Перегляд за Автор "Orynyak, I.V."

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    Applications of randomly selected sets of exact Voight’s solutions for vibration of thin plates
    (Igor Sikorsky Kyiv Polytechnic Institute, 2022) Orynyak, I.V.; Bai, Yu.P.; Kostiushko, I.A.
    The principally new method of selected exact solutions, SES, for plate vibration based on fundamental solutions of Voigt is suggested. In contrast to similar known methods, it employs the frequency dependent functions for both space coordinates. The sets of exact solutions which depends on some arbitrary chosen parameters are constructed. This allows to choose any number of exact solutions, while the required number of them depends on the boundary conditions which should satisfy in considered collocation points. The efficiency of method is demonstrated for the most unfavorable case of all sides clamped rectangular plate. Nevertheless, the accuracy is quite satisfactory for first six natural frequencies even for relatively small number of collocation boundary points, and testify about big prospects as to application for complex structures, different geometries, various boundary conditions. Additionally two variants of the Galerkin method are realized and compared. First one, employs the exponential functions, while the second one – the very popular beam functions. The calculation results show the superiority of first variant as in technical realization as in accuracy, and in further applications in structural mechanics.
  • Ескіз
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    Semi-analytical implicit direct time integration scheme on example of 1-D wave propagation problem
    (Igor Sikorsky Kyiv Polytechnic Institute, 2022) Orynyak, I.V.; Mazuryk, R.; Tsybulskyi, V.
    The most common approach in dynamic analysis of engineering structures and physical phenomenas consists in finite element discretization and mathematical formulation with subsequent application of direct time integration schemes. The space interpolation functions are usually the same as in static analysis. Here on example of 1-D wave propagation problem the original implicit scheme is proposed, which contains the time interval value explicitly in space interpolation function as results of analytical solution of differ- ential equation for considered moment of time. The displacements (solution) at two previous moments of time are approximated as polynomial functions of position and accounted for as particular solutions of the differential equation. The scheme demonstrates the perfect predictable properties as to dispersion and dissipation. The crucial scheme parameter is the time interval – the lesser the interval the more correct results are obtained. Two other parameters of the scheme – space interval and the degree of polynomial approximation have minimal impact on the general behavior of solution and have influence on small zone near the front of the wave.