Axisymmetric response of a fluid-filled spherical shell in free vibrations

Abstract

this paper is concerned with a theoretical model of the head. Neuroanatomical and analytical considerations lead to a fluid-filled spherical shell as a first-generation model. The shell is considered thin, elastic, homogeneous, and isotropic. The shell equations include both membrane and bending effects in axisymmetric torsionless motion. The motion of the fluid is governed by the wave equation. A free vibration analysis of the fluid-shell system is obtained in the form of a frequency equation. Compared with a fluid-filled rigid shell and an elastic shell in vacuo, the frequency spectrum of the fluid-shell system is almost a `superposition' of the spectra of the two special cases. The exceptions appear as slight distortions in the neighborhood of the `curve' intersections.