粘弾性管内の気体中の波動伝ぱ

Abstract

In fluidic and pneumatic control systems, vinyl hoses and tubes made of rubber-like materiah have come to be widely used as transmission conduits. Therefore, any analysis of the dynamics of those systems must consider the effects of the transmission tubing. So far, most of the studies conducted on gases have been limited to rigid tubes. Those studies limited to a certain extent, are not expected to give an adequate description of the system dynamics. Therefore, in this research the propagation of small amplitude harmonic pressure waves through gas contained in an infinitely long, thin-walled, viscoelastic tube is analyzed when the effects of the gas viscosity and heat transfer are included while the tube is assumed to move in the radial and axial directions. Axially symmetric wave solutions are obtained for the linearized equations governing the motion of the fluid and the tube. The solution leads to a complicated equation, the so-called frequency equation, relating the propagation constant with the system parameters. Furthermore, this equation is simplified and two fundamental modes of propagation are obtained. One mode of motion has a phase velocity similar to the speed of sound in the tube; whereas, the other one has a phase velocity similar to the speed of sound in the gas. In this analysis the latter mode, which is defined as the first mode, is mainly discussed. The effect of the viscoelastic parameters of the tube materials on the dispersion of waves through the fluid is made clear for different viscoelastic models.