Nonlinear vibration analysis of a circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method

作     者：Milad Saadatmand Alireza Shooshtari 

作者机构：Department of Electrical EngineeringTechnical University of DenmarkKgs.LyngbyDenmark Department of Mechanical EngineeringBu-Ali Sina UniversityHamedanIran 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2019年第35卷第1期

页      面：129-143,I0004页

核心收录：

学科分类：08[工学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Danmarks Tekniske Universitet  DTU 

主　　题：Nonlinear vibration Two-sided MEMS capacitor Circular plate Harmonic balance method 

摘      要：In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.