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

Small 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.