Resonant modal interactions in micro/nano-mechanical structures
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Published:2021-04-05
Issue:3
Volume:104
Page:1801-1828
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ISSN:0924-090X
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Container-title:Nonlinear Dynamics
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language:en
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Short-container-title:Nonlinear Dyn
Author:
Shoshani Oriel, Shaw Steven W.ORCID
Abstract
AbstractThis paper considers nonlinear interactions between vibration modes with a focus on recent studies relevant to micro- and nanoscale mechanical resonators. Due to their inherently small damping and high susceptibility to nonlinearity, these devices have brought to light new phenomena and offer the potential for novel applications. Nonlinear interactions between vibration modes are well known to have the potential for generating a “zoo” of complicated bifurcation patterns and a wide variety of dynamic behaviors, including chaos. Here, we focus on more regular, robust, and predictable aspects of their dynamics, since these are most relevant to applications. The investigation is based on relatively simple two-mode models that are able to capture and predict a wide range of transient and sustained dynamical behaviors. The paper emphasizes modeling and analysis that has been done in support of recent experimental investigations and describes in full detail the analysis and attendant insights obtained from the models that are briefly described in the experimental papers. Standard analytical tools are employed, but the questions posed and the conclusions drawn are novel, as motivated by observations from experiments. The paper considers transient dynamics, response to harmonic forcing, and self-excited systems and describes phenomena such as extended coherence time during transient decay, zero dispersion response, and nonlinear frequency veering. The paper closes with some suggested directions for future studies in this area.
Funder
United States - Israel Binational Science Foundation National Science Foundation
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering
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