Growth/decay of transverse acceleration waves in nonlinear elastic media

A study of transverse acceleration wave phenomena in the context of nonlinear elasticity is carried out. Using singular surface theory, exact amplitude expressions for acceleration waves arising from a sinusoidal boundary condition (BC) are obtained and their temporal evolution and propagation speeds determined. It is shown that amplitude blow up is possible only if the medium ahead is in motion, otherwise a constant amplitude wave occurs. Analytical results are illustrated numerically using simple computational methods/tools. Lastly, erroneous results that were reported in a recently published related study are noted and/or corrected.