Parametric resonance and Hopf bifurcation analysis for a MEMS resonator
type: Item
instance of: scholarly article
title: Parametric resonance and Hopf bifurcation analysis for a MEMS resonator
zbMATH Open document ID: 1222.37044
author: Cas van der Avoort
author: R. van der Hout
author: Josephus Hulshof
published in: Physica D
publication date: 2011-06-14T00:00:00Z
review text: The response of a MEMS resonator, driven in an in-plane length-extensional mode of excitation, is studied. It is observed that the amplitude of the resulting vibration has an upper bound, i.e., the response shows saturation. A model for this phenomenon, incorporating interaction with a bending mode, is presented in terms of the equation of motion. It is demonstrated that this model accurately describes the observed phenomena. The in-plane (so-called ``trivial'') mode is shown to be stable up to a critical value of the amplitude of the excitation. At this value, a new ``bending'' branch of solutions bifurcates. For appropriate values of the parameters, a subsequent Hopf bifurcation causes a beating phenomenon, in accordance with experimental observations.
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37J20
zbMATH DE Number: 5907634
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: MEMS resonator
zbMATH Keywords: clipping
zbMATH Keywords: beating
zbMATH Keywords: equation of motion
zbMATH Keywords: Euler-Largrange equation
zbMATH Keywords: combination resonance
reviewed by: Denis Sidorov
MaRDI profile type: Publication
full work available at URL: j.physd.2011.01.004
OpenAlex ID: W2146920161
cites work: Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes
cites work: Der eingespannte, achsial pulsierend belastete Stab als Stabilit�tsproblem
cites work: Simple and combination resonances of columns under periodic axial loads
cites work: Simultaneous combination resonances in an autoparametrically resonant system
cites work: Parametric excitations of linear systems having many degrees of freedom
cites work: Q4154174
cites work: Averaging methods in nonlinear dynamical systems
DOI: 10.1016/J.PHYSD.2011.01.004
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description: scientific article; zbMATH DE number 5907634