Analysis of Nonlinear Propagation and Interactions of Higher Order Modes in a Circular Waveguide

This paper treats the nonlinear interactions and propagation of two primary waves in higher order modes of a circular duct each at arbitrary different frequency and finite amplitude. The analysis develops a perturbation expression for the velocity potential that satisfies the nonlinear wave equation as well as the boundary conditions. The lowest modes resulting from the nonlinear interaction of the two primary signals are also considered in the analysis. Both dispersive and nodispersive interactions are incorporated. The renormalization method is used to annihilate secular terms in the pressure expression. The resulting pressure signal exhibits harmonics and intermodulation distortion. Typical spatial profiles for sum and difference frequency signals and for higher harmonics as well as temporal responses are discussed in an example.