Nonlinear Mode Coupling in a MEMS Resonator

David A. Czaplewski, Daniel López, Oriel Shoshani, Steven W. Shaw

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


A single micro-electromechanical (MEMS) resonator can be shown to exhibit behaviors unexpected in a simple resonant structure. For small driving forces, the resonator displays typical simple harmonic oscillator response. As the driving force is increased, the resonator shows the slightly more complex, but well understood, Duffing response. Rather unexpected response behavior can appear when the resonator frequency is detuned by nonlinearity to where two oscillatory modes of the resonator begin to interact through nonlinear coupling due to an internal resonance. The paper focuses on how the resonator response changes as the internal resonance is approached in the operating parameter space and how that behavior is conveniently represented in a bifurcation diagram. This behavior is accurately captured by a generic mathematical model. We describe an analysis of the model which shows how this coupled response varies with the system and drive parameters, especially focusing on the nonlinear coupling strength between the two modes.

Original languageEnglish
Title of host publicationNovel Patterning Technologies for Semiconductors, MEMS/NEMS and MOEMS 2020
EditorsMartha I. Sanchez, Eric M. Panning
Place of PublicationSan Jose, CA USA
ISBN (Electronic)9781510634152
StatePublished - 23 Mar 2020
EventNovel Patterning Technologies for Semiconductors, MEMS/NEMS and MOEMS 2020 - San Jose, United States
Duration: 24 Feb 202027 Feb 2020

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceNovel Patterning Technologies for Semiconductors, MEMS/NEMS and MOEMS 2020
Country/TerritoryUnited States
CitySan Jose


  • Bifurcation diagram
  • Coupling strength
  • MEMS
  • Mode coupling
  • NEMS
  • Non-linear
  • Resonance

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


Dive into the research topics of 'Nonlinear Mode Coupling in a MEMS Resonator'. Together they form a unique fingerprint.

Cite this