Numerical Investigation of Modal Amplitude Saturation in Micromechanical Cantilever Beam Resonators

Abstract

Micromechanical resonators have extensive applications but unavoidably exhibit nonlinearities that may degrade the devices’ performances. A good understanding of their nonlinear dynamics is essential to the design of resonant devices. In this paper, we numerically investigated the dynamics of a cantilever beam resonator working at a coupled extensional and flexural vibrational modes with a 2:1 internal resonance. An amplitude saturation behavior is observed in the cantilever beam resonator by controlling the external driving force. The flexural mode shows a complex nonlinear behavior changing from a softening effect to a hardening effect and the extensional mode shows nonlinear behavior due to the nonlinear mode coupling.