A closed form solution for linear and nonlinear free vibrations of composite and fiber metal laminated rectangular plates

In this paper, the nonlinear equations of motion for laminated composite rectangular plates based on first order shear deformation theory, which include shear deformation and rotary inertia, have been derived. Then, through introducing a force function, these equations reduced to a set of coupled nonlinear partial differential equations and a compatibility equation. By using the Galerkin method, for the first time, a nonlinear ordinary differential equation is obtained, which includes nonlinear inertia and stiffness terms. By using the multiple time scales method, analytical relations for nonlinear frequency and transverse displacement have been obtained. Results are compared with the literature and good agreement is achieved for both linear and nonlinear frequencies. After proving the validity of our work for isotropic rectangular plates and laminated rectangular plates, linear and nonlinear free vibration of a Fiber Metal Laminate panel have been investigated. Also the effects of some system parameters on the nonlinear frequency have been investigated.