Sharif University of Technology Scientia Iranica 1026-3098 23 5 2016 10 01 Analytical solutions to nonlinear oscillations of micro/nano beams using higher-order beam theory Analytical solutions to nonlinear oscillations of micro/nano beams using higher-order beam theory 2179 2193 3947 10.24200/sci.2016.3947 EN M.M. Roozbahani School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran. N. Heydarzadeh Arani School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran. M. Moghimi Zand School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran. M. Mousavi Mashhadi School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran. Journal Article 2016 11 09 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 eects 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 dierential 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 eects of high thicknesses and dierent values of residual stress on the nonlinear frequency and the midpoint de ection of the beam. https://scientiairanica.sharif.edu/article_3947_444a9572216f16b08c9597e7e9a2b4db.pdf