Propagation of nonlinear acoustic plane waves in an elasticgas-filled tube

摘要

This paper deals with modeling of nonlinear plane acoustic waves propagating through an elastictube filled with thermoviscous gas. A description of the interactions between gas and an elastic tubewall is carried out by the continuity equation of a wall velocity. Simplification on the basis of thelocal reaction assumption enables to model an acoustic treatment on the tube wall by using a wallimpedance. Because there are considerable losses due to wall friction, the influences of the acousticboundary layer were also considered. Using certain assumptions a special form of the Burgersequation was derived which enables to describe the propagation of nonlinear waves in the elastictube. This model equation takes into account nonlinear, dissipative, and dispersion effects whichcompete each other. Characteristic lengths of the supposed effects and numerical results with respectto the source frequency were used for a qualitative analysis of the model equation. Applicability ofthis model equation was demonstrated by series of measurements. By application of the long-waveapproximation the Korteweg–de Vries–Burgers and Kuramoto–Sivashinsky equations were derivedfrom the modified Burgers equation.