Simulation of hydroelastic vibrations of structure elements using finite and boundary element methods
Abstract
For studying the vibration frequencies and modes of structural elements that operate in interaction with a liquid, an approach has been proposed. The approach is based on coupled usage of finite and boundary element methods. For description the motion of both structural elements and the fluid, the method deals with basic relations of the continuous medium mechanics. In the study of structural elements, the linear relations between stresses and strains have been accepted, i.e. elastic elements have been considered. The relations between the components of stress tensors and strain rates are used to describe the fluid motion. The fluid is considered to be ideal and incompressible. The Laplace equations have been obtained considering the fluid pressure on the wetted surfaces of structural elements. The corresponding boundary conditions have been formulated for one-sided and two-sided contact of a structural element with a liquid. Integral equations for pressure determination have been received. In the case of a two-sided contact of a structural element with a liquid, a hypersingular integral equation has been obtained. If the contact with the liquid is one-sided, then the indicated singular integral equations have logarithmic singularities and Cauchy-type singularities. In the presence of axial symmetry of the structure, these hypersingular integral equations are being reduced to one-dimensional ones. A round elastic plate under different fastening conditions has been considered. Modes of free oscillations of this structural element have been received; these ones serve as basic functions in the study of plate oscillations taking into account the added liquid masses. The finite element method was used. A one-dimensional hypersingular integral equation is implemented to find the fluid pressure on the plate. The frequencies and oscillation forms of the plate have been obtained with considering the attached masses of the liquid. Accuracy and reliability of the proposed method have been ascertained.
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Karaiev A., Strelnikova E. Axisymmetric polyharmonic spline approximation in the dual reciprocity method ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, pp. e201800339. DOI: 10.1002/zamm.201800339 URL: https://scholar.google.com/citations?user=5d87MvoAAAAJ&hl=de
Karaiev A. Singular integrals in axisymmetric problems of elastostatics / A. Karaiev, E. Strelnikova //International Journal of Modeling, Simulation, and Scientific Computing. 2020 Vol. 11, № 1, 2050003 . DOI: 10.1142/S1793962320500038. URL: https://www.worldscientific.com/doi/10.1142/S1793962320500038
V. Gnitko, K. Degtyariov, A. Karaiev, and E. Strelnikova, “Multi-domain boundary element method for axisymmetric problems in potential theory and linear isotropic elasticity“ WIT Transactions on Engineering Sciences, Vol. 122, WIT Press, pp.13-25, 2019. DOI: 10.2495/BE410021 URL: https://www.witpress.com/elibrary/wit-transactions-on-engineering-sciences/122/37070
Strelnikova E., Kriutchenko D., Gnitko V. and Degtyarev K. Boundary element method in nonlinear sloshing analysis for shells of revolution under longitudinal excitations. Engineering Analysis with Boundary Elements, 2020, Vol. 111, p. 78-87. Available from: doi: 10.1016/j.enganabound.2019.10.008 URL: https://www.sciencedirect.com/science/article/abs/pii/S0955799719306149
