Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane

Bongwon Jeong, Hanna Cho, Hohyun Keum, Seok Kim, D. Michael McFarland, Lawrence Bergman, William Paul King, Alexander F Vakakis

Research output: Contribution to journalArticle


Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

Original languageEnglish (US)
Article number465501
Issue number46
StatePublished - Nov 21 2014



  • complex mode
  • geometric nonlinearity
  • micro/nanomechanical resonator
  • nonlinear damping
  • nonlinear resonance

ASJC Scopus subject areas

  • Bioengineering
  • Chemistry(all)
  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Electrical and Electronic Engineering

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