基于模态应变能分布的压电致动器/传感器位置优化遗传算法

本文由线弹性压电结构有限元动力方程，推导了压电智能结构的振动控制方程。建立了准确模拟层合压电结构动力行为的有限元模型。基于主结构模态应变能分布提出了一种新的优化目标函数，将压电致动器/传感器位置编号作为优化变量，建立了离散变量表示的智能结构优化问题，并通过二进制编码的遗传算法（GA）求解了该最优问题。以四边固支复合层合压电智能板为数值算例，采用比例反馈控制, 研究了最优位置配置致动器/传感器智能结构目标模态的控制效果。数值结果表明基于模态应变能分布的遗传算法所得优化解具有较好的振动控制效果。

Optimal Placement of Piezoelectric Actuator/Sensor Using Genetic Algorithm Based on the Distribution of Modal Strain Energy

In this paper, the active vibration control equation is derived from the finite element dynamic equations of linear elastic piezoelectric structure. Finite element model of laminated piezoelectric structure for modal analysis and vibration control has been established by use of ANSYS/APDL parameter language. Based on the distribution of host structure modal strain energy, a new objective function is developed. Taking actuator/sensor numbers as optimization variables, the optimization problem of smart structure represented by discrete variable is formulated and solved using binary-coded genetic algorithm (GA). Taking a clamped composite laminated piezoelectric plate as numerical example, considering direct proportional feedback control law, the control performance of objective modal vibration is studied with optimal location collocated actuator/sensor. Numerical results show that the optimal solution by genetic algorithm has better vibration control effect based on the distribution of modal strain energy.