Linear and Nonlinear Acoustic Bloch Wave Propagation in Periodic Waveguides

摘要

Propagation of acoustic waves (linear arid nonlinear, time harmonic and pulsed)in a broad class of periodically nonuniform wave guides is investigated theoretically and experimentally. It is shown that the linear, time harmonic solution wave functions are Bloch wave functions. Expressions for parameters characterizing Bloch waves (such as the Bloch wave number) are derived and the features of their band structure determined. Propagation of linear Bloch wave pulses is investigated using the standard dispersion integral. Several new dispersive pulse solutions exhibiting highly unusual behavior (such as acceleration, carrier frequency shifting, and near infinite group velocity) are found. In the case of nonlinear time harmonic Bloch wave propagation, a forward traveling fundamental Bloch wave generates both forward and backward traveling second harmonic Bloch waves, the amplitudes of which oscillate with distance. An effective coefficient of nonlinearity for Bloch waves is identified and found to be, dependent upon frequency, either larger or smaller than that of the host fluid. The dispersion associated with Bloch waves provides an effective means of suppressing the waveform distorting effect of nonlinearity. These findings are verified with measurements made in an air filled, rectangular aluminum duct loaded with a periodic array of scattering side branches.