Nonlinear behavior of a vibrating axially moving small‐size beam under an electrostatic force

Abstract

AbstractSmall size (micro/nano)‐scale beams constitute important building blocks of microelectromechanical systems (MEMS)/nanoelectromechanical systems (NEMS). Emerging roll‐based, high rate, manufacturing processes can make these small size‐beams vibrate, while they are axially moving. In this paper, an analytical‐numerical study on the nonlinear transverse vibration of the representative case of axially moving micro‐beam under an electrostatic force is conducted. The analytical model is realized by employing Hamilton's principle together with Galerkin discretization. The method of multiple time‐scales and Runge‐Kutta based numerical scheme are utilized to investigate the nonlinear dynamic behavior of the micro‐beam. Results are obtained for the influence of axial beam velocity and modified couple stress theory length scale parameter (i) on the values of pull‐in instability voltage of the small‐size beam, and (ii) on the small‐size beam nonlinear softening/hardening characteristics. The effect of axial load on the frequency response is investigated.