The Influence of the Material Properties of an Inhomogeneous Pre-Stressed Hollow Cylinder Containing an Inviscid Fluid on the Dispersion of Quasi-Scholte Waves

Abstract

The influence of the material properties of a pre-stressed cylinder containing a compressible inviscid fluid on the dispersion of axisymmetric quasi-Scholte waves is studied. It is supposed that the inhomogeneous pre-stresses in the cylinder are caused by the fluid pressure acting on the internal face surface of the cylinder before the wave propagation. The motion of the cylinder during wave propagation is described by the so-called three-dimensional linearized equations of the theory of elastic waves in bodies with initial stresses, and the flow of the fluid, by the linearized Euler equations. For solving the corresponding eigenvalue problem, the discrete-analytical solution method is employed and the related dispersion equation is solved numerically. The dispersion curves containing the first roots of the dispersion equation refer to quasi-Scholte waves, which play an important role in helping to understand the solid-fluid dynamic interaction. A study of the influence of the cylinder material properties on the character of these curves is the main novelty of the present paper. The numerical results are presented and discussed on. For this purpose, steel, aluminum, lucite, and soft rubber are selected as cylinder materials, and water is chosen as the fluid. It is established, in particular, according to the numerical results, that an increase in the shear wave velocity in the cylinder material causes an increase in the propagation velocity of quasi-Scholte waves.