A thermo-viscoelastic analysis using the eigenvector expansion method

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A novel eigenvector expansion method under the symplectic system is introduced for boundary condition problems of thermo-viscoelastic materials. On the basis of the state space formalism and the use of the Laplace integral transform, the general solutions of the governing equations, zero and non-zero-eigenvalue eigenvectors, are obtained analytically. Since the eigenvectors are expressed in concise analytical forms, the adjoint symplectic relation in the Laplace domain is generalized to the time domain. Using this method, various boundary conditions and the particular solution of non-homogeneous governing equations can be conveniently described by combinations of the eigenvectors.