Abstract
This paper deals with the study of the influence of the inhomogeneous prestresses (initial stresses) in a hollow sphere made of a functionally graded material (FGM) filled with an inviscid compressible fluid on the natural vibration of this sphere. For this study, the three-dimensional exact field equations of the linearized theory of elastic waves in bodies with initial stresses are employed. The motion of the fluid is described by the linearized Navier–Stokes equations for inviscid barotropic compressible fluids. The discrete-analytical solution method proposed by the first author is employed for the solution to the corresponding mathematical problems. Numerical results related to the natural vibration of the mentioned sphere and the influence of the problem parameters on these frequencies are presented and discussed. In particular, it is established that the existence of the fluid leads to a decrease in the natural vibration frequencies. However, a change in the FGM properties of the sphere’s material can lead to an increase in these frequencies.