Nonlinear vibration and dynamic stability analysis of composite plates

Large amplitude flexural vibration characteristics of composite plates under transverse harmonic pressure or periodic in-plane load are investigated here using the shear deformable finite element method. The nonlinear stiffness matrix is formulated based on von Kármán's assumptions to obtain the stiffness interaction between the in-plane and bending degrees of freedom. Further, the flexural motion of the plate is assumed to be harmonic and the in-plane movement is assumed to be periodic. The nonlinear matrix amplitude equation is obtained by employing Galerkin's method. The coupled nonlinear matrix amplitude equation (in-plane motion is coupled with flexural motion) is solved to obtain (1) nonlinear free flexural vibration frequencies of isotropic and composite plates with different in-plane boundary conditions, (2) flexural vibration amplitudes of such plates under transverse harmonic pressure or periodic in-plane load. Finally, the time history analysis is carried out to understand the steady-state or unsteady nature of the flexural vibration under different loading and boundary condition.