Phase switch in the stochastic response of a micromechanical beam resonator

Abstract

In this paper, the phase switch in the stationary stochastic response induced by random disturbance is investigated in a micromechanical clamped–clamped beam resonator. First, a reduced-order stochastic dynamic model of the resonator involving the main sources of nonlinearities is developed based on the Galerkin decomposition method. Using stochastic averaging, a Fokker–Planck–Kolmogorov equation governing the stationary stochastic response is derived, from which the stationary probability density (SPD) is obtained analytically. Based on the qualitative change of the shape of SPD, the phase switch in the stationary motion of the resonator is observed for the first time. Then, the effects of various parameters including AC voltage, nonlinearity strength and random excitation intensity on the phase switch are examined. Furthermore, the critical values of the phase switch in the parameter plane are detected.