The Symplectic Method in Polar Coordinates for Linear Viscoelastic Materials

Abstract

In this study, the symplectic method is applied to a two-dimensional annular-sector viscoelastic domain under the polar coordinate system. By applying variable separation approach, all fundamental solutions are derived in analytical form. Further more, using the method of variable substitution, lateral conditions are transformed into finding a particular solution of the governing equations, and the particular solution is derived with the use of eigensolution expansion. In the numerical example, the boundary condition problem is dentally discussed to analyze the stress responds of viscoelastic solids.