Assessment of Homotopy Perturbation Method for Study the Forced Nonlinear Vibration of Orthotropic Circular Plate on Elastic Foundation

Abstract In this paper the nonlinear forced vibration of an orthotropic circular plate resting on Winkler, Pasternak and nonlinear Winkler foundation is investigated. Plates with edges elastically restrained against rotation and inplane displacement are analyzed and the Von-Karman geometric nonlinear equations are employed. In this study it is assumed that the plate can be subjected to any periodic distributed lateral loading with respect to time. The Galerkin method is used to obtain Duffing's equation for the central deflection. The Homotopy Perturbation Method was used to study the effects of various parameters including orthotropic parameter, elastic foundation parameters and initial deflection on frequency ratio. Highly accurate results were obtained by the application of the aforementioned method.