基于能量辨识的非线性静电-结构系统的自由度缩减建模方法

A REDUCED ORDER MODELING OF NONLINEAR ELECTROSTATIC-MECHANICAL SYSTEMS BASED ON THE ENERGY IDENTIFICATION APPROACH

给出了一种基于系统能量函数辨识的静电致动微薄板系统自由度缩减建模方法.从Von Karman应变-位移关系式出发,推导出以广义模态坐标为变量的系统动能、应变能以及电容函数的函数表达式.为了将应变能以及电容函数写成广义模态坐标的多变量多项式形式,利用一系列经静态非线性结构有限元计算的结果,拟合得到多变量多项式的未知系数.由Lagrangian方程获得原系统的自由度缩减模型.利用该模型对器件的静/动态特性进行仿真,其计算费用很低.与有限元结果比较,验证了建模方法的正确性.

To build the reduced order model（ROM） of an electrostatically actuated micro-plate device,a system identification modeling based on the energy identification approach is proposed.The kinetic energy,strain energy and capacitance of the nonlinear system are written as the multivariate polynomial functions of the structural modals.The unknown coefficients of these polynomials are fitted using the least squares from a set of steady state,high-fidelity,nonlinear finite element models.The resulting strain energy and capacitance expressions can be used to develop the ROM.The simulation with the ROM is with a much lower computational cost,and the calculating results agree very well with those from high-fidelity finite element model under various electric loads,and thus,the modeling approach in this paper has been validated.