ЧОТИРЬОХМОДОВА МОДЕЛЬ ДИНАМІКИ РОЗПОДІЛЕНИХ СИСТЕМ

• Datum: 2020
• Hauptverfasser: Kaliukh, Yu.I., Berchun, Ya.A.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Schlagworte: чотирьохмодова модель; розподілені системи; петля; чисельне моделювання
• Online Zugang: https://jais.net.ua/index.php/files/article/view/441
• Назва журналу: Problems of Control and Informatics

Distributed systems are widely used in practice. These are cosmic ligaments in the near-Earth space with a length of tens of kilometers. They approximate reinforced concrete piles in the soil when calculating the stress-strain state and assessing the technical condition; pipelines both in air and in liquid, underwater towed systems. Known underwater airlift systems of great length for the extraction of minerals (nodules) from the ocean floor with a length of 5-10 km. To solve the problems of the dynamics of such systems in various environments, the well-known mathematical models are not quite correct from the point of view of taking into account the variety of wave processes. This determines the need to build refined wave models. A new quasilinear mathematical model, which describes the nonlinear four-mode dynamics of the distributed system in the spatially inhomogeneous field of mass and surface forces, has been obtained. It is described by a nonlinear system of twelve first-order partial differential equations. For her, the principles of ultimate and hyperbolicity are fulfilled. Together with the boundary and initial conditions, it can be used to describe dynamics and statics of geometrically and physically nonlinear rod elements, piles in the ground, crane equipment ropes, mine lifts, aerial cableways, towed systems in liquid and gas flow, etc. For two-mode spatial reduction of the model, the theorem about correctness of Cauchy problem has been considered. The model was tested on the basis of a numerical solution of the spatial problem of the propagation of four waves of three types: longitudinal, configurational in the direction of the normal and binormal, torsion. Using the proposed model and the numerical algorithm based on the finite-difference method, to determined necessary quantitative estimates of the rope twist angle and the torque for specific distributed system in a fluid flow.