Nonlinear axisymmetric waves in compressible hyperelastic rods : long finite amplitude waves

This paper investigates nonlinear axisymmetric waves in compressible hyperelastic circular cylindrical rods. We consider first a compressible Mooney-Rivlin material to obtain exact governing equations. To further study the problem, we introduce the notion of long finite amplitude waves and derive the corresponding simplified model equations, which gives the framework for studying problems like wave-interactions arising through collision or reflection. The asymptotically valid far-field equation is consequently deduced from the simplified model equations. Then, using a strained-coordinate method, we obtain the second-order solitary wave solution. The result is not only of interest itself, but also provides a suitable initial condition for wave interaction problems. Finally, the results for a general hyperelastic rod are presented. © 1993 Springer-Verlag.