SPECTRAL ANALYSIS OF LIQUID OSCILLATIONS IN A RESERVOIR DEPENDING ON THE PARTITION POSITION

Abstract

The purpose of this study is to develop an effective numerical method for assessing the influence of baffles that damp liquid oscillations in rigid shells of revolution under the action of intensive vertical and horizontal loads. It is assumed that the liquid filling the shell is ideal, incompressible, and exhibits irrotational motion. Under these assumptions, its dynamics are described by the velocity potential, which satisfies Laplace’s equation. The shell is subjected to external harmonic loading, the frequency of which may approach the natural frequencies of the liquid oscillations, leading to resonance and, consequently, an unbounded increase in the amplitude of free-surface oscillations. To prevent this phenomenon, horizontal baffles are introduced into the structure to reduce sloshing intensity and provide effective damping of wave energy. The installation of baffles alters the spectrum of the liquid’s natural frequencies, allowing the system to be tuned away from undesirable resonant modes. This makes it possible to optimize the parameters of tanks and reservoirs used in aerospace, energy, and transportation engineering. For numerical analysis, the subdomain method, also known as the boundary superelement method, is applied. The computational domain is divided into several subdomains, each with its own boundary conditions. Within each subdomain, the velocity potential satisfies Laplace’s equation; at the rigid boundaries, non-penetration conditions are imposed, while on the free surface, both kinematic and dynamic conditions are applied. Compatibility conditions for the potential and its normal derivative are enforced at the interfaces between subdomains. To determine the unknown potentials, the third Green’s formula is used, which makes it possible to reduce the original boundary-value problem to a system of singular integral equations, solved by the boundary element method. The numerical results demonstrate that the oscillations of the liquid inside the reservoir can be effectively controlled by a rational choice of the number, shape, and arrangement of the baffles. It is shown that optimal design of damping elements can significantly reduce the amplitude of oscillations even under high-frequency loading, thereby improving the stability and reliability of structures containing liquid.