Nonlinear Vibrations of FGM Circular Conical Panel Under In-Plane and Transverse Excitation

Abstract

In this study, nonlinear forced vibrations of a functionally graded material circular conical panel under the transverse excitation and the in-plane excitation are discussed. The temperature field of the system is considered as a steady-state temperature. Material properties of temperature-dependence for the system vary along the thickness direction in the light of a power law. The nonlinear geometric partial differential equations expressed by general displacements are derived by the first-order shear deformation theory and Hamilton’s principle. Furthermore, the ordinary differential equations of the system are acquired by the Galerkin method. The nonlinear dynamic behaviors of the system are fully analyzed. Based on numerical simulations, time history records, Poincare maps, phase portraits and bifurcation diagrams are depicted to clarify the existence of complex nonlinear dynamic behaviors of the system.