Size effect on the free vibration of geometrically nonlinear functionally graded micro-beams under electrical actuation and temperature change

This paper investigated the size effect on the free vibration of functionally graded micro-beams under the combined electrostatic force, temperature change and Casimir force based on Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. Taking into consideration the temperature-dependency of the effective material properties, material properties of the functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to the Voigt model and exponential distribution model. The principle of minimum total potential energy is used to derive the nonlinear governing differential equation which is then solved using the differential quadrature method (DQM). A parametric study is conducted to show the significant combined effects of the size effect, material gradient, temperature change, geometric parameters and Casimir force.