Solution of nonlinear vibration problem of shear deformable multilayer nonhomogeneous orthotropic plates using Poincare-Lindstedt method

Abstract

In this study, one of the first attempts is made to solve the nonlinear (NL) vibration problem of shear-deformable multilayer plates consisting of nonhomogeneous orthotropic layers (NHOLs) using the Poincaré-Lindstedt method. First, the shear deformation theory (SDT) for homogeneous plates is extended to multilayer plates composed of NHOLs. In the framework of von-Karman type nonlinear theory, the basic relations of the plates in question are established and then NL equations of motion based on four functions such as rotation angles, Airy stress and deflection functions are derived. Then, NL-partial differential equations (NL-PDEs) are reduced to NL-ordinary differential equations (NL-ODE) and the solution of NL-ODE is performed for the first time by the modified Poincaré −Lindstedt method, yielding new amplitude dependent expressions for NL frequency, and for the ratio of NL frequency to linear (NL/L) frequency for multilayer plates consisting of NHOLs. Finally, detailed parametric studies are carried out to gain insight into the effects of various factors such as shear strains, non-homogeneity, number and array of layers on the NL frequencies under different rectangular plate characteristics.