Shock Formation and Pulse Attenuation in a Nonlinear, Geometrically Dispersive Solid

摘要

A generalization of the effective stiffness theory of Herrmann and Achenbach is used with weak shock theory to derive a set of approximate equations describing the propagation of a stress pulse in a nonlinear, geometrically dispersive material. The purpose of this investigation is to determine the effect of an interaction between these mechanisms on shock formation and pulse amplitude attenuation. The nonlinearity which is considered is that due to an increase with increasing stress in the material's bulk modulus. Both step wave and rectangular wave boundary pressure histories are considered. By using a coordinate perturbation technique, a first order solution is found. This solution describes the first order effect of dispersion on shock formation and propagation but not the effect of nonlinearity on the solution for the state variables which describe the dispersing wave. (Author)