Vibrations of a solid sphere or shell of Functionally Graded Materials

We have solved the equation of equilibrium for torsional vibrations of a sphere in which the density and rigidity are functions of the radial distance and co-latitude. Making use of the particular forms of heterogeneity the exact frequency equations are derived. The work is motivated by the recent research activity on functionally graded materials (FGM), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications.