Dynamic Analysis of Multilayers Based MEMS Resonators

Hassen M Ouakad,Ali H Nayfeh,Abdulrahman M Alofi

doi:10.1155/2017/1262650

Abstract

The dynamic behavior of a microelectromechanical system (MEMS) parallel and electrically coupled double-layers (microbeams) based resonator is investigated. Two numerical methods were used to solve the dynamical problem: the reduced-order modeling (ROM) and the perturbation method. The ROM was derived using the so-called Galerkin expansion with considering the linear undamped mode shapes of straight beam as the basis functions. The perturbation method was generated using the method of multiple scales by direct attack of the equations of motion. Dynamic analyses, assuming the above two numerical methods were performed, and a comparison of the results showed good agreement. Finally, a parametric study was performed using the perturbation on different parameters and the results revealed different interesting features, which hopefully can be useful for some MEMS based applications.

Highlights

Microelectromechanical systems (MEMS) were mostly developed during the industrial revolution in the late of 20th century [1]
The selected parameters are the same as assumed in the static analysis [18] and shown in Table 1, with the only difference being the applied voltages, VDC = 10 Volts and VAC = 0.5 Volts. It can be seen from all figures that overall both assumed numerical methods are in good agreement for all different cases
An investigation into the nonlinear dynamics of a multilayers based MEMS resonator made of clamped-clamped microbeams under electrostatic actuation was conducted

Summary

Introduction

Microelectromechanical systems (MEMS) were mostly developed during the industrial revolution in the late of 20th century [1]. Many researchers extensively used reduced-order modeling (ROM) techniques to obtain the structural behavior of MEMS microstructures [13, 14] It became nowadays among the most common numerical methods used in the MEMS community. Turner and Andrews [17] used the perturbation method to obtain an approximation for the nonlinear resonance frequency of a microbeam They modeled the problem by using a spring mass model, and they included a cubic restoring force to represent the mid-plane stretching. This work considers the nonlinear dynamical behaviors for this MEMS structure by using the ROM and the perturbation method This is due to the different features this device has as it is compared with the single microbeam. A parametric study will be done to investigate some dynamical features for the microactuator

Problem Formulation

Perturbation Analysis

ROM and Perturbation Results

Parametric Study

Conclusion