Homotopy Analysis Method for Large-Amplitude Nonlinear Vibration of Flat Plates

Abstract

In this study, the homotopy analysis method is employed to analyze nonlinear vibration of a flat plate by simply supports. The governing equation of vibration is derived based on large-amplitude assumption. Also, the effects of shear deformation and rotary inertia of the cross section of the plate is considered. Because of these factors, the cubic nonlinear terms are created in the characteristic equation of vibration. To transform partial differential equations into ordinary differential equation, Galerkin method is used. After solving of this equation, the analytical relationship for natural frequency of vibration is obtained. With employing of this relationship, the effect of design parameters on vibration frequency is investigated. In order to accurately assess and examine the precision of analyses, the results with the numerical solution by Runge- Kutta method fourth order are compared. The results show that in this case, the respond of analytical method has a good correspondence with a numerical method. According of results, increasing of thickness ratio to width of plate and Poisson’s ratio caused the natural nonlinear frequency increases. Furthermore, the obtained results show that, increasing the factor term of rotary inertia effect caused frequency increases, where increasing the factor term of shear deformation caused frequency decreases.