Analysis of non-linear vibrations of a microresonator under piezoelectric and electrostatic actuations

In this article, the non-linear vibrations of a piezoelectrically actuated microresonator is studied. The microresonator is assumed as a clamped-clamped Bernouli-Euler microbeam. In contrast to previous researches in which the piezoelectric layer has been deposited on the integral length of the microbeam, here it is assumed that the piezoelectric layer is deposited on a part of microbeam length with equal distance from two ends. The microbeam is actuated by an AC voltage between upper and lower sides of the piezoelectric layer. Also, an electrostatic actuation is applied between the microbeam and an electrode plate, for the first time. The nonlinear equation of motion has been derived by using the Hamilton principle by stretching the neutral axis assumption. The obtained equations are solved using the Galerkin, Rayleigh-Ritz, and multiple scale perturbation methods. It is shown that the sensitivity and natural frequency of the piezoelectrically actuated microresonator may be altered and controlled conveniently by applying an electrostatic actuation to the microresonator. Also, it has been shown that the system shows softening or hardening behaviour depending on the value of piezoelectric actuation, electrostatic actuation, axial load, thickness, length, and elasticity module of piezoelectric layer; thickness of microbeam; and its distance from the electrode plate. It is shown that non-linear behaviour of the piezoelectrically actuated microbeam may be changed to a linear behaviour by applying a suitable electrostatic actuation to the microbeam.