Search Results

Fast and accurate characterization of stability regions and operational range with respect to pull-in voltage and displacement is critical in the design and development of MEMS resonators and switches. This paper presents a mathematical and computational procedure for modeling and analysis of static and dynamic instabilities of capacitive microdevices employing resonant microbeams. The mathematical model consists of a nonlinear microbeam under distributed electrostatic actuation and squeeze film damping. The coupled system is described by the nonlinear beam equation and a modified compressible Reynolds equation to account for the rarefied gas in the narrow gap between the microbeam and substrate. The Differential Quadrature Method (DQM) is used to discretize partial differential equations of motion and solve for static deflection, natural frequencies, static pull-in voltage, and quality factors for various encapsulation air pressures and applied DC voltages.

The objective of this paper is to investigate the influence of the non-linearity and time dependence of friction force between disc and pads on the generation of low and high frequency squeal. For this purpose, a non-linear mathematical model of a disc-pad system, that includes the transverse (out-of-plane) and circumferential (in-plane) motions, is developed. The contact normal pressure includes a non-uniform distribution and is represented by a non-linear function of the relative displacement (penetration) of the disc and pad. Friction is assumed as a distributed follower-type force nonlinearly dependent on the relative velocity. Deterministic and random friction coefficient is considered. Numerical simulations reveal a modulated-intermittent response of both disc and pad. It is found that the frequency component corresponding to circumferential vibrations of the disc is always dominant in the case of deterministic friction.