Mechanical Behaviors of Electrostatic Microbeams with Nonideal Supports

Abstract

Deviation of the actual system from the ideal supporting conditions caused by micromachining errors and manufacturing defects or the requirement of innovative design and optimization of microelectromechanical systems (MEMS) make the nonideal boundary in the micro-/nanoresonator system receive wide attention. In this paper, we consider the neutral plane tension, fringing field, and nonideal boundary factors to establish a continuum model of electrostatically driven microbeam resonators. The convergent static solution with nine-order Galerkin decomposition is calculated. Then, based on the static solution, a 1-DOF dynamic equation of up to the fifth-order of the dynamic displacement using a Taylor expansion is derived. The method of multiple scales is used to study the effect of spring stiffness coefficients on the primary frequency response characteristics and hardening-softening conversion phenomena in four cases. The various law of the system’s static and dynamic performances with the spring stiffness coefficients is obtained. The conditions for judging the hardening-softening transition are derived. So, adjusting the support stiffness values can be a measure of optimizing the resonator performance.