COMPUTER MODELING HYDROELASTIC VIBRATIONS OF STRUCTURE ELEMENTS UNDER FUZZY LOADING CONDITIONS
DOI:
https://doi.org/10.32782/mathematical-modelling/2023-6-2-6Keywords:
hydroelastic oscillations, hypersingular integral equation, boundary element method, methods of fuzzy mathematicsAbstract
Modern equipment usually operates under increased power and temperature loads. This requires determining the strength and dynamic characteristics of structural elements at the design stage in order to substantiate the reliability of operation. Experimental studies make it possible to estimate such characteristics with sufficient accuracy. But conducting natural experiments is an expensive and not always safe procedure. Therefore, studies of the strength and vibrations characteristics of structural elements based on computer modelling are relevant. But the external load parameters cannot always be determined unambiguously. In this work, an effective method of analysing hydroelastic vibrations of structural elements is developed, based on the application of potential theory methods, and elements of fuzzy logic. First, the problem of forced hydroelastic oscillations of a structural element is solved in a deterministic formulation. It is assumed that the fluid is ideal and incompressible, and its motion, induced by small oscillations of the elastic element, is vortex-free. Then there exists a velocity potential that satisfies the Laplace equation. The method of given modes is used, the oscillation modes of the structural element without taking into account the attached fluid masses are chosen as the basic functions. To find the pressure of the liquid on the structural element, a hypersingular integral equation is received, the solution of which is carried out by the boundary element method, using the unknown density approximation by constants on the boundary elements. Next, the load parameters are fuzzified using triangular membership functions. Then the randomness of load parameters was added to the mathematical model. Fuzzy stochastic differential equations are obtained, which are solved by a numerical method. The presented numerical results demonstrate the influence of the uncertainty of the initial data on the behaviour of structural elements.
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