中文摘要：

根据压电方程和材料力学方程推导出机电耦合情况下压电元件表面电荷计算公式，以此为优化目标，对压电分流阻尼抑振系统中的压电元件形状和位置／布局进行了优化分析。在考虑了压电元件附加质量和附加刚度的影响下，采用ANASYS的APDL语言对四边固支弹性薄铝板进行参数化建模，根据压电元件的模态应变来计算电荷数量。使用拓扑优化方法得到对应于各阶模态的压电元件最优形状，并针对采用单片和多片压电元件的情况，进行了对应于结构各阶振型的布局优化。根据分析结果，提出了压电分流阻尼系统的压电元件形状和位置／布局优化的基本原则。将分析结果应用于一四边固支薄板的振动响应抑制实验，取得了良好的抑振效果，分流电路闭合后第1阶和第5阶模态响应的幅值分别降低了52．9％与62．6％，验证了压电元件形状和位置／布局优化的有效性。

英文摘要：

In this paper, the calculation equation for electrical charges of the piezoelectric patches electromechanically coupled with the structure is derived from the piezoelectric equation and the theory of material mechanics. Then the investigation of profile and placement optimization for piezoelectric shunt damping system is performed while the amount of electrical charges is selected as the objective function. In the finite element modeling of the clamped thin aluminum plate with piezoelectric patches by APDL tool of ANSYS software, the effects of additional stiffness and additional mass of the bonded piezoelectric patches are considered. Then the modal strains of the piezoelectric patches are adopted to calculate the amount of electrical charges. The optimal profile of the piezoelectric patches corresponding to different modes is obtained by topological optimization and the optimization of placement for single or multi piezoelectric patches is also conducted. Base on these results, some concluding remarks are proposed for the profile and placement optimization of piezoelectric patches in designing piezoelectric shunt damping systems. As an example for verifying the proposed optimization techniques, the vibration control experiment on a clamped plate was performed. Under the control of the piezoelectric shunt circuit, the harmonic vibration responses of the first mode and the fifth mode are decreased successfully by 52.9% and 62.6% respectively. The test results validate the effectiveness of profile and placement optimization of piezoelectric patches for piezoelectric shunt damping system.