Linear and nonlinear acoustic Bloch wave propagation in periodic waveguides

The propagation of acoustic waves in a class of periodically nonuniform waveguides is investigated both theoretically and experimentally. The waveguides under study are rigid, isothermal ducts of arbitrary cross-section that are filled with a thermoviscous fluid. The ducts may have arbitrary periodic boundary deformations and may contain a periodic array of scattering inclusions. It is shown that the solution functions are Bloch wave functions, and the properties of the Bloch waves are investigated theoretically and experimentally. The experiments are carried out in a rigid, air-filled rectangular duct that is loaded with a periodic array of rigidly terminated side branches.;In the investigation of linear, time-harmonic Bloch waves, many features of the band structure found in both the Bloch wave dispersion relation and the Bloch wave functions are derived analytically and verified in measurements. In the problem of linear Bloch wave pulse propagation the standard dispersion integral may be used. It is found that the validity of the solutions of the dispersion integral and hence the concept of group velocity are distance dependent. Both the Bloch wave group velocity and several new dispersive pulse solutions are derived and verified with measurements. A new approach to the problem of nonlinear, time-harmonic Bloch wave propagation is used and it is found that a progressive fundamental Bloch wave gives rise both forward and backward travelling second harmonic Bloch waves, each of which oscillates in amplitude as it propagates. According to both theory and measurement the Bloch wave dispersion is able to disrupt the cumulative waveform distortion that is characteristic of nonlinear wave propagation.