Nonlinear free vibration analysis of clamped circular ber metal laminated plates

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 rst time, ve equations of motion of circular FML plates are erived in terms of plate displacements. The obtained equations are simplied for analyzing the rst mode of symmetric circular plates. Using the Galerkin method, ve coupled nonlinear Partial Dierential Equations (PDEs) of motion are transformed to a single nonlinear Ordinary Dierential Equation (ODE), which is solved analytically by the 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 agreement is found. Moreover, the eects of several parameters on linear and nonlinear frequencies and the free vibration response are investigated.