Time and frequency domain finite element models for axial wave analysis in hyperelastic rods

The propagation of axial waves in hyperelastic rods is studied using both time and frequency domain Finite Element models. The nonlinearity is introduced using the Murnaghan strain energy function and the equations governing the dynamics of the rod are derived assuming linear kinematics. In the time domain, the standard Galerkin Finite Element Method, Spectral Element Method and Taylor-Galerkin Finite Element Method are considered. A frequency domain formulation based on the Fourier Spectral Method is also developed. It is found that the time domain Spectral Element Method provides the most efficient numerical tool for the problem considered