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

Abstract

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.

A Nonlocal Strain Gradient Approach for Out‐of‐Plane Vibration of Axially Moving Functionally Graded Nanoplates in a Hygrothermal Environment

“…Unlike most research studies applying Galerkin method to investigate the moving nanosystems [39,41,46], the present work employs the composite beam function method [47] to develop the dynamic stability of axially moving nanoplates. e approach assumes the displacement function according to boundary conditions, so that the governing equation can be solved numerically directly.…”

Instability analysis of quasicrystal nano‐switch with thermal effect and surface distributed forces

“…A typical electrostatically actuated NEMS consists of a fixed electrode and a deformable electrode [3][4][5] For the two poles with applied electric potential difference, the deformable electrode bends under the electrostatic force and moves closer to the fixed electrode [6]. When the voltage exceeds a critical value, the deformable electrode loses its stability and suddenly adheres to the fixed electrode, which is called the pull-in phenomenon [7]. In this case, the critical voltage and the corresponding displacement are called pull-in voltage and pull-in displacement, respectively.…”