In this paper a comprehensive theory is formulated for the dynamic response of structural members with a constitutive relation in the form of a hereditary integral. A modal approach is taken to uncouple the response due to an arbitrary excitation force and general nonhomogeneous surface tractions. The result of this theory is a general set of formulas which may be used for both nonself-adjoint and self-adjoint systems of governing equations of motion. This general formulation is applied to the specific cases of a Voigt-Kelvin beam and a viscoelastic circular plate.

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