基于多目标优化设计的主动约束层阻尼板振动控制研究

航天器隔振器多目标优化方法罗军;唐国金【摘要】It is common to use passive isolator to protect the payload from the platform noise in space applications.The design of a passive isolator involves a trade-off between the resonant peak reduction and the high frequency attenuation.Firstly,the equation of motion and transfer function model for single-stage and two-stage connector model was derived,and then the multiobjective optimization model,in which the objective functions are the resonant peak reduction and the high frequency attenuation,was proposed,.Secondly,the multiobjective optimization design method for the design of the passive isolator was proposed,using the multiobjective evolutionary algorithm based on decomposition (MOEA/D). The simulation result shows that the proposed method is effective for the design process of the passive isolator,and can provide multiple candidate solutions for the designer.%由于存在各种高频内部扰动，高精度航天器通常需要进行隔振设计，而被动隔振装置被广泛采用。

基于粒子群优化算法主动悬架作动器多目标优化设计彭冲;郑玲;李以农【摘要】To achieve high thrust density, low ripple and low copper loss of electromagnetic linear actuator in active suspension system of the electric wheel, a multi-objective optimization design method of tubular Halbach permanent magnet linear synchronous motor using stochastic particle swarm optimization was presented. The analytical formulas of gap magnetic field, induced voltage and electromagnetic force were deduced, and the validity of formulae was verified by FEM. The optimum range of Halbach permanent magnet parameter was obtained through the parametric analysis of gap magnetic field. Setting permanent magnet, gap and slot depth as optimization variables and taking thrust volume coefficient and copper loss coefficient as optimization objective, the actuator structure parameters were optimized with multi-objective stochastic particle swarm optimization based on self-adaptive punishment. The best Pareto optimal solution is selected based on the fuzzy set theory. The results show that after optimization, the actuator structure is more compact, and both the copper loss and thrust ripple decrease significantly. The validity of multi-objective optimization is verified.%为了使电动轮主动悬架系统的电磁直线作动器具有高推力密度、低铜耗和低推力波动特性,提出基于粒子群算法的圆筒形Halbach永磁直线同步电机作动器多目标优化设计方法,推导Halbach直线作动器径向气隙磁场密度、空载感应电动势、电磁力解析式,并采用有限元法对其进行了验证.基于Halbach磁体结构的气隙磁场进行参数化分析,获得磁体参数优化范围,以永磁体、气隙与槽深尺寸为优化变量,以推力体积比系数、铜耗系数为优化目标,采用基于自适应罚函数的多目标随机粒子群优化算法对作动器结构参数进行优化,并利用模糊集合理论对Pareto最优解进行选优.研究结果表明:优化后作动器结构紧凑,且作动器铜耗及波动明显降低,验证了作动器设计的正确性与多目标优化的有效性.【期刊名称】《中南大学学报（自然科学版）》【年(卷),期】2017(048)004【总页数】9页(P968-976)【关键词】电磁作动器;气隙磁场;多目标优化;随机粒子群算法【作者】彭冲;郑玲;李以农【作者单位】重庆大学机械传动国家重点实验室,重庆,400044;重庆大学机械传动国家重点实验室,重庆,400044;重庆大学机械传动国家重点实验室,重庆,400044【正文语种】中文【中图分类】TM359.4轮边驱动式电动汽车以其空间利用率高、传动链短、开发成本低、能量回收等优点，成为了未来汽车工业最佳选择[1]，然而，轮边驱动电动汽车随着轮毂电机的引入导致整车非簧载质量及车轮转动惯量显著增加，影响着车辆的平顺性和操作稳定性[2]，目前解决方法主要采取电磁可控悬架，相比空气、液压等可控悬架系统，电磁主动悬架系统可提供主动力，可实现在不同的行驶条件下悬架性能最优，显著改善车辆的行驶平顺性和操纵稳定性，成为电动汽车悬架的最佳选择。

约束阻尼板结构振动声辐射优化郑玲;祝乔飞【摘要】On the basis of the classical plate theory,a laminated damping plate model was built.Regarding the plate inlaid in an infinite rigid baffle,its acoustical power and sensitivity expressions were obtained using Rayleigh integral.A topology optimization model for placement of constraint damping material was established with the objective function defined as the minimum of acoustical power under the exciting force with the first order modal frequency or the corresponding frequency band and the constraint condition defined as the volume fraction of damping material.With the evolutionary structural optimization (ESO)method,the topology optimization of damping plate was conducted and the optimal placement of the damping material under the volume requirement was pared with acoustic radiations of plates without constraint damping material and with full constraint damping material,it was concluded that the optimization method adopted can achieve an effective control on the acoustic radiation of the plate with less damping material usage,and provides a crucial theoretical reference and technical means for the low noise design of plates.%根据经典薄板理论，建立约束阻尼板有限元模型，将其视作镶嵌于无限大刚性障板，利用Rayleigh积分法推导结构的辐射声功率及灵敏度表达式。

2
（A） （B）
图 6-1 积极隔振
此时，机器通过弹簧、阻尼器传到地基上的动压力
& = − kB sin(ωt − ϕ ) − cBω cos(ωt − ϕ ) FD = F + FC = − kx − cx
即 F 和 R 是相同频率，在相位上相差 力的最大值
π 的简谐力。根据同频率振动合成的结果，得到传给地基的动压 2
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6.4 动力减振器
6.4.1 无阻尼减振器
图 6-3 是一个无阻尼动力减振器的系统。其中由质量 m1 和弹簧 k 1 组成的系统，称为主系统；由质 量 m2 和弹簧 k 2 组成的辅助系统，称为减振器。显然，这是两自由度的无阻尼受迫振动系统。现建立该 系统的运动微分方程为
图 6-2 频响曲线
6.3 阻振
阻振方法是采用阻尼减振方法的简称， 即用附加的子系统连接于需要减振的结构或系统以消耗振动 能量，从而达到控制振动水平的目的。阻尼减振技术能降低结构或系统在共振频率附近的动响应和宽带 随机激励下响应的均方根值，以及消除由于自激振动而出现的动不稳定现象。阻尼减振有两种方式，一 类是非材料阻尼，如各种成型的阻尼器，另一类是材料阻尼，如各种粘弹性阻尼材料以及复合材料等。 目前粘贴在结构上的自由阻尼层和约束阻尼层应用很广泛。 前者利用拉伸变形来消耗振动能量， 后 者则利用剪切变形来消耗振动能量。尤其是多层约束阻尼层，往往较之前种方法更为有效。如美国 F-4 战斗机的武器发射装置的中央腹板由于宽带激励下的多模态共振而迅速破坏。粘贴了多层约束阻尼层 后，由于在其工作温度条件下的多个模态上都提供了一定的损耗因子，解决了这种振动疲劳造成的破坏 问题。 复合材料由于它具有重量轻、刚度大、强度高的优点已被广泛地应用于各个工业部门，尤其是在航 空航天工业中得到了广泛的应用。基底材料的粘弹性能对纤维增强的复合材料有可能提供一定的内阻。 对于较大的纤维阻尼，长纤维能够提供最佳的内阻，而对较小的纤维阻尼，一般短纤维能够提供最佳的 内阻。另外，对于一些具有小阻尼的结构，当难以安装阻尼器时，利用连接处的干摩擦也可以有效地减 振。