Resonance frequency response of geometrically nonlinear micro-switches under electrical actuation

This paper presents an analytical study on the forced vibration of electrically actuated micro-switches near resonance region, taking into consideration the intermolecular force, axial residual stress, and geometrical nonlinearity due to mid-plane stretching. The micro-switch is made of either homogeneous material or non-homogeneous functionally graded materials with two material phases and subjected to a time-varying applied voltage consisting of a DC component and a small AC component. The perturbation-based method of averaging is employed to solve the nonlinear partial differential governing equations to obtain the resonance frequency responses of both the vibration amplitude and phase angle. The present analysis is validated through direct comparisons with published experimental results and excellent agreement has been achieved. A parametric study is conducted to show the effects of geometrical nonlinearity, intermolecular Casimir force, the electrostatic force due to DC voltage, the AC voltage induced harmonic force, quality factor, axial residual stress and material composition on the frequency response characteristics. ► A comprehensive study of the nonlinear dynamics of micro-switches is conducted. ► Nonlinear theoretical formulations of micro-switches are developed. ► Nonlinear resonance responses of homogeneous micro-switches have been obtained. ► Effect of graded microstructure on the nonlinear resonance response is discussed. ► An extensive parametric study has been carried out.