Nonlinear free vibration analysis of clamped circular Fiber Metal Laminated plate


Mechanical Engineering Department, Bu-Ali Sina University, 65175-4161 Hamedan, Iran


Nonlinear free vibration of symmetric circular fiber metal laminated (FML) hybrid plates is investigated. Considering the Von Karman geometric nonlinearity, the first order shear deformation theory (FSDT) is used to obtain the equations of motion. For the first time, five equations of motion of circular FML plates are derived in terms of plate displacements. The obtained equations are simplified for analyzing the first mode of symmetric circular plates. Using Galerkin method, five coupled nonlinear partial differential equations (PDEs) of motion are transformed to a single nonlinear ordinary differential equation (ODE) which is solved analytically by multiple time scales method, and an analytical relation is found for the nonlinear frequency of these plates. The obtained results are compared with the published results and good agreements are found. Moreover, the effects of several parameters on linear and nonlinear frequencies and the free vibration response are investigated.