Nonlinear elastic shear waves

The dynamics of one-dimensional two-component shear motion in elastic-isotropic homogeneous media is studied assuming isentropic finite displacements. Wave breaking of initially continuous waves on the infinite interval is discussed for weakly nonlinear waves. The problem of a resonating finite-thickness shear layer in primary resonance for single-component motion exhibits jump discontinuities of particle velocity, shear strain and stress in a finite frequency band near primary resonance, Under certain conditions two-component motion can be reduced to a quasi-single-component motion.