Free vibration of a fluid-filled hollow sphere of a functionally graded material with spherical isotropy

An exact, three-dimensional method is developed in the paper to analyze the free vibration of a spherically isotropic hollow sphere made of a functionally graded material and filled with a compressible fluid medium. The material is assumed to be inhomogeneous along the radial direction. By introducing three displacement functions and employing the function expansion method, the governing equations are simplified to an uncoupled second-order ordinary differential equation, and a coupled system of two such equations. Solutions to these equations are given when the elastic constants and the mass density are power functions of the radial direction. To investigate the effect of material gradient on the natural frequencies, numerical calculations are finally performed. (C) 1999 Acoustical Society of America. [S0001-4966(99)03010-6]'.