Free vibration of geometrically nonlinear functionally graded micro-switches under electrostatic force and temperature change

This paper investigates the free vibration characteristics of functionally graded micro- switches under combined electrostatic, axial residual stress and temperature change, with an emphasis on the effect of geometric nonlinear deformation due to mid-plane stretching, the influence of volume fraction profile parameter and temperature change. The micro-switch considered in this study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. Take into consideration the temperature-dependency of the effective material properties, the Voigt model is used to simulate the material properties of the functionally graded materials (FGMs). The principle of virtual work is used to derive the nonlinear governing differential equation. The eigenvalue problem which describes free vibration of the micro-beam at its statically deflected state is then solved using differential quadrature method (DQM). The natural frequencies of clamped-clamped micro-switches are obtained. The solutions are validated through direct comparisons with experimental results reported in previous studies. A parametric study is conducted to show the effects of geometric nonlinearity, material composition and temperature change for the natural frequencies