Time-harmonic acoustic Bloch wave propagation in periodic waveguides. Part III. Nonlinear effects

Abstract

The effect of nonlinearity in the propagation of time-harmonic acoustic Bloch waves in periodic waveguides is investigated theoretically and experimentally. It is found that a forward traveling fundamental Bloch wave generates both forward and backward traveling second harmonic Bloch waves, the amplitudes of which oscillate with distance. A local second harmonic field is also generated. An effective coefficient of nonlinearity for Bloch waves is identified and found to be strongly frequency dependent. Measurements of the second harmonic field amplitude show good agreement with the theory; both the oscillations in amplitude and the change in effective nonlinearity are clearly evident.