Elastic waves in media with bimodular nonlinearity taking into account the effects of reflection from shock fronts

Abstract

A theoretical study of the propagation of longitudinal strong low-frequency and weak high-frequency elastic waves in non-dispersing solids with a bimodular nonlinearity is carried out, taking into account the effects of reflection from the shock fronts of the wave. Expressions are obtained for the waveform, as well as for the amplitudes, frequencies, and phases of the harmonic components of the perturbation reflected from the discontinuities of the nonlinear wave. Numerical and graphical analysis of the obtained solutions is carried out. It is noted that the experimental study of the effects of wave reflection from discontinuities can be used to determine the nonlinear parameter of the bimodular solids. Keywords: longitudinal elastic waves, bimodular nonlinearity, shock waves, reflection from a discontinuity.