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The topology of MEMS devices is characterized by a large surface-to-volume ratio and a small gap distance between the movable and fixed electrodes. Under such conditions, the slender air layer confined in the narrow gap can be condensed or expanded due to micro beam vibrations. This phenomena gives rise to squeeze film damping effect, considered as the most important cause of energy dissipation in MEMS structures. The pressure variation surrounding the doubly clamped micro beam is expressed by Reynolds equation and has zero flux at fixed ends and atmospheric pressure at free boarders. Several methodologies had been proposed in previous work to describe the effect of squeeze film damping. The common used one is based on linearizing the Reynolds equation by assuming small pressure and displacement variation leading to a partially coupled multi-domain system. For rigid body assumption, the Reynolds equation can be decoupled leading to a simple equivalent spring-mass-damped model under electrostatic actuation.
In this study, we present a strong coupled modeling strategy for MEMS micro beam under electrostatic, mechanical and fluidic effects. In this approach, we construct a fully coupled system of dynamic equations using the nonlinear compressible Reynolds equation and the nonlinear Euler-Bernoulli beam equation taking into account geometric nonlinearity due to midplane stretching and the fully nonlinear form of the electrostatic force including the fringing field effect. Unlike previous studies that considered the pressure solution as a product of a parabolic function across the width and cosine series across the length, we develop here a reduced-order model obtained by applying the Differential Quadrature Method (DQM) to both structural and fluidic domains. Taking advantage from the symmetric beam configuration, we reduce the system size to gain in computational simulation time solved by means of Runge-Kutta integration scheme. Effect of surrounding air pressure is investigated and results of the proposed model are compared with previously published results.