Nonlinear acoustic propagation within two-dimensional rectangular duct

Nonlinear acoustic waves that propagate within a two-dimensional rectangular duct are fully studied by using partial wave and second-order perturbation theory. With second-harmonic boundary condition and initial exciting condition the second-harmonic analytical expressions, which have clearly physical pictures and are applicable to quantitative computation, are obtained. The results show that the interaction between two arbitrary fundamental modes does not possess second-order nonlinearity,the second harmonics caused by a steady exciting source with arbitrary vibration amplitude distribution equal the sum of second harmonics associated with each fundamental mode, and the spatial distribution of second-harmonic field within the duct is of symmetry.