Natural Vibration of a Multilayered Hollow Sphere Filled with a Compressible Fluid

Abstract

The paper deals with the study of the natural vibration of a multilayered sphere contained compressible barotropic inviscid fluid. This study is made within the scope of the 3D exact equations of elastodynamics in the framework of the piecewise homogeneous body model and the motion of the fluid is described within the scope of the linearized Euler equations. It is assumed that the perfect contact conditions satisfy between the layers and the spherical mode of the vibration is considered. The solution of the corresponding equations is found analytically, however concrete numerical results are determined numerically with the use of the PC. These numerical results are presented for the three-layered case and it is established the character of the influence of the fluid on the values of the natural frequencies of the mentioned three-layered sphere.