Distortion and Dispersion of Nonlinear Waves in a Rectangular Duct Due to a Bifrequency Excitation

摘要

The nonlinear interactions and propagation of the two-dimensional acoustic waves that occurs within a hard-walled rectangular duct as a result of a bifrequency periodic excitation are investigated. The analysis develops a perturbation solution that satisfies a nonlinear wave equation for the velocity potential, as well as the boundary conditions. Uniformly valid expression for the acoustic pressure is then derived with the aid of a set of coordinate straining transformations. The response is found to be formed from the linear superposition of two pairs of oblique planar waves that mutually interact collinearly and noncollinearly, generating sum and difference harmonics. Both dispersive and nondispersive interactions are incorporated in the analysis. Asymptotic behaviour for the pressure signal in the high frequency limits is also derived. Theoretical predictions for sum and difference frequency waves compare favourably with previous experimental observations. Typical spatial profiles for harmonics and for sum and difference frequency signals as well as temporal responses are discussed.