Investigation of the ultrasonic wave propagation along the boundary of two half-spaces: the elastic one of a solid and the viscoelastic one of a liquid

Abstract

By considering the problem of the travelling wave propagation along two half-spaces: the ideally elastic (solid) and the viscoelastic (liquid), with bulk viscosity, as a result of solving the wave equations and taking into account the boundary conditions, the complex characteristic equation was obtained. The characteristic equation was solved numerically for a frequency of 2.5 MHz for two different viscoelastic bodies, for biological tissue and the acetic acid CH3COOH, bordering on an elastic medium, steel. The wave velocity was sought close to the longitudinal wave velocity characteristic of the given media. It was shown that the wave could propagate at a velocity only slightly less than that of longitudinal waves, but with attenuation being slightly larger than that in an unbounded medium. It follows from the representations obtained of the displacement potentials that, apart from the wave propagation along the boundary of the media, there is also wave propagation towards the liquid damping medium. This phenomenon did not occur in considering the ideal liquid medium. In both cases, the distributions of the normal and tangential stresses and of the partial displacements were obtained. The wave decays exponentially as the distance from the boundary increases (on both sides). The distributions are close in character to those of stresses and displacements obtained in the previous paper of the author, where a similar, but a lossless, model was considered. The acoustic impedance in a viscoelastic medium was also found for the wave type propagating along and across the boundary.