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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.

The mixed state Hamiltonian canonical equation and a semi-analytical solution are presented for analyzing the laminated composite plates. The method accounts for the separation of variables. The discrete element is employed in the plane of the lamina, and the exact solution in the thick direction is derived by the state space approach. Furthermore, in order to apply the transfer matrix method, the continuity of interlaminar stresses and displacements is satisfied, and the relational expression at the top and bottom plate surface is established. No matter how many layers are considered, by introducing the traction boundary condition at the top and bottom surface, the final problem always leads to solve a set of algebraic equations of unknown joint displacements at the top surface, the number of joint variables compared with the layer-wise theory is 3(2Q + 3), in which Q is the total layers. The number of variables is greatly reduced. The present solution is compared to those obtained using the classical theory and the higher theory.