Spectral boundary value problem for coaxial shells of revolution

Abstract

The main objective of this study is to develop an efficient numerical approach using boundary elements to estimate natural frequencies of liquid vibrations in composite tanks. The spectral boundary value problem for liquid tanks is to find the natural frequencies and modes of free surface sloshing. The calculation of hydrodynamic forces on the walls of tanks with liquid is an important problem for ensuring the strength and stability of movement of industrial tanks and vessels. The vibrations of shell structures, including cylindrical and conical shells connected by rings, are analyzed. The area between the shells is filled with an ideal incompressible fluid. Numerical modeling uses the superposition method in combination with the boundary element method. A numerical solution of the spectral boundary value problem regarding fluid vibrations in rigid shell structures has been carried out. Frequencies and modes are determined by solving systems of singular integral equations. For the shells of revolution, these systems are simplified to one-dimensional equations, where the integrals are calculated along curves and line segments. Efficient numerical procedures are used to calculate one-dimensional integrals with logarithmic and Cauchy features. Test calculations confirm the high accuracy and efficiency of the proposed method. The importance and practical significance of the method lies in the ability to study fluid fluctuations in real compound fuel tanks of launch vehicles under different load conditions. This makes it possible to study the movement of liquid in fuel tanks and reservoirs under the action of external loads. The elaborated method will be used in computer modeling the dynamic behavior of liquid tanks and the stability study of liquid movement in compound fuel tanks of launch vehicles. In the future, it is planned to study the vibrations of elastic coaxial shells with liquid, using various composite materials.