Fluid-filled Shell Structures and Their Applications in Biomechanics

Structures in the form of thin-walled shells containing liquid are extremely common in various areas of modern technology, as oil storage facilities, water towers, rocket launch tanks and manifolds for storing chemicals. Failure of such structures is fraught with a wide range of negative consequences. The problems of fluid-structure interaction of structural elements partially filled with liquids, are in the focus of many research since the 60s of last century. The growing interest in biological materials and medicine has also accentuated the importance of studying the dynamical behavior of shell-like structures with fluids. In this paper, effective numerical methods to estimate the frequencies and modes of elastic shell vibrations coupled with liquid sloshing are elaborated. The approach is relied on using the mode superposition method as well as boundary and finite element methods. The problem under consideration consists of three stages. At first, it is necessary to obtain the frequencies and modes of empty elastic shell, at second stage the sloshing modes and frequencies are received. At third stage and modes and frequencies of elastic shell vibrations coupled with liquid sloshing are obtained. Own modes and frequencies of spherical and conical steel shells are estimated, as well as modes and frequencies of eardrum interacting with liquids. The influence of impact loads on the tympanic membrane is analyzed.