We present a theoretical investigation of the dynamic behavior of a microelectromechanical system (in brief, MEMS) device modelled as a clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. We use the Galerkin projection technique to reduce the partial integro-differential equation governing the dynamics of the microbeam to a system of coupled ordinary differential equations which describe the interactions of the linear mode shapes of the microbeam. Analytical solutions are derived and their stability is studied for the simplest reduced-order model which takes into account only the first linear mode in the Galerkin procedure. We further investigate the influence of the first few higher modes on the Galerkin procedure, and hence its convergence, by analysing the boundaries between pull-in and pull-in-free vibrations domains in the space of actuation parameters. These are determined for the various multimode combinations using direct numerical time integration. Our results show that unsafe domains form V-like shapes for actuation frequencies close to the superharmonic, fundamental, and subharmonic resonances. They also reveal that the single first-mode reduced model usually considered underestimates the left branches and overestimates the right branches of these boundaries. 1. Introduction Microelectromechanical systems (henceforth, MEMS) are structures that generally combine silicon based electrical and mechanical components at the scale of micrometers. MEMS technology emerged as a logical extension of microelectronics and integrated circuits technology [1–3] and was initially developed for realizing microsensors. Due to their small size, low fabrication cost, unique performance, and suitability for integration into complex functional engineering systems, they have become key components of many commercial systems. These include RF microresonators for wireless communication [4], accelerometers for airbag deployment in automobiles, ink jet printer heads, atomic force microscopes, optical switches, and chemical sensors [5]. The use of MEMS technology in the modelling of deformable mirrors for very high resolution giant telescopes has recently been addressed in adaptative optics [6]. The vibrating gyroscope is one of the MEMS devices that are commonly used for measuring angular velocity in area such as aviation, navigation, automotive, biomedicine, military affairs, and consumer electronics [7]. This large variety of MEMS can generally be classified according to their actuation mechanisms which can be pneumatic, thermal,
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