Coupled Frequencies of a Fluid in a Circular Cylindrical Tank with a Membrane on its Upper End and Permanent Axial Loading

Abstract

A compressible and inviscid fluid fills a closed circular cylindrical tank. The tank bottom and its side wall are rigid. The whole upper end is covered with a flexible weightless clamped membrane. The tank is under conditions of a specified permanent axial loading. The fluid—structure interaction system obtained is assumed to have small vibrations. Such tanks are used in the aviation industry, so that study of the dynamic behaviour of fluid in tanks is important for their design and reliability assessment. The problem under consideration concerns the determination of the coupled vibrations in this fluid—structure interaction system. The frequency equation is obtained using the Bubnov—Galerkin method. Numerical examples show that with increased axial loading the corresponding first dimensionless frequency of the fluid—structure interaction system also increases.