Frequency spectrum of the bispherical hollow system: the case of the nonuniform thickness human skull

In the present work we discuss the role of the thickness nonuniformities of the human dry skull on its frequency spectrum. The mathematical modelling is based on the three-dimensional theory of elasticity, the approximation of the skull by an isotropic material occupying the region bounded by two non-concentric spheres and the introduction of the bispherical coordinates system. The mathematical analysis is based on the construction of the Navier eigenfunctions of the problem and the representation of the solution in terms of them. The frequency equation is solved numerically and the role of various parameters entering the problem is extensively discussed.