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research-article

On the Nonlinear Dynamics of a Doubly Clamped Microbeam near Primary Resonance

[+] Author and Article Information
Nizar R. Jaber

Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
nizar.jaber@kaust.edu.sa

Karim M. Masri

Department of Mechanical Engineering, State University of New York, Binghamton, NY, 13850, USA
kmasri1@binghamton.edu

Mohammed Ibrahim Younis

Physical Science and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi ArabiaDepartment of Mechanical Engineering, State University of New York, Binghamton, NY, 13850, USA
mohammad.younis@kaust.edu.sa

1Corresponding author.

ASME doi:10.1115/1.4036399 History: Received November 28, 2016; Revised March 25, 2017

Abstract

This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency-response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of DC bias revealing hardening, mixed, and softening behavior of the microbeam. A multi-mode Galerkin model combined with a shooting technique are implemented to generate the frequency response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show good agreement with the experimental data.

Copyright (c) 2017 by ASME
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