A comparative analysis of axisymmetric vibrations of conical and cylindrical fluid-filled elastic shells

Abstract

This paper presents the comparison of low- frequency vibrations in liquid-filled cylindrical and truncated conical elastic shells. The liquid is supposed to be an ideal and incompressible one and its flow is irrotational. To evaluate a velocity potential the system of singular boundary integral equations has been obtained. The boundary element method is used for their numerical simulation. The vibration modes of the shells with liquids are determined as linear combinations of their natural vibration modes without liquids. Sloshing frequencies and modes of fluid-filled cylindrical and truncated conical shells are estimated. The solution of the hydro-elasticity problem is obtained using a combination of boundary and finite element methods. Shells with both rigid and elastic bottoms are considered. The illustrative examples are provided to demonstrate the accuracy and efficiency of the method.