Analysis of dynamic instability for arbitrarily laminated skew plates

The dynamic instability and nonlinear response of rectangular and skew laminated plates subjected to periodic in-plane load are studied. Based on von Karman plate theory, the large amplitude dynamic equations of thin laminated plates are derived by applying the approach of generalized double Fourier series. On the assumed mode shape, the governing equations are reduced to the Mathieu equation using Galerkinʹs method. The incremental harmonic balance (IHB) method is applied to solve the nonlinear temporal equation of motion, and the region of dynamic instability is determined in this work. Calculations are carried out for isotropic, angle-ply and arbitrarily laminated plates under two cases of boundary conditions. The principal region of dynamic instability associated with the effect of the stacking sequence of lamination and the skew angle of plate are also investigated and discussed. The results obtained indicated that the instability behavior of the system is determined by the several parameters, such as the boundary condition, number of the layers, stacking sequence, in-plane load, aspect ratio, amplitude and the skew angle of plate.