Finite amplitude standing waves in resonators terminated by a general impedance

Abstract

A general inhomogeneous Burgers equation describing finite-amplitude standing waves in resonators terminated by a general impedance is derived. This model equation can be used for modeling of nonlinear acoustic processes connected with some methods for enhancement of Q-factor of acoustic resonators. One of them is the method based on using a second-harmonics absorber. For better understanding of this method, it is convenient to know at least an approximate analytical solution of the model equation. This work presents some approximate solutions, which improve and extend the solutions that have been published previously. The solutions are compared with results obtained by numerical integration of the corresponding equations.