Symplectic system analysis for finite sector plates of viscoelastic media

The symplectic method is applied to boundary condition problems of finite viscoelastic solids in a sector domain. On the basis of the state space formalism and the use of the Laplace integral transform, the general eigensolution of the governing equations are obtained in the polar coordinate system. Since the eigenvectors are expressed in concise analytical forms, the adjoint symplectic relation of the Laplace domain is generalized to the time domain. Therefore, the particular solution and boundary condition problems can be discussed directly in the eigenvector space of the time domain with the use of the eigenvector expansion method. Numerical examples show a good agreement between the numerical results and the exact analytical ones. Thus, the correctness and accuracy of the proposed method are well guaranteed.