Time reversal invariance for a one-dimensional model of contact acoustic nonlinearity

The interaction of a one-dimensional (1D) wave packet with a contact interface characterized by a unilateral contact law is investigated analytically and through a finite difference model. It is shown that this interaction leads to the generation of higher harmonic, sub-harmonic and zero-frequency components in the reflected wave, resulting in a pulse distortion that is attributable to contact acoustic nonlinearity. However, the results also show that the re-emission of a time reversed version of this distorted first reflection results in a healing of the distortions and a perfect recovery of the original pulse shape, thereby demonstrating time reversal invariance for this type of contact acoustic nonlinearity. A step-by-step analysis of the contact interaction provides insights into both the distortion arising from the first interaction and the subsequent healing during the second interaction. These findings suggest that time reversal invariance should also apply more generally for scatterers exhibiting non-dissipative contact acoustic nonlinearity.