Analytical solutions to nonlinear oscillations of micro/nano beams using higher-order beam theory

Abstract

In this study, the nonlinear oscillations of micro/nano beams, modeled by Timoshenko beam theory and actuated by suddenly applied electrostatic forces, are investigated. The e ects of electrostatic actuation, residual stress, mid-plane stretching, and fringing eld are considered in modeling. In order to develop the governing equations and the boundary conditions, the Hamilton's principle is employed. After combining governing equations, the Galerkin's decomposition method is used to convert the governing nonlinear partial equation to a nonlinear ordinary di erential equation. The Homotopy Analysis Method (HAM) is used to present semi-analytical solutions to the strongly nonlinear behavior of system. To verify the present model, in special limiting cases, the results are compared with numerical results; and in low values of beam thickness, the results are compared with those obtained with the assumption of Euler-Bernoulli beam theory, which are available in literature. Some numerical results are presented to investigate the e ects of high thicknesses and di erent values of residual stress on the nonlinear frequency and the midpoint de ection of the beam.