Finite-difference scheme for elastic wave propagation in a circular disk

A second-order accurate, explicit finite-difference scheme is presented for the numerical solution of elastic wave propagation in a circular disk subjected to traction boundary conditions. One face of the disk is subjected to an axisymmetric loading while the remainder of the boundary is free of tractions. The temporal dependence of the forcing function is taken to be trapezoidal. The governing partial differential equations are discretized by using second-order accurate central difference schemes in both time and space. A stability criterion is analytically derived by using the classical von Neumann analysis. The numerical results are compared with the analytical results based on a modal analysis approach and the agreement is excellent until times as late as 60 mu s where, the traversal time of a longitudinal wave across the thickness is approximately 4.5 mu s. Furthermore, for time-dependent loading, the numerical results are compared with those from a corresponding mixed problem. Present results show that, even for time-dependent loading, the solution of the mixed problem provides a very accurate approximation to the solution of the nonmixed problem for sufficiently large distances in the axial direction. (C) 1996 Acoustical Society of America.