Nonlinear interactions in elastic resonators

Abstract

This work is dedicated to nonlinear interactions in elastic resonators. It is supposed that a resonator wall yields locally to the inner pressure. The elastic wall of the resonator induces strong dispersion and dissipation of acoustic energy. The dispersion can significantly influence studied nonlinear interactions which are ineffective because the synchronous conditions are not satisfied and hence a coherence length is too short. In the frame of this work conditions for generation of subharmonics are studied on the basis of topological and numerical analyze. For this reason the method of local stability is applied. For description of nonlinear standing wave is derived modified inhomogeneous Burgers equation and the inhomogeneous Korteweg–de Vries–Burgers equation. These equations take into account thermo-viscous losses of supposed fluids, boundary layer losses, wall losses and dispersion effects caused by both the resonator wall and the acoustic boundary layer. Number of numerical solutions of these model equations is shown and unsteady solitary waves are investigated.