# Simulation of hydroelastic vibrations of structure elements using finite and boundary element methods

• Ivan Vierushkin Інститут проблем машинобудування ім. А. М. Підгорного НАНУ, вул. Пожарського, 2/10, Харків, 61046, Україна http://orcid.org/0000-0002-3837-5567
• Yehor Kononenko Інститут проблем машинобудування ім. А. М. Підгорного НАНУ, вул. Пожарського, 2/10, Харків, 61046, Україна https://orcid.org/0000-0001-6221-3608
Keywords: finite and boundary element method, ideal incompressible fluid, hydroelastic vibrations, hypersingular integral equation

### 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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### Author Biographies

Ivan Vierushkin, Інститут проблем машинобудування ім. А. М. Підгорного НАНУ, вул. Пожарського, 2/10, Харків, 61046, Україна

аспірант

Yehor Kononenko, Інститут проблем машинобудування ім. А. М. Підгорного НАНУ, вул. Пожарського, 2/10, Харків, 61046, Україна

аспірант

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### References

Published
2021-03-29
How to Cite
Vierushkin, I., & Kononenko, Y. (2021). Simulation of hydroelastic vibrations of structure elements using finite and boundary element methods. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 49, 16-28. https://doi.org/10.26565/2304-6201-2021-49-02
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