SLOSHING IN LIQUID-FILLED CYLINDRICAL-CONICAL SHELLS

Abstract

The issue of fluid oscillations poses a challenge for various industrial sectors, including aerospace, maritime, civil mechanical engineering, nuclear engineering, and is a complex task for physicists and mathematicians as well. Fluid oscillations can lead to catastrophic damage of reservoirs used for storing water and oil. The design of each new rocket launcher, new vehicles necessitate producing new fuel tanks, and reservoirs with intricate shapes. The main aim of this research is to develop a reliable numerical approach by coupling finite and boundary element methods for evaluating the natural frequencies of vibrations in compound liquid-filled reservoirs. The study specifically focuses on analysing the inherent vibrations of shell structures, comprising interconnected cylindrical and conical shells with rings. The region between these shells is filled with an ideal, incompressible fluid. The numerical simulations utilize mode superposition methods, along with boundary element techniques. Numerical solution is presented for the spectral boundary problem of liquid vibrations in rigid shell structures. The frequencies and modes are determined by solving singular integral equations. In situations involving shells of revolution, these systems are simplified to one-dimensional forms, where integrals are computed along curves and line segments. Efficient numerical procedures are employed to compute one-dimensional integrals with logarithmic and Cauchy-type singularities. The frequencies and modes of liquid-filled shells are determined through basis functions obtained by solving systems of singular integral equations. Test calculations validate the high precision and efficiency of the proposed method. The significance and practical utility of these findings lie in the capability to investigate the vibrations of different fuel tanks under diverse flight conditions and different loads. The additional objective is to investigate the potential utilization of nanomaterials for improving the mechanical properties of the system under consideration. This could involve developing computational models and carrying out experiments to evaluate alterations in strength, stability, and other mechanical attributes.