圆形薄板的横向振动
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加热压电纤维复合材料圆板的横向自由振动王硕;滕兆春【摘要】基于经典薄板理论和极正交各向异性材料的本构理论,建立了加热压电纤维复合材料圆板的线性振动控制微分方程.采用打靶法分别获得了加热压电纤维复合材料圆板在周边固支和简支情况下,无量纲固有频率随温度和电场强度变化的关系曲线,并分析了压电纤维体积分数、刚度参数、电场强度和温度变化对压电纤维复合材料圆板无量纲固有频率的影响.结果表明,一定体积分数或者电场强度下,压电纤维复合材料圆板的无量纲固有频率都随温度的升高而单调下降;同一温度下,刚度参数越小,无量纲固有频率越低;电场强度越大,无量纲固有频率越高.%Based on the classical thin plate theory and the constitutive theory for orthotropic materials,the linear differential equations of vibration for circular plate of heated piezoelectric fibre composite materials are derived.By using a shooting method,the relationship curves of the dimensionless natural frequencies of the heated piezoelectric fibre composite circular plate versus temperature rise and electric field strength change are presented with clamped and simply supported boundary conditions.And the influence of the volume fraction of piezoelectric fibre,stiffness parameters,electric field strength and temperature rise on the dimensionless natural frequencies of piezoelectric fibre composite materials circular plate is also discussed.The results show that the dimensionless natural frequency of the piezoelectric fibre composite material circular plate monotonically decreases with the temperature.Itdecreases with decreasing the stiffness parameters,but increases with increasing electric field strength at certain fixed values of temperature.【期刊名称】《计算力学学报》【年(卷),期】2017(034)003【总页数】6页(P286-291)【关键词】压电纤维复合材料;圆板;自由振动;固有频率;打靶法【作者】王硕;滕兆春【作者单位】兰州理工大学理学院,兰州 730050;兰州理工大学理学院,兰州730050【正文语种】中文【中图分类】O343因为具有力电耦合的性能,压电材料常用于传感器和致动器的制造,并广泛应用于机电系统和智能结构[1,2]。
毕业设计(论文)任务书摘要随着科技水平的发展,随着振动理论以及结构学的发展,越来越多的结构,开始使用薄板,薄板,即为厚度小于长度方向的1/6。
由于薄板,重量轻,体积小,节省材料。
在一定程度上,尤其是对以工业生产,可以降低成本。
但是,由于薄板的厚度比较薄,在实际情况中的振动,尤其是长期的振动条件下,损坏可能会较严重。
为了解决薄板的耐震寿命,以及了解在振动环境中,薄板结构的振动特点,做了实验研究。
首先,薄板的理论研究,已经趋于成熟。
无论是从基本的薄板的振动理论,还是发展到今天的各种薄板振动精确解的求解方法。
所以,对于理论的学习,是做薄板振动实验的基础。
从理论的角度,了解了薄板结构在边界条件下的振动特点,包括振动阻尼、频率以及振型函数的特点。
其次,是对于实验仪器的选择。
包括,激振方式的选择,传感器的选择,以及后续处理实验设备的选择和选择的注意事项。
再次,在实验模拟条件下,进行薄板的振动研究。
通过力锤进行敲击,通过传感器采集信号,以及后续的处理系统,得到薄板振动的振型函数、振动频率、以及直观的了解薄板结构在试验状态下的振动特点,分析了自由振动条件下和强迫振动条件下,薄板结构的振动特点,而且还分析了,不同的试验条件下,不同的输入条件下得到不同的输出响应,以及各自的特点。
本文对薄板结构的振动特性做了实验研究。
重点探讨了,在不同的激振条件下,薄板结构所表现出来的振动特性。
即在三种不同情况下,包括单输入单输出(SISO)、单输入多输出(SIMO)和多输入多输出(MIMO)情况下,薄板结构表现出来的各自的振动特点,以及不同点。
从而验证了理论研究中,所得到的结果。
而且,还可以通过比较,确定在实际的情况中,根据不同的需要,使用不同的约束条件、可以避免减少对薄板结构的损害,延长耐振寿命。
关键词:薄板结构;振动特性;实验研究AbstractWith the development of scientific and technological level, with the development of the vibration theory and the structure of science, more and more of the structure, start using the thin plate, that is, the length of the direction of thickness of less than 1 / 6. As the thin, light weight, small size, material savings. To some extent, especially in industrial production, to reduce costs. However, due to the thickness of thin sheet metal, the vibration in the actual case, especially in long-term vibration conditions, the damage may be more serious. In order to solve the seismic plate life, and to understand the vibration environment, the vibration characteristics of thin plate and do experiments.Fristly,the thin plate theoryhas been maturing. Either from the basic theory of thin plate, or developed to a variety of thin plate solution of the exact solutions. Therefore, study of the theory is the basis for doing sheet metal vibration test. From a theoretical point of view, understanding of the thin structure in the vibration characteristics of the boundary conditions, including vibration damping, frequency and vibration mode function features.Secondly, the choice of the experimental apparatus. Include the choice of excitation methods, sensor selection, and subsequent processing laboratory equipment selection and choice of notes.Thirdly, the experiment simulated conditions, to the vibration of sheet metal. Carried out by hammer tapping, collecting signals through sensors, and follow-up treatment systems, are rectangular plate vibration mode function, vibration frequency, and the intuitive understanding of thin plate vibration in the experimental conditions to the characteristics of the free vibration conditions and under forced vibration, the vibration characteristics of thin plate structures, but also analyzes the different experimental conditions, different input conditions are different output response, and their respective characteristics. In this paper, thin structure of the vibration characteristics is studied. Focus on, and at different excitation conditions, plate structure shown by vibration. That is, in three different cases, including single-input single-output (SISO), single-input multiple-output (SIMO) and multiple-input multiple-output (MIMO) case, the thin plate shown their vibration characteristics, and different points. To verify the theoretical study, the results obtained. Moreover, it can be compared to determine the actual situation, according to the different needs of different constraints, can be avoided to reduce the damage to the sheet structure, vibration-resistant to extend life span.Keywords: thin plate; vibration characteristics; experimental study目录摘要 (I)ABSTRACT (II)第1章绪论 (1)1.1课题研究的意义及现状 (1)1.2薄板理论的发展简况 (1)1.3振动实验研究的发展简况 (2)1.4论文主要研究内容 (3)第2章薄板振动的基本原理 (4)2.1振动的基本概念以及特点 (4)2.1.1 振动的基本概念 (4)2.1.2 振动的基本特征量 (4)2.1.3 振动的基本形式 (4)2.2薄板的横向振动的微分方程 (4)2.2.1 弹性薄板横向振动的基本假设 (5)2.2.2 弹性薄板横向振动的几何方程与物理方程 (5)2.2.3 弹性薄板的内力分析 (8)2.2.4 弹性薄板自由振动的微分方程和边界条件 (10)2.3矩形板的固有振动 (11)2.3.1 四边简支矩形板 (12)2.3.2 一对边简支一对边任意的矩形板 (14)2.4薄板的强迫振动 (16)第3章薄板振动的实验研究 (18)3.1研究振动的意义 (18)3.2研究薄板振动的意义 (19)3.3工程测振的一般方法 (19)3.4实验仪器的选择 (20)3.4.1 激振方式的选择 (20)3.4.2 激振试验设备的选择 (22)3.4.3 传感器的选择 (23)3.5不同试验条件下,薄板振动特性的研究 (28)3.5.1 自由振动下,薄板振动特性的研究 (30)3.5.2 谐振激励下,薄板振动特性的研究 (30)3.5.3 三种不同的激励方式下的,薄板振动特性的研究 (30)致谢 (31)附件1 ........................................................................... 错误!未定义书签。