An eigenfunction expansion method for the elastodynamic response of an elastic solid with mixed boundary surfaces

The method of eigenfunction expansion is one of the most elegant methods for solving elastodynamic problems. The solution obtained from it is more concise than that obtained from the integral transform technique. Traditional eigenfunction expansion method is used for the elastodynamic problems with displacement and traction boundary conditions. In this paper, the method is generalized to study the elastodynamic response of an elastic solid with mixed boundary surfaces, and the exact analytical solution is derived. The dynamic response of a finite-length solid aluminum cylinder with two mixed end boundaries is numerically evaluated. The result computed from the analytical solution agrees very well with that obtained from finite element method (FEM).