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Parametric excitation of a micro-beam-string with asymmetric electrodes - multimode dynamics and the effect of nonlinear damping

[+] Author and Article Information
Karin Mora

Department of Mathematics University of Paderborn 33098 Paderborn Germany
kmora@math.upb.de

Oded Gottlieb

Faculty of Mechanical Engineering Technion - Israel Institute of Technology Haifa, 32000 Israel
oded@technion.ac.il

1Corresponding author.

ASME doi:10.1115/1.4036632 History: Received November 30, 2016; Revised April 27, 2017

Abstract

The dynamic motion of a parametrically excited micro-beam-string affected by nonlinear damping is considered asymptotically and numerically. It is assumed that the geometrically nonlinear beam-string, subject to only modulated AC voltage, is closer to one of the electrodes, thus resulting in an asymmetric dual gap configuration. A consequence of these novel assumptions is a combined parametric and hard excitation in the derived continuum-based model that incorporates both linear viscous and nonlinear viscoelastic damping terms. To understand how these assumptions influence the beam's performance, the conditions that lead to both principal parametric resonance and a three-to-one internal resonances are investigated. Such conditions are derived analytically from a reduced-order nonlinear model for the first three modes of the micro-beam-string using the asymptotic multiple-scales method which requires reconstitution of the slow-scale evolution equations to deduce an approximate spatio-temporal solution. The response is investigated analytically and numerically and reveals a bifurcation structure that includes coexisting in-phase and out-of-phase solutions, Hopf bifurcations, and conditions for the loss of orbital stability culminating with non-stationary quasiperiodic solutions and chaotic strange attractors.

Copyright (c) 2017 by ASME
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