陈昌萍　李良中　胡海涛　钱长照　洪力

摘 要：以压电层合微梁为研究对象，基于连续介质力学理论和Euler-Bernoulli梁理论，在考虑其尺寸效应和损伤效应的情况下，推导了具损伤压电层合微梁的非线性动力控制方程.采用伽辽金法和龙格库塔法进行求解，分析了多种参数对微梁结构坍塌特性的影响.结果表明，考虑几何非线性项使得损伤微梁具有更高的坍塌阈值电压；控制电压、微梁长度等参数的变化均对损伤微梁的坍塌阈值电压造成影响.最后，采用有限元软件进行仿真模拟计算，验证了理论计算结果的合理性.本文所得结论对微机电系统压电层合微梁结构的设计具有理论指导意义.

关键词：压电效应；层合微梁；损伤效应；尺寸效应；坍塌

中图分类号：O345 文献标识码：A

Abstract：The nonlinear pull-in behavior of piezoelectric laminated micro-beam was studied with consideration of the size effect and damage effect. Based on the theories of continuum mechanics and Euler-Bernoulli beam hypothesis， the nonlinear governing equation of piezoelectric laminated micro-beam with damage was established and solved in Galerkin method and Runge-Kutta method. The influence of various parameters on the pull-in voltage of the micro-beam was discussed， and the results have shown that the geometry nonlinearity can improve the value of critical pull-in voltage of the micro-beam； the changes of governing voltage， micro-beam length and other parameters have influences on the critical pull-in voltage of the micro-beam. Besides，the FEM software was used to carry out the check-up calculations， and the results were compared with the theoretical results. The findings of this research can offer guidance to the design of micro-structures.

Key words： miezoelectric effect； laminated micro-beam； damage effect； size effect； pull-in

MEMS作为智能化和集成化的微型系统在物理、生物、机械等多个行业中广泛运用.MEMS具有多种结构形式，其中压电微结构由于压电特性在MEMS结构中具有重要地位.一种主要的压电梁式微结构形式就是将压电片通过粘结剂粘结在弹性基体而形成层合压电微梁.层合压电微梁可作为执行器和传感器两种功能结构[1]，研究层合压电微梁在电场中的力学特性具有重要的意义.

近年来国内外已有许多学者对梁式微结构在电场中的静动力特性进行研究.Pamidighantam等[2]基于Euler-Bernoulli梁理论研究了两端固支和悬臂结构形式压电微梁的静、动力学特性，并得到了微梁结构的静力坍塌阈值电压.Younis和Nayfeh[3]研究……