Non-linear propagation of complex sound fields in rectangular ducts. I - The self-excitation phenomenon

Nonlinear acoustic interactions at the second order (so-called weak interactions) of the perturbation scheme have been recognized for a long time. This paper examines the possibility of stronger interactions at the first order which are found in rigid rectangular ducts and to a lesser degree in slightly soft rectangular ducts. The strong interactions occur if any two modes have identical phase speeds, the case of multimode and multifrequency input for example. An important consequence of the strong interaction is the self-generation of subharmonics. Even a small amount of subharmonic can, given the right phase conditions, grow through a strong interaction with a higher harmonic.