Acoustic conductance of an anisotropic shell submerged in a liquid 2. A parametric analysis of frequency characteristics

Based on a model of radial vibrations of a hollow sphere caused by a harmonic source located on its inner radius, the frequency spectrum of a spherical shell, made of a transversely isotropic material and contacting a liquid medium, under changes in its thickness and in material properties in the circumferential and radial directions is investigated. The eigenvalues of the boundary-value problem are considered in an arbitrary range of physical parameters of the model by using functions of complex variable and the theory of residues. The solution of the transcendental equation for eigenvalues (frequencies), which is obtained as a combination of modified Bessel functions, is analyzed in the cases of light and heavy incompressible liquids (or vacuum). The values of eigenfrequencies are presented and analyzed with respect to depth of the region of disturbance (or thickness of the shell) and material properties. The approximate values of thickness of the anisotropic sphere corresponding to a steep rise in the natural frequencies of radial vibrations are revealed. The wave model of a thick-wall sphere is transformed into the vibration analog of a thin-wall shell.