Nonlinear evolution of initially sine-like wedge acoustic waves

The nonlinear behaviour of antisymmetric wedge acoustic waves propagating along the tip of a sharp elastic wedge is investigated theoretically. The nonlinear evolution equation is derived taking into account geometrical-acoustics approximation for wedge waves. In contrast to the case of surface acoustic waves for which the quadratic nonlinearity dominates the lowest order of nonlinearity in this equation is cubic. For arbitrary propagation distances, the numerical solution taking into account 10 interacting wave harmonics has been carried out. The results show that an initially sine-like antisymmetric wedge wave distorts to a wave of trapezoidal form propagating with changed phase velocity