MODELING OF LIQUID SLOSHING DYNAMICS IN TANKS WITH A FLOATING PLATE ROOF WITH A FREE EDGE

Abstract

The aim of the study is to develop numerical methods for investigating the dynamics and stability of liquid motion in tanks in the presence of a floating cover. The study of the dynamics and stability of liquid motion in tanks, taking into account sloshing phenomena, is of significant theoretical and practical importance for a wide range of industries, including aerospace engineering, marine transport, and ground-based liquid storage systems (fuels, oil, technological and chemical media). The intensity of sloshing can be significantly reduced through the use of damping devices such as baffles, annular dampers, and elastic free-surface covers. At the same time, experimental investigations of damper efficiency are complex, costly, and associated with increased safety requirements, especially when dealing with toxic or explosive media. In this regard, the development of adequate mathematical models and efficient numerical methods for the computer simulation of liquid sloshing processes in tanks with free-surface covers is becoming increasingly important. In this work, the method of separation of variables and the method of prescribed normal modes are employed. Two auxiliary problems are solved: the eigenvalue problem for the cover and the problem of oscillations of an ideal incompressible liquid in a rigid cylindrical tank without a cover. The floating cover is modeled as a circular plate with a free edge within the framework of the Kirchhoff–Love plate theory. To solve the coupled boundary-value problem, two sets of basis functions obtained from the solutions of the auxiliary problems are used. Particular attention is paid to the fundamental sloshing mode corresponding to the inclination of the free surface, which is the most critical in terms of resonant interaction with the structure. The natural frequencies and mode shapes of the liquid in the presence of an elastic cover are determined. A complete coupled model of hydroelastic interaction of the “liquid–cover” system is developed. It is shown that the presence of a floating cover significantly alters the spectral characteristics of the system: the natural frequencies decrease compared to the case of a free surface due to the added-mass effect and the influence of gravity. It is established that the spatial mode shapes of the liquid are governed by the vibration modes of the cover.