Abstract
Since microplates are extensively used in MEMS devices such as microbumps, micromirrors, and microphones, this work aims to study nonlinear vibration of an electrically actuated microplate whose four edges are clamped. Based on the modified couple stress theory (MCST) and strain equivalent assumption, size effect and damage are taken into consideration in the present model. The dynamic governing partial differential equations of the microplate system were obtained using Hamilton’s principle and solved using the harmonic balance method after they are transformed into ordinary differential equation with regard to time. Size effect and damage effect on nonlinear free vibration of the microplate under DC voltage are discussed using frequency-response curve. In the forced vibration analysis, the frequency-response curves were also employed for the purpose of highlighting the influence of different physical parameters such as external excitation, damping coefficient, material length scale parameter, and damage variable when the system is under AC voltage. The results presented in this study may be helpful and useful for the dynamic stability of a electrically actuated microplate system.
Highlights
Since a microelectromechanical system (MEMS) received a considerable amount of attention in recent years, numerous works related to nonlinear responses and characteristics because of intrinsic existence of nonlinearity of these microdevices have been carried out in recent years
Zhang and Meng [3] proposed a simplified model in order to study the resonant responses and nonlinear dynamics of microcantilever under electronic excitation
Saghir and Younis [9] conducted a study on nonlinear vibration behavior of rectangular microplate under static and dynamic load. ey found an interesting phenomenon where the microplate shows a hardening behavior which switches to softening as the DC load increases
Summary
Since a microelectromechanical system (MEMS) received a considerable amount of attention in recent years, numerous works related to nonlinear responses and characteristics because of intrinsic existence of nonlinearity of these microdevices have been carried out in recent years. Using the multiple scale method, Younis and Nayfeh [1] studied nonlinear vibration of a resonant microbeam under dynamic electrostatic force. An electromechanical coupled nonlinear dynamic response was presented by Xu and Jia [4], who employed the perturbation method to discuss influence of mechanical and electric parameters on nonlinear natural frequencies and vibrating amplitudes of a microbeam. Jia et al [7] conducted a parametric study on forced vibration of microswitches to show effects of Casimir force, residual stress, and geometrical nonlinearity on the frequency response characteristics. Saghir and Younis [9] conducted a study on nonlinear vibration behavior of rectangular microplate under static and dynamic load. Sheikhlou et al [10] investigated nonlinear resonant behavior of diaphragm-type micropumps
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