ON THE NATURAL OSCILLATION OF AN INHOMOGENEOUSLY PRE-STRESSED MULTILAYERED HOLLOW SPHERE FILLED WITH A COMPRESSIBLE FLUID

Abstract

The paper studies natural vibrations of the inhomogeneously pre-stressed multilayered hollow sphere containing the compressible barotropic inviscid fluid. The motion of the sphere is described with the linearized equations and relations of the three-dimensional linearized theory of elastic waves in initially stressed bodies, however the fluid flow is described through the linearized Navier-Stokes equations for inviscid compressible fluids. It is assumed that in the initial state the sphere is loaded by the uniformly distributed radial compressional forces acting on the face surfaces and then this sphere starts to vibrate. It is required to determine how the inhomogeneous initial stresses in the sphere caused with these forces act on the natural vibration frequencies this question is studied in the paper and corresponding numerical results are presented and discussed.