Resonant modal interactions in micro/nano-mechanical structures

Oriel Shoshani, Steven W. Shaw

Research output: Contribution to journalArticlepeer-review


This 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.

Original languageAmerican English
Pages (from-to)1801-1828
Number of pages28
JournalNonlinear Dynamics
Issue number3
StatePublished - 1 May 2021


  • MEMS
  • Modal interaction
  • Nonlinear resonance

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering


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