Size-dependent nonlinear behavior of a piezoelectrically actuated capacitive bistable microstructure

Abstract

Size-dependent behavior of a bistable microelectromechanical system subjected to electrostatic and piezoelectric actuations is investigated. The system is comprised of an Euler–Bernoulli slightly curved capacitive microbeam which is laminated between piezoelectric layers. Applying DC voltage to piezoelectric layers induces axial force in the beam and modulates its stiffness and consequently, its frequencies. Hamilton’s principle is used to derive the governing equation of motion and the size effect is introduced into the formulation through the so-called strain gradient theory. The proposed model accounts for nonlinearities due to mid-plane stretching, curvature, and the electrostatic loading. The reduced order model is obtained via utilizing the Galerkin approach. A detailed study is carried out to reveal the influences of initial curvature, size effect, and piezoelectric actuation on the behavior of the system. The primary resonance is characterized using shooting method and the stability of the limit cycles is determined using the Floquet theorem. The results are compared in some cases with the method of multiple time scales. The static and dynamic snap-through are identified and the influences of the system parameters on the snap-through bandwidth is investigated. It is shown that by applying appropriate piezoelectric actuation, the bandwidth and center frequency of the dynamic snap-through as well as the static bistability band can be tuned effectively. The results can be used in design and analysis of bistable MEMS-based devices especially in switch and filter design applications.