Longitudinal Wave Propagation in an Elastic Cylinder Embedded in a Viscoelastic Fluid

Abstract

A novel analytical investigation of longitudinal wave propagation in an elastic cylinder embedded in a viscoelastic fluid is proposed. The Maxwell model is used to describe the viscoelastic fluid behavior. With appropriate boundary conditions, a complex dispersion equation of longitudinal waves has been established. The aim of this paper is to study the effect of the fluid rheological properties on the longitudinal wave characteristics (attenuation and velocity). It is shown that the attenuation is the sum of a viscous and nonviscous component. The viscosity-induced attenuation is predominant at low frequencies. On the other hand, the effect of the liquid amount and elastic cylinder radius on the attenuation and velocity are studied. A critical normalized liquid thickness is highlighted. Beyond this critical value, the influence of the outer boundary condition can be neglected. At last, among other interesting phenomena, it is highlighted that if the Deborah number increases, the attenuation decreases. This variation characterizes a stiffening of the viscoelastic medium. In addition, the obtained results show that the viscosity measurement should be performed at low frequencies using a small elastic cylinder radius. Accordingly, these investigations are novel and can be applied in geophysics, the food industry, medicine, nondestructive testing of materials, and the design and development of fluid sensors.