Viscosity-induced attenuation of longitudinal guided waves in fluid-loaded rods

Abstract

The main goal of this paper is to extend the analytical treatment of longitudinal wave propagation along the fiber direction of multilayered coaxial fibers to immersion in a viscous fluid. The viscous fluid is modeled as a hypothetical isotropic solid having rigidity c44=−iωη, where η denotes the viscosity of the fluid and ω is the angular frequency, i.e., the vorticity mode associated with the viscosity of the fluid is formally described as the shear mode in the hypothetical solid. Among other interesting phenomena, the analytical results revealed the presence of a sharp minimum in the viscosity-induced attenuation of the lowest-order longitudinal mode of thin rods. This minimum occurs at a particular frequency when the otherwise elliptical polarization of the surface vibration becomes linearly polarized in the radial direction. Generally, the experimental results on immersed and fluid-covered wires and fibers showed good agreement with the analytical predictions. In particular, the existence of the theoretically predicted minimum in the attenuation spectrum of the lowest-order longitudinal mode was verified.