Size-dependent secondary resonance of a piezoelectrically laminated bistable MEMS arch resonator

Abstract

This paper deals with the size-dependent nonlinear dynamics of a bistable fully clamped resonant shallow microarch under subharmonic resonance of order 1/2. The microarch is laminated between thin piezoelectric layers and subjected to a combination of piezoelectric and electrostatic actuations. Nonlinearities associated with clamped ends, curvature and electrostatic actuation are taken into account in the formulation of the problem. Size effect is considered using the so-called strain gradient theory, and the result is compared with the classical theory. The frequency response is numerically obtained using the shooting technique and in some cases analytically using multiple time scales method. The effect of piezoelectric actuation and the initial rise on the resonant behavior of the system are investigated in the pre and post-buckling configurations as well as the bistability band of the microarch. Applying a DC voltage to the piezoelectric layers imposes a longitudinal compression or tension force along the microbeam depending on the polarity of the voltage. As a result, the initial rise and bending stiffness of the microarch changes. This property is used as a frequency tuning tool in this paper. It is shown that the resonance frequency of the microarch resonator can be tuned in both forward and backward directions thanks to appropriate piezoelectric actuation either in the pre-buckling or the post-buckling configuration. It is also revealed that taking advantage of piezoelectric actuation, the bandwidth of the static bistable band can be adjusted effectively. The results of this paper can be used for designing MEMS resonators.