On the propagation of transient waves in a viscoelastic Bessel medium

TL;DR

This paper analyzes the propagation of transient waves in a viscoelastic Bessel medium, providing analytic expressions for the response function near the wave-front and at long times, with applications to fluid-filled elastic tubes.

Contribution

It introduces a revisited Buchen-Mainardi algorithm and applies Tauberian theorems to derive new analytic expressions for wave response functions in viscoelastic Bessel media.

Findings

Analytic response function near wave-front

Long-time behavior of the response function

Application to fluid-filled elastic tubes

Abstract

In this paper we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave-front. To do so, we take profit of a revisited version of the so called Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the long time behavior of the response function of the material. This result is obtained by means of the Tauberian theorems for the Laplace transform. Finally, we relate the obtained results to a peculiar model for fluid-filled elastic tubes.