Nonlinear wave propagation in a viscoelastic thin rod

The problem of finite amplitude wave propagation in a viscoelastic semi-infinite and finite rod is treated. The rod is made of a material having a constitutive equation taken from Schapery's thermodynamic constitutive theory. The end of the rod is disturbed by a time-dependent input. A numerical method which is able to treat shocks is used and the linearly elastic, viscoclastic and nonlinearly elastic cases are obtained as special cases. The accuracy of the numerical procedure is checked by comparison with some special cases in which analytical conclusions could be drawn.