Wave Propagation in Viscous, Compressible Liquids Confined in Elastic Tubes

Abstract

The problem of steady-state, small amplitude, periodic wave propagation in a viscous, compressible liquid contained in an infinitely long, elastic tube is solved for the complex propagation constants of the two lowest modes of motion. One mode has a speed of propagation and decay constant characteristic of acoustic waves propagating in a liquid; the other mode corresponds to acoustic waves propagating in an elastic tube. The behavior of these two modes is investigated as a function of frequency, viscosity, and tube rigidity. A third mode of motion corresponding to edge loads on the tube is also investigated. This mode, unlike the other two modes, is characterized by a cut-off frequency above which the propagation distance is infinite and below which it is finite.