THE INFLUENCE OF THE INHOMOGENEOUS INITIAL STRESSES IN THE HOLLOW CYLINDER CONTAINING AN INVISCID FLUID ON THE DISPERSION OF THE QUASI-SCHOLTE WAVES PROPAGATING IN THIS CYLINDER

Abstract

The paper deals with the study of the influence of the axisymmetric inhomogeneous initial stresses in the hollow cylinder containing an inviscid compressible barotropic fluid on the dispersion of the axisymmetric quasi-Scholte wave propagating in this hydro -elastic system. It is assumed that the mentioned inhomogeneous initial stresses appear as a result of the fluid pressure on the internal surface of the cylinder. The equation of motion of the cylinder is described by the so-called three-dimensional linearized equations and relations of the theory of waves propagating in elastic bodies with initial stresses. The flow of the fluid is described by the corresponding linearized Euler equations. For the solution to the formulated eigenvalue problem, the discrete - analytical method is used. The corresponding dispersion equation is obtained and solved numerically. The dispersion curves containing minimum roots of this equation relate to the quasi-Scholte waves. Numerical results on the above mentioned influence on these dispersion curves are presented and discussed. In particular, it is established that the inhomogeneous initial stresses not only in the quantitative sense but also in the qualitative sense can change the dispersion curves of the quasi-Scholte waves not only in the quantitative but also in the qualitative sense.