Oscillating Nonlinear Acoustic Waves in a Mooney-Rivlin Rod

Harmonic wave excitation in a semi-infinite incompressible hyperelastic 1D rod with the Mooney-Rivlin equation of state reveals the formation and propagation of the shock wave fronts arising between faster and slower moving parts of the initially harmonic wave. The observed shock wave fronts result in the collapse of the slower moving parts being absorbed by the faster parts; hence, to the attenuation of the kinetic and the elastic strain energy with the corresponding heat generation. Both geometrically and physically nonlinear equations of motion are solved by the explicit Lax-Wendroff numerical tine-integration scheme combined with the finite element approach for spatial discretization.

Automated summary

Exciting a harmonic wave in a one-dimensional rod with the Mooney-Rivlin equation of state reveals the formation and propagation of shock wave fronts between faster and slower moving parts. The observed shock wave fronts result in the absorbed collapse of slower moving parts by faster parts, leading to attenuation of kinetic and elastic strain energy.