Multi-Mode Interactions in a Nonlinear Structural-Acoustic Cylindrical Waveguide

Nonlinear structural acoustic wave propagation inside an infinite flexible circular cylindrical waveguide is investigated. The acoustic fluid inside the waveguide is taken to be inviscid with zero mean flow and is modelled using the NTT equation. For the cylindrical waveguide, Donnell's nonlinear shell theory is used, that takes into account only the radial displacement. At the fluid structure interface, the nonlinear boundary condition is used. A monochromatic wave composed of multiple cross-sectional modes is considered to be propagating in the system. The amplitudes of these modes are known at the first order. The asymptotic method is used to resolve the system into a set of linear and nonlinear equations. This results in a dispersion equation at the first order from which the coupled wavenumbers are found using the regular perturbation technique. At second order, interaction of multiple non-orthogonal modes is sought. The nonlinear interaction of the different modes in the system gives rise to non-resonant, nearly resonant and weakly resonant phenomena. Different criteria that govern the occurrence of these phenomena and the effect of the non-zero admittance of the boundary on these phenomena are discussed.