8.By plotting the magnitude in decibels vs logarithmic (log) frequency, it is possible to cover a wider frequency range and conveniently display the range of amplitude. This type of plot, often known as a Bode plot, also has some useful parameter character-istics which are described in the following plots.When ω<< ωn the frequency response is approximately equal to the asymptote shown in Figure 1.9. This asymptote is called the stiffness line and has a slope of 0, 1 or 2 for displacement, velocity and accelera-tion responses, respectively. When ω>> ωn the frequency response is approximately equal to the asymptote also shown in Figure 1.9. This asymp-tote is called the mass line and has a slope of -2, -1 or 0 for displacement velocity or acceleration responses, respectively. Figure 1.7Frequencyresponse —rectangularcoordinatesFigure 1.8Nyquist plotof frequencyresponseRealImaginaryH() =ω-2n(n- )+ (2n)ξωωωωζωω22 2 2H() =ωωωωωζωω2222 2 2n -(n- )+ (2n)7The various forms of frequency response function based on thetype of response variable are also defined from a mechanical engineer-ing viewpoint. They are somewhat intuitive and do not necessarily corre-spond to electrical analogies. These forms are summarized in Table 1.1.Figure 1.9 Different forms of frequency responseTable 1.1Different formsof frequency responseDefinition Response Variable Compliance X DisplacementF Force Mobility V VelocityF Force Accelerance A AccelerationF DisplacementAccelerationVelocityFrequency89Structural Dynamics for a Multiple Degree of Freedom (MDOF) SystemThe extension of SDOF concepts to a more general MDOF system, with n degrees of freedom, is a straightfor-ward process. The physical system is simply comprised of an interconnec-tion of idealized SDOF models, as illustrated in Figure 1.10, and is described by the matrix equationsof motion as illustrated in Figure 1.11. The solution of the equation with no excitation again leads to the modal parameters (roots of the equation) of the system. For the MDOF case,however, a unique displacement vector called the mode shape exists for each distinct frequency and damp-ing as illustrated in Figure 1.11. The free vibration response is illustrated in Figure 1.12.The equations of motion for the forced vibration case also lead to frequency response of the system. It can be written as a weightedsummation of SDOF systems shown in Figure 1.13.The weighting, often called the modal participation factor, is a function of excitation and mode shape coeffi-cients at the input and output degrees of freedom.Figure 1.10MDOF discrete parameter modelFigure 1.11Equations of motion —modal definitionsFigure 1.12MDOF impulse response/free decay[m]{x} + [c]{x} + [k]{x} = {f(t)}{}r , r = 1, n modesφ...A m p l i t u d e 0.0Sec 6.010The participation factor identifies the amount each mode contributes to the total response at a particular point.An example with 3 degrees of free-dom showing the individual modal contributions is shown in Figure 1.14.The frequency response of an MDOF system can be presented in the same forms as the SDOF case. There are other definitional forms and proper-ties of frequency response functions,such as a driving point measurement,that are presented in the next chap-ter. These are related to specific locations of frequency response measurements and are introduced when appropriate.Figure 1.13MDOF frequency responseFigure 1.14SDOF modal contributionsd B M a g n i t u d e0.0ω1ω2ω3FrequencyΗ(ω) = Σnr =1φφi j /m(n - )+ (2n )ωωξωω222 2d B M a g n i t u d e 0.0ω1ω2ω3FrequencyDamping Mechanism and Damping ModelDamping exists in all vibratory systems whenever there is energy dissipation. This is true for mechani-cal structures even though most are inherently lightly damped. For free vibration, the loss of energy from damping in the system results in the decay of the amplitude of motion.In forced vibration, loss of energy is balanced by the energy supplied by excitation. In either situation, the effect of damping is to remove energy from the system.In previous mathematical formula-tions the damping force was called viscous, since it was proportional to velocity. However, this does not imply that the physical damping mechanism is viscous in nature. It is simply a modeling method and it is important to note that the physical damping mechanism and the mathe-matical model of that mechanism are two distinctly different concepts. Most structures exhibit one or more forms of damping mechanisms, such as coulomb or structural, which result from looseness of joints, inter-nal strain and other complex causes. However, these mechanisms can be modeled by an equivalent viscous damping component. It can be shown that only the viscous compo-nent actually accounts for energy loss from the system and the remaining portion of the damping is due to non-linearities that do not cause energy dissipation. Therefore, only theviscous term needs to be measured to characterize the system when using a linear model.The equivalent viscous damping coefficient is obtained from energy considerations as illustrated in the hysteresis loop in Figure 1.15. E isthe energy dissipated per cycle ofvibration, c eq is the equivalent vis-cous damping coefficient and X is theamplitude of vibration. Note that thecriteria for equivalence are equalenergy distribution per cycle and thesame relative amplitude.Figure 1.15Viscous dampingenergy dissipationFigure 1.16Systemblock diagramFigure 1.17Definition oftransfer functionx.InputSystemOutputResponseTransfer Function =G(s) =OutputInputY(s)X(s)Frequency Response Function and Transfer Function RelationshipThe transfer function is a mathemati-cal model defining the input-output relationship of a physical system. Figure 1.16 shows a block diagram of a single input-output system. System response (output) is caused by system excitation (input). The casual relationship is loosely defined as shown in Figure 1.17. Mathemati-cally, the transfer function is definedas the Laplace transform of the out-put divided by the Laplace transform of the input.The frequency response function is defined in a similar manner and is related to the transfer function. Mathematically, the frequency response function is defined as the Fourier transform of the output divid-ed by the Fourier transform of the input. These terms are often used interchangeably and are occasionally a source of confusion. This relationship can be furtherexplained by the modal test process.The measurements taken during amodal test are frequency responsefunction measurements. The parame-ter estimation routines are, in gener-al, curve fits in the Laplace domainand result in the transfer functions.The curve fit simply infers the loca-tion of system poles in the s-planefrom the frequency response func-tions as illustrated in Figure 1.18. The frequency response is simply thetransfer function measured along thejωaxis as illustrated in Figure 1.19.Figure 1.18S-planerepresentationiωSystem AssumptionsThe structural dynamics background theory and the modal parameter estimation theory are based on two major assumptions:Figure 1.193-D Laplace representationReal PartImaginary PartMagnitudePhaseσσσωj ωωTransfer Function – surface Frequency Response – dashedqThe system is linear.qThe system is stationary.There are, of course, a number of other system assumptions such as observability, stability, and physical realizability. However, these assump-tions tend to be addressed in the inherent properties of mechanical systems. As such, they do not pres-ent practical limitations when making frequency response measurements as do the assumptions of linearity and stationarity.IntroductionThis chapter investigates the current instrumentation and techniques available for acquiring frequency response measurements. The discus-sion begins with the use of a dynamic signal analyzer and associated periph-erals for making these measurements. The type of modal testing known as the frequency response function method, which measures the input excitation and output response simul-taneously, as shown in the block dia-gram in Figure 2.1, is examined. The focus is on the use of one input force, a technique commonly known as sin-gle-point excitation, illustrated in Figure 2.2. By understanding this technique, it is easy to expand to the multiple input technique.With a dynamic signal analyzer, which is a Fourier transform-based instrument, many types of excitation sources can be implemented to meas-ure a structure’s frequency responsefunction. In fact, virtually any physi-cally realizable signal can be input or measured. The selection and implementation of the more common and useful types of signals for modal testing are discussed.Transducer selection and mounting methods for measuring these signals along with system calibration meth-ods, are also included. Techniques for improving the quality and accuracy of measurements are then explored. These include processes such as averaging, windowing and zooming, all of which reduce mea-surement errors. Finally, a section on measurement interpretation is included to aid in understanding the complete measurement process.Chapter 2Frequency Response MeasurementsFigure 2.1 System block diagram Figure 2.2 Structure under testResponseGeneral Test System Configurations The basic test setup required for making frequency response measure-ments depends on a few major factors. These include the type of structure to be tested and the levelof results desired. Other factors, including the support fixture andthe excitation mechanism, also affect the amount of hardware needed to perform the test. Figure 2.3 showsa diagram of a basic test system configuration.The heart of the test system is the controller, or computer, which is the operator’s communication link to the analyzer. It can be configured with various levels of memory, displays and data storage. The modal analysis software usually resides here, as well as any additional analysis capabilitiessuch as structural modification and forced response.The analyzer provides the data acquisition and signal processing operations. It can be configured with several input channels, for force and response measurements, and with one or more excitation sources for driving shakers. Measurement func-tions such as windowing, averaging and Fast Fourier Transforms (FFT) computation are usually processed within the analyzer. For making measurements on simplestructures, the exciter mechanismcan be as basic as an instrumentedhammer. This mechanism requiresa minimum amount of hardware.An electrodynamic shaker may beneeded for exciting more complicatedstructures. This shaker system re-quires a signal source, a power ampli-fier and an attachment device. Thesignal source, as mentioned earlier,may be a component of the analyzer.Transducers, along with a powersupply for signal conditioning, areused to measure the desired forceand responses. The piezoelectrictypes, which measure force andacceleration, are the most widelyused for modal testing. The powersupply for signal conditioning may bevoltage or charge mode and is some-times provided as a component of theanalyzer, so care should be taken insetting up and matching this part ofthe test system.Figure 2.3General testconfigurationSupporting The StructureThe first step in setting up a structure for frequency response measurements is to consider the fix-turing mechanism necessary to obtain the desired constraints (boundary conditions). This is a key step in the process as it affects the overall struc-tural characteristics, particularly for subsequent analyses such as structur-al modification, finite element corre-lation and substructure coupling. Analytically, boundary conditions can be specified in a completely free or completely constrained sense. In testing practice, however, it is gener-ally not possible to fully achieve these conditions. The free condition means that the structure is, in effect, floating in space with no attachments to ground and exhibits rigid body behavior at zero frequency. The airplane shown in Figure 2.4a is an example of this free condition. Physically, this is not realizable,so the structure must be supported in some manner. The constrained condition implies that the motion, (displacements/rotations) is set to zero. However, in reality most struc-tures exhibit some degree of flexibili-ty at the grounded connections. The satellite dish in Figure 2.4b is an example of this condition.In order to approximate the free sys-tem, the structure can be suspended from very soft elastic cords or placed on a very soft cushion. By doing this, the structure will be constrained to a degree and the rigid body modes will no longer have zero frequency. However, if a sufficiently soft support system is used, the rigid body fre-quencies will be much lower than thefrequencies of the flexible modes andthus have negligible effect. The ruleof thumb for free supports is that thehighest rigid body mode frequencymust be less than one tenth that ofthe first flexible mode. If this criteri-on is met, rigid body modes will havenegligible effect on flexible modes.Figure 2.5 shows a typical frequencyresponse measurement of this typewith nonzero rigid body modes.The implementation of a constrainedsystem is much more difficult toachieve in a test environment. Tobegin with, the base to which thestructure is attached will tend to havesome motion of its own. Therefore, itis not going to be purely grounded.Also, the attachment points will havesome degree of flexibility due to thebolted, riveted or welded connec-tions. One possible remedy for theseproblems is to measure the frequency Figure 2.4aExample offree supportsituationFigure 2.4bExample ofconstrainedsupportsituationFreeBoundaryresponse of the base at the attach-ment points over the frequency range of interest. Then, verify that this response is significantly lower than the corresponding response of the structure, in which case it will have a negligible effect. However, the frequency response may not be mea-surable, but can still influence the test results.There is not a best practical or appropriate method for supportinga structure for frequency response testing. Each situation has its own characteristics. From a practical standpoint, it would not be feasible to support a large factory machine weighing several tons in a free test state. On the other hand, there may be no convenient way to ground a very small, lightweight device for the constrained test state. A situation could occur, with a satellite for exam-ple, where the results of both tests are desired. The free test is required to analyze the satellite’s operating environment in space. However, the constrained test is also needed to assess the launch environment attached to the boost vehicle. Another reason for choosing the appropriate boundary conditions is for finite element model correlation or substructure coupling analyses. At any rate, it is certainly important dur-ing this phase of the test to ascertain all the conditions in which the results may be used.Figure 2.5Frequencyresponseof freelysuspendedsystemFxdXY-30.0dB10.0/Div50.0Table 2.1Excitation functionsExciting the StructureThe next step in the measurement process involves selecting an excitation function (e.g., random noise) along with an excitation sys-tem (e.g., a shaker) that best suits the application. The choice of excitation can make the difference between a good measurement and a poor one.Excitation selection should be approached from both the type of function desired and the type of exci-tation system available because they are interrelated. The excitation func-tion is the mathematical signal used for the input. The excitation system is the physical mechanism used to prove the signal. Generally, the choice of the excitation function dictates the choice of the excitation system, a true random or burstrandom function requires a shaker system for implementation. In gener-al, the reverse is also true. Choosing a hammer for the excitation system dictates an impulsive type excitation function.Excitation functions fall into four general categories: steady-state, random, periodic and transient.There are several papers that go into great detail examining the applica-tions of the most common excitation functions. Table 2.1 summarizes the basic characteristics of the ones that are most useful for modal testing.True random, burst random and impulse types are considered in the context of this note since they are the most widely implemented. The best choice of excitation function depends on several factors: available signalprocessing equipment, characteristics of the structure, general measure-ment considerations and, of course,the excitation system.A full function dynamic signal analyz-er will have a signal source with a sufficient number of functions for exciting the structure. With lower quality analyzers, it may be necessary to obtain a signal source as a sepa-rate part of the signal processing equipment. These sources often provide fixed sine and true random functions as signals; however, these may not be acceptable in applications where high levels of accuracy are desired. The types of functionsavailable have a significant influence on measurement quality.Periodic*Transientin analyzer window in analyzer window Sine True steady random random sine sine random state Minimze leakage No No Yes Yes Yes Yes Yes Yes Signal to noise Very Fair Fair Fair High Low High Fair high RMS to peak ratioHigh Fair Fair Fair High Low High Fair Test measurement time Very Good Very Fair Fair Very Very Very long good good good good Controlled frequency content Yes Yes*Yes*Yes*Yes*No Yes*Yes*Controlled amplitude content Yes No Yes* No Yes*No Yes*No Removes distortionNo Yes No Yes No No No Yes Characterize nonlinearityYesNoNoNoYesNoYesNo* Requires additional equipment or special hardwareThe dynamics of the structureare also important in choosing the excitation function. The level of nonlinearities can be measured and characterized effectively with sine sweeps or chirps, but a random func-tion may be needed to estimate the best linearized model of a nonlinear system. The amount of damping and the density of the modes within the structure can also dictate the use of specific excitation functions. If modes are closely coupled and/or lightly damped, an excitation function that can be implemented in a leakage-free manner (burst random for exam-ple) is usually the most appropriate. Excitation mechanisms fall into four categories: shaker, impactor, step relaxation and self-operating. Step relaxation involves preloading the structure with a measured force through a cable then releasing the cable and measuring the transients.Self-operating involves exciting thestructure through an actual operatingload. This input cannot be measuredin many cases, thus limiting its useful-ness. Shakers and impactors are themost common and are discussed inmore detail in the following sections.Another method of excitation mecha-nism classification is to divide theminto attached and nonattacheddevices. A shaker is an attacheddevice, while an impactor is not,(although it does make contact for ashort period of time).Shaker TestingThe most useful shakers for modaltesting are the electromagneticshown in Fig. 2.6 (often calledelectrodynamic) and the electrohydraulic (or, hydraulic) types. Withthe electromagnetic shaker, (the morecommon of the two), force is generat-ed by an alternating current thatdrives a magnetic coil. The maximumfrequency limit varies from approxi-mately 5 kHz to 20 kHz dependingon the size; the smaller shakershaving the higher operating range.The maximum force rating is also afunction of the size of the shaker andvaries from approximately 2 lbf to1000 lbf; the smaller the shaker, thelower the force rating.With hydraulic shakers, forceis generated through the use ofhydraulics, which can provide muchhigher force levels – some up toseveral thousand pounds. The maxi-mum frequency range is much lowerthough – about 1 kHz and below. Anadvantage of the hydraulic shaker isits ability to apply a large static pre-load to the structure. This is usefulfor massive structures such as grind-ing machines that operate underrelatively high preloads which mayalter their structural characteristics.。

femFEM: An Introduction to Finite Element MethodIntroductionThe Finite Element Method (FEM) is a numerical technique used to solve problems in engineering and applied mathematics. It is widely used in various fields such as structural analysis, heat transfer, fluid dynamics, and electromagnetics. In this document, we will provide an introduction to FEM, its principles, and its applications.1. The Basics of Finite Element Method1.1. What is FEM?FEM is a numerical method that represents a problem domain using a finite number of elements. These elements are interconnected at points called nodes, forming a mesh. The problem domain is divided into smaller subdomains or elements, and the governing equations are then approximated locally within each element. By assemblingthese elements, a global equation system is constructed to solve the problem.1.2. FEM WorkflowThe FEM workflow involves several steps, including the pre-processing, solution, and post-processing stages. In the pre-processing stage, the problem domain is discretized into elements and meshed. Once the mesh is generated, the governing equations are formulated. In the solution stage, the system of equations is solved, often using iterative numerical methods. Finally, in the post-processing stage, the results are evaluated and visualized.2. Principles of Finite Element Method2.1. Approximation of Field VariablesIn FEM, field variables such as displacement, temperature, or pressure are approximated within the elements using interpolation functions. These interpolation functions define the variation of the field variable within an element based on the values at its nodes. By using these functions, the field variable can be approximated at any point within an element.2.2. Assembly of EquationsOnce the interpolation functions are defined within each element, the system of equations is assembled by connecting the elements at their common nodes. This process ensures that the continuity conditions are satisfied across the element interfaces. The assembly of equations yields a global equation system that represents the problem domain.2.3. Solution of Equation SystemThe global equation system obtained from the assembly stage is typically solved using numerical methods such as direct solvers (e.g., Gaussian elimination) or iterative solvers (e.g., conjugate gradient method). The choice of solver depends on factors such as the size of the equation system, sparsity pattern, and desired accuracy.3. Applications of Finite Element Method3.1. Structural AnalysisFinite Element Method is widely used in structural analysis to predict the behavior of structures under various loading conditions. It allows engineers to determine the stresses, deformations, and stability of structures, such as buildings, bridges, and mechanical components. FEM can be used to analyze linear and nonlinear structural problems, including static, dynamic, and buckling analysis.3.2. Heat TransferFEM is also used to analyze heat transfer problems, such as conduction, convection, and radiation. It enables engineers to predict the temperature distribution within solids and fluids, evaluate thermal stresses, and design efficient heat exchangers and cooling systems. FEM can handle steady-state and transient heat transfer problems, as well as coupled heat transfer with structural deformations.3.3. Fluid DynamicsFEM plays a crucial role in analyzing fluid flow problems, including incompressible and compressible flows. It can simulate the behavior of fluids in various applications, such as pipe flow, aerodynamics, and hydrodynamics. FEM allows engineers to predict velocity, pressure, and turbulencecharacteristics, optimize the design of fluid systems, and study complex phenomena like multiphase flows and free surface flows.3.4. ElectromagneticsIn electromagnetics, FEM is used to study electromagnetic fields, analyze electromagnetic devices, and design electrical machines. It enables the modeling of electric and magnetic fields, current flows, and electromagnetic wave propagation. FEM can be applied to various applications, including motors, transformers, antennas, and electromagnetic compatibility (EMC) analysis.ConclusionIn conclusion, the Finite Element Method (FEM) is a powerful numerical technique used in engineering and applied mathematics. Through its principles and workflow, FEM allows engineers to solve a wide range of problems in various fields. From structural analysis to heat transfer, fluid dynamics, and electromagnetics, FEM has proven to be an invaluable tool in solving complex engineering problems.。

SEM模型结构方程模型（Structural equation modeling, SEM）是一种融合了因素分析和路径分析的多元统计技术。

它的强势在于对多变量间交互关系的定量研究。

在近三十年内，SEM大量的应用于社会科学及行为科学的领域里，并在近几年开始逐渐应用于市场研究中.SEM模型Structural Equation Modeling, 简称SEM模型顾客满意度就是顾客认为产品或服务是否达到或超过他的预期的一种感受。

结构方程模型（SEM）就是对顾客满意度的研究采用的模型方法之一。

其目的在于探索事物间的因果关系，并将这种关系用因果模型、路径图等形式加以表述。

如下图：图: SEM模型的基本框架SEM模型的基本框架在模型中包括两类变量：一类为观测变量，是可以通过访谈或其他方式调查得到的，用长方形表示；一类为结构变量，是无法直接观察的变量，又称为潜变量，用椭圆形表示。

各变量之间均存在一定的关系，这种关系是可以计算的。

计算出来的值就叫参数，参数值的大小，意味着该指标对满意度的影响的大小，都是直接决定顾客购买与否的重要因素。

如果能科学地测算出参数值，就可以找出影响顾客满意度的关键绩效因素，引导企业进行完善或者改进，达到快速提升顾客满意度的目的。

SEM的主要优势一，它可以立体、多层次的展现驱动力分析。

这种多层次的因果关系更加符合真实的人类思维形式，而这是传统回归分析无法做到的。

SEM根据不同属性的抽象程度将属性分成多层进行分析。

第二，SEM分析可以将无法直接测量的属性纳入分析，比方说消费者忠诚度。

这样就可以将数据分析的范围加大，尤其适合一些比较抽象的归纳性的属性。

第三，SEM分析可以将各属性之间的因果关系量化，使它们能在同一个层面进行对比，同时也可以使用同一个模型对各细分市场或各竞争对手进行比较。

統計分析入門與應用序科學研究就是不斷地探究人、事、物的真理，其目的在追求「真、善、美」即使無法達到盡善盡美，但是仍盡量貼近事實，我們經過20多年的多變量分析學習和實戰經歷，提供正確的多變量分析研究論文參考範例：有量表的發展、敘述性統計，相關分析、卡方檢定、平均數比較、因素分析、迴歸分析、區別分析和邏輯迴歸、單因素變異數分析、多變量變異數分析、典型相關分析、信度和效度分析、聯合分析多元尺度和集群分析，回歸(Regression) 模型、路徑分析(Path analysis) 和Process功能分析、第二代統計技術–結構方程模式(SEM)，終於完成《統計分析入門與應用SPSS (中文版) + SmartPLS 4 (PLS-SEM)》，希望能幫助更多需要資料分析的人，尤其是正確的報告多變量分析的結果。

近年來，多變量統計分析慢慢地產生巨大變化，例如：SEM的演進、以評估研究模式的適配。

發展量表，CB_SEM和PLS_SEM的區別，辨別模式的指定，反映性和形成性指標的發展和模式的指定，二階和高階潛在變數的使用，中介和調節變數的應用，Formative (形成性) 的評估、中介因素的5種型態、調節效果的多種型態、測量恆等性(Measurement Invariance)、MGA呈現的範例、被中介的調節(中介式調節)、被調節的中介(調節式中介)。

作者歷經多場演講和工作坊，也參加多場講座，培訓班，研討會，很多參加者表示不清楚如何正確的提供分析結果，另外，我們審過很多投稿到期刊的論文後，發現很多論文寫得不錯，但是由於分析或報告結果不精確，而被拒稿了。

《統計分析入門與應用SPSS (中文版) + SmartPLS 4 (PLS-SEM)》的完成可以幫助更多需要正確報告多變量分析的研究者，順利發表研究成果於研討會、期刊和碩博士論文。

感謝眾多讀者對於《多變量分析最佳入門實用書SPSS + LISREL》、《統計分析SPSS (中文版) + PLS_SEM (SmartPLS)》和《統計分析入門與應用SPSS (中文版) + SmartPLS 3 (PLS_SEM)》第二版&第三版的厚愛，本書已經更新至SmartPLS 4版本。

Standardized structural equation model (SEM) is a statistical technique used to test and estimate causal relationships between variables. It allows researchers to analyze complex relationships between multiple variables and to examine the direct and indirect effects of variables on each other.In a standardized SEM, all of the variables are standardized, meaning that they have a mean of zero and a standard deviation of one. This allows for a more accurate comparison of the strength of relationships between variables. By standardizing the variables, researchers can better understand the relative importance of each variable in the model.The standardized SEM involves multiple steps, including specifying the theoretical model, estimating the model parameters, and assessing the model fit. Researchers begin by developing a theoretical model that represents their hypotheses about the relationships between variables. They then use data to estimate the model parameters and assess how well the model fits the observed data.One of the key advantages of using a standardized SEM is that it allows for a more straightforward interpretation of the results. By standardizing the variables, researchers can easily compare the strength of relationships between variables and determine which variables have the most significant impact on the model.Furthermore, a standardized SEM can be used to test complex theoretical models and to evaluate the fit of these models to the data. This allows researchers to assess the overall validity of their theoretical model and to determine if the model accurately represents the relationships between variables.In conclusion, the standardized structural equation model is a valuable tool for researchers interested in understanding complex relationships between variables. By standardizing the variables and testing theoretical models, researchers can gain insight into the direct and indirect effects of variables on each other and assess the overall fit of their model to the data.。

Creative Education Studies 创新教育研究, 2023, 11(4), 766-771 Published Online April 2023 in Hans. https:///journal/ces https:///10.12677/ces.2023.114118数学基础课支撑土木类专业拔尖人才培养与 创新实践刘 超1,2*，王旭东1，邵珠山1，何春辉21西安建筑科技大学理学院，陕西 西安 2西安建筑科技大学土木工程学院，陕西 西安收稿日期：2023年3月2日；录用日期：2023年4月12日；发布日期：2023年4月21日摘 要数学基础课是土木类专业学生必修的一门公共基础课，对于培养其逻辑思维、抽象能力、创新意识和解决实际问题的能力具有重要作用。

文章分析了当前数学基础课在土木类专业拔尖人才培养中存在的问题和挑战，提出了改革和优化数学基础课教学内容、方法、模式和评价机制的建议，同时提出一系列有效的创新实践的方法，以期提高数学基础课教学质量和效果，为土木类专业拔尖人才培养与创新实践提供坚实的理论支撑。

关键词数学基础课，土木类专业，拔尖人才，创新实践Basic Mathematics Courses to Support the Cultivation of Top Talents and Innovative Practices in Civil EngineeringChao Liu 1,2*, Xudong Wang 1, Zhushan Shao 1, Chunhui He 21College of Science, Xi’an University of Architecture and Technology, Xi’an Shaanxi 2College of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an Shaanxi Received: Mar. 2nd , 2023; accepted: Apr. 12th , 2023; published: Apr. 21st , 2023AbstractThe basic mathematics course is a compulsory public foundation course for civil engineering stu-*通讯作者。

欧拉法解微分方程原理Euler's method is a numerical technique used to solve ordinary differential equations. It approximates the solution of a differential equation by taking small steps in the direction of the derivative at each point. 欧拉法是一种数值技术，用于解决常微分方程。

它通过在每个点沿着导数方向采取小步骤来近似求解微分方程的解。

One of the key principles behind Euler's method is the idea of tangent approximation. By using the derivative at a certain point, we can estimate the slope of the curve and take a small step in that direction to update the solution. 欧拉法背后的一个关键原理是切线逼近的概念。

通过在某一点使用导数，我们可以估计曲线的斜率，并在该方向上采取小步骤以更新解。

The algorithm starts with an initial value and then iteratively updates the solution by calculating the derivative at each step. By repeating this process, we can approximate the values of the solution at different points along the curve. 该算法从初始值开始，然后通过在每一步计算导数来迭代更新解。

structural equation model 文献综述Structural Equation Model（结构方程模型）是一种统计方法，用于检验和估计一组关于变量间因果关系的假设。

这种模型可以同时估计多个因果关系，并且可以考虑到变量间的交互作用和误差项。

在文献综述中，通常会涉及到以下几个方面的内容：1.结构方程模型的定义和原理：这部分内容主要介绍结构方程模型的基本概念、原理和特点，以及它在不同领域中的应用。

2.结构方程模型的方法论：这部分内容主要介绍如何构建结构方程模型的假设，如何选择合适的样本和测量工具，以及如何进行模型的估计和检验。

3.结构方程模型的应用研究：这部分内容主要介绍结构方程模型在不同领域中的应用研究，例如心理学、社会学、经济学等。

这些研究通常会探讨某个特定领域的变量之间的关系，并检验这些关系是否符合理论预期。

4.结构方程模型的优缺点：这部分内容主要介绍结构方程模型的优点和局限性。

优点包括能够同时估计多个因果关系、能够考虑到变量间的交互作用和误差项等；局限性包括对样本量要求较高、对测量工具的要求较高等。

5.未来研究方向：这部分内容主要探讨未来可能的研究方向和挑战，例如如何改进结构方程模型的方法和技术、如何更好地应用结构方程模型来解决实际问题等。

在撰写文献综述时，需要注意以下几点：1.保持客观和公正：在评价不同研究时，应该尽可能地保持客观和公正，避免主观偏见和错误。

2.引用准确：在引用不同文献时，应该尽可能地引用准确，包括作者、年份、文章标题等。

3.结构清晰：在撰写综述时，应该尽可能地保持结构清晰，让读者能够容易地理解各个部分的内容。

4.语言简练：在撰写综述时，应该尽可能地使用简练的语言，避免冗长和复杂的句子和段落。

structural equation modelling结构方程建模(StructuralEquationModeling，简称SEM）是现代思维研究中广泛使用的统计模型，它为研究者提供了一种用来检测、诊断和预测复杂构建之间关系的有力工具。

结构方程建模分析的本质是描述多变量的复杂关系，它涉及到变量的构建，建模和评估过程，它通常是利用统计学习和最优化的方法来判断统计模型是否合理，以实现更有力的研究结论。

结构方程建模分析是以假设和推理机制为基础的，它主要用于推断多种因素和结果变量之间的因果关系。

结构方程建模可以测试复杂构建之间的关系，比如自变量、内在变量、反映出可能直接或间接影响因素的中介变量。

结构方程建模的优势在于它的可拓展性，它可以满足多变量模型构建的需求，同时也可以用于大量数据的分析。

结构方程模型用于建模复杂结构之间关系，它是一种混合模型，可以一次考虑多个变量，而不用担心数据中多个变量之间的相关性，它能够检测研究者所提出的复杂和多变量构建之间的因果关系。

结构方程模型采取分析因变量和自变量之间联系的步骤，这些步骤包括：指定模型的假设；定义模型的构建，这些构建可以是线性、非线性等；定义相应的数据集；运用模型所包含的参数来识别变量之间的因果关系；提出模型的结果，这些结果可以用于检测要检测的因素是否是研究者所假设的因素，从而间接验证分析的结果。

结构方程建模对于研究者有许多优势。

它能够从复杂的数据集中推断出因果关系，而且能够考虑多变量和多方面的内容，如非线性变量等。

它还能够检测潜在的中介变量，以此作为有效的预测模型，而且运行起来比较容易和快捷。

结构方程模型分析也有一些局限性，比如对于潜在变量的收集或测量，往往需要更多的精力和资源，而且还可能出现信息损失的情况。

而且，SEM模型也受到样本大小的约束，从而影响到模型本身的准确性和可靠性。

综上所述，结构方程建模是一种有力的工具，它可以帮助研究者从复杂数据集中找出潜在的构建和因果关系，它的优势在于可拓展性，可以满足多变量模型构建的需求；而它的局限性在于运行时可能会出现信息损失的情况，以及受到样本大小的约束。