Nonlinear scattering of acoustic waves by vibrating obstacles

The problem of scattering of an acoustic wave (at angular frequency ω) by an obstacle whose surface vibrates harmonically (at angular frequency Ω) was studied both theoretically and experimentally. The theoretical approach involved solving the nonlinear wave equation, subject to appropriate boundary conditions, by use of a perturbation expansion of the fields and a Green's function method. This problem was previously studied theoretically by D. Censor [(J. Sound Vib. 25, 101–110 (1972)], who used the linear wave equation together with nonlinear boundary conditions to obtain his solution. In addition to ordinary rigid‐body scattering, Censor predicted nongrowing waves at the sum and difference frequencies ω± = ω ± Ω. The solution to the nonlinear wave equation also yields scattered waves at frequencies ω±. However, the amplitudes of these waves tend to grow with increasing distance from the scatterer's surface and after a very small distance dominate those predicted by Censor. Preliminary experimental resu...