Analysis of damped waves using the boundary element method

The subject of this paper is the one-dimensional, damped wave equation including both viscous damping, where resistance is proportional to velocity, and material damping, where resistance is proportional to displacement. Disturbances propagating in a material of finite length subject to distributed forces, surface forces and initial conditions will be examined. The purpose of the paper is to develop a numerically accurate and computationally efficient solution using the boundary element method (BEM) and to use this solution to examine the physical behavior of systems subjected to a variety of forcing functions. The model equations are important in both mechanical and thermal wave propagation. The BEM is particularly well suited for this class of problems since discontinuities at wave fronts could exist. The solution is based on the associated full space Green's function (GF), which naturally possesses the propagating wave front characteristics of the actual response. Representative plots are presented to show the fundamental effects of damping on the GF since characteristic responses to actual disturbances can be seen in the GF. Results are then presented to show how various degrees of damping effect the propagation of waves caused by applied surface forces.