Nonlinear tuning of microresonators for dynamic range enhancement

M. Saghafi, H. Dankowicz, W. Lacarbonara

Research output: Contribution to journalArticlepeer-review


This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators.

Original languageEnglish (US)
Article number20140969
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2179
StatePublished - Jul 8 2015


  • Bifurcation
  • Boundary value problems
  • Design optimization
  • Dynamic range
  • Finite-element analysis
  • Nonlinear dynamical systems

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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