A semi-analytical solution for the dynamic response of thick composite plates in Hamilton systems

By introducing canonical functions in the time direction, the mixed state Hamilton equation and a semi-analytical solution are presented for analyzing the dynamic response of laminated composite plates. This method incorporates the separation of variables, the finite element discretization employed in the plane of lamina, and the exact solution in the thickness direction derived by the state-space control method. For applying the transfer matrix method, the continuity of displacements and stresses at the two interfaces is satisfied, and the relational expression at the top and bottom surfaces is established. No matter how many layers are considered, by introducing the traction boundary condition at the top and bottom plate surfaces, the final problem always leads to solving a set of algebraic equations of unknown joint displacements at the top surface, so that the number of variables is reduced greatly.