Nonlinear Acoustic Waves in a Slender Wedge

Abstract

This contribution is concerned with the nonlinear propagation of acoustic waves that have displacement field localized at the tip of an elastic wedge. The energy associated with a wedge wave is confined in two dimensions. This means that high energy densities can be reached and certain nonlinear effects should be more pronounced for wedge acoustic waves than for bulk or surface waves. There are two important features which distinguish wedge acoustic waves from wave propagation in one-dimensional optical waveguides and attract particular attention. Firstly, wedge waves are very slow. Their velocity has to be smaller than that of Rayleigh waves, and for slender wedges, it is proportional to the wedge angle. Secondly, an ideal elastic wedge is a nondispersive system since the geometry does not involve any length scale and the parameters entering the equations of elasticity theory are independent of frequency. This has important implications on nonlinear wave propagation in this system since it leads to resonant interaction between different harmonics. While the existence of linear wedge acoustic waves has been known since a long time, only few investigations have yet been carried out on the influence of nonlinearity on these waves^{1, 2}.