COMPUTER MODELING VIBRATIONS OF ELASTIC COXIAL LIQUID-FILLED SHELLS OF REVOLUTION CONSIDERING SLOSHING
DOI:
https://doi.org/10.32782/mathematical-modelling/2024-7-1-5Keywords:
coaxial elastic shells, boundary and finite element methods, sloshingAbstract
The primary aim of this study is to create an effective numerical approach by combining finite and boundary element methods for assessing the natural frequencies of vibrations in compound liquid-filled reservoirs. The research focuses on analysing the natural vibrations of elastic structures, which consist of interconnected cylindrical and conical shells connected by rings. The space between these shells is occupied by an ideal, incompressible fluid. Numerical simulations employ mode superposition methods, as well as boundary and finite element methods. The key advantage of proposed approach is its capability to investigate both free and forced vibrations in structures composed of empty and liquid-filled shells, all within the unified computer technology framework. The developed method allows for the exploration of elastic shell vibrations with and without considering the free surface sloshing. Additionally, a separate solution is provided for the spectral boundary problem related to liquid vibrations in rigid shells. The frequencies and modes of liquid-filled shells are determined through basis functions evaluated by solving singular integral equations. For shells of revolution, these systems are reduced to one-dimensional ones, where integrals are computed along curves and segments of lines. Efficient numerical procedures are employed for the computation of one-dimensional integrals with logarithmic and Cauchy-type singularities. Test calculations affirm the high precision and efficiency of the proposed method. The significance and practical usage of these findings lie in the ability to investigate the vibrations of complex-shaped fuel tanks under various flight conditions.
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