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Документ Transitional regimes under route to chaos in vibroimpact system(КНУБА, 2019) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.In recent years in nonlinear dynamics particular attention was paid to studying the chaotic behaviour of dynamical systems and their routes to chaos. Sometimes this route may be intricate. We watched such intricate route to chaos when studying the quasi-periodic route to chaos in strongly nonlinear non-smooth discontinuous vibroimpact system that was two-body 2-DOF one. After Neimark-Sacker bifurcation many different regimes replace each other. There are transitional regimes with inconsistent characteristics among them. We analyze these regimes with continuous wavelet transform CWT applying. CWT plots confirm just their transition kind and give clear picture of different frequencies presence in time series and their distribution in time.Документ Wavelet transform using for analysis of vibroimpact system chaotic behavior(КНУБА, 2018) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.; Lukianchenko, O. O.Chaotic behaviour of dynamical systems, their routes to chaos, and the intermittency are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in nonsmooth dynamical systems is of the special scientists’ interest. In this paper we apply relatively young mathematical tool – continuous wavelet transform CWT – for investigating the chaotic behavior and intermittency in particular in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate route to chaos via intermittency, to distinguish and analyze the laminar and turbulent phases.Документ Definition of the failure region of the oil tank with wall imperfections in combined loading(КНУБА, 2018) Bazhenov, V. А.; Lukianchenko, O. O.; Kostina, О. V.The stability of an oil reservoir with real imperfections of a wall under the joint action of axial compression and surface pressure is studied using a program complex of finite element analysis. To determine the permissible range of fail-safe operation of the reservoir, irregular imperfections of the middle wall surface are simulated as ratios of the buckling forms with different maximum amplitudes obtained in solving the problem of loss of stability by the Lanczos method. The stability of the shell with real and simulated imperfections of the wall is investigated using the nonlinear static problem by the Newton-Raphson method. Critical ratios of axial compression and surface pressure are determined to ensure overall stability of the reservoir wall. The region of failure on the stability of the oil reservoir with real imperfections is obtained.Документ Invariant torus break-down in vibroimpact system – route to crisis ?(КНУБА, 2018) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.Chaotic vibrations of dynamical systems and their routes to chaos are interesting and investigated subjects in nonlinear dynamics. Particularly the routes to chaos in non-smooth dynamical systems are of the special scientists’ interest. In this paper we study quasiperiodic route to chaos in nonlinear non-smooth discontinuous 2-DOF vibroimpact system. The break-down of invariant torus or of the closed curve occurs just under the quasiperiodic route to chaos. Is it route to crisis? In narrow frequency range different oscillatory regimes have succeeded each other many times under very small control parameter varying. There were periodic subharmonic regimes − chatters, quasiperiodic, and chaotic regimes, the zones of prechaotic and postchaotic motion. The hysteresis effects (jump phenomena) occurred for increasing and decreasing frequencies. The observed chaos was the transient one.The chaoticity of obtained regime has been confirmed by typical views of Poincaré map and Fourier spectrum, by the positive value of the largest Lyapunov exponent, and by the fractal structure of Poincaré map. These investigations confirm the theory by Newhouse, Ruelle, and Takens who suggested a new bifurcation scenario where a periodic solution produces subsequently a torus and then a strange attractor.Документ Numerical solution of the problem of porous solids vibration(КНУБА, 2017) Каrа, І. D.In this paper vibration of fluid-saturated porous solids under the equal distribution load is studied using two different approaches. One of them is analytical way. Biot’s equations in terms of displacement, pore pressure, porosity and effective densities are used for one-dimensional column. Using boundary conditions analytical expressions for parameters of stress-strain state: the solid and fluid displacements and stresses are obtained. Another way is Boundary Integral Equation Method. Equilibrium equations for 3-D linear dynamic poroelasticity are presented. Also required components of fundamental solution tensors as weighting displacement fields are obtained and analyzed with the help of the analogy between poroelastisity and thermoelastisity. The solution of the porous solid vibration problem for two types of boundary conditions is presented in the figures. Graphs present the comparison of the normalized solid displacement u3 at the top and normalized pressure σ33 in elastic region and in porous solid of poroelastic region depending on frequency ω that are computed using Boundary Integral Equation and analytical methods. Figures show that graphs of the displacements and pressure in poroelastic and elastic region have the same character but different values. The numerical solution of this problem was calculated using material properties which are corresponding to the Barea Sandstone. It shows that massive porous bodies cannot be modeling as homogeneous elastic media but it is necessary to use two phase model and equations of poroelasticity. Since the agreement between the BEM results and the analytical solution is good so such an approach can be used for development and testing of numerical techniques for analyzing of 3-D porous solids vibration.Документ A methodology of determining of parameter j* in discrete models of finite element method(КНУБА, 2017) Bazhenov, V. A.; Pyskunov, S. О.; Shkryl, О. О.Based on the method of reactions, a technique for determining of the parameter J * by the method of subdomain moving in discrete models of finite element method (FEM) has been developed. A number of test problems solved. The obtained results confirm the effectiveness of the technique.Документ Effect of static loads on the natural vibrations of ribbed shells(КНУБА, 2018) Кrivenko, О. P.The article is devoted to a further analysis of the natural vibrations of inhomogeneous shells under the action of static loads. The method of investigation is based on a unified methodology that combines the problems of static stability and the vibrations of elastic shells. The problems of natural vibrations take into account the presence of a prestressed state of the shell structure from the action of static loads. The presence of a static load significantly affects the spectrum of the natural frequencies of the shell. This approach allows us to determine the critical load by the dynamic criterion. The method of investigating of inhomogeneous shells is based on the uniform methodological positions of the 3-d geometrically nonlinear theory of thermoelasticity and the finite-element method in the form of the moment finite-element scheme. So, a thin shell is considered by this method as a three-dimensional body which is modeled throughout the thickness by one isoparametric solid finite element with multilinear shape functions. Two nonclassical hypotheses are used to describe the stress–strain state of a thin inhomogeneous shell. The kinematic hypothesis of deformed straight line in the thickness direction: though stretched or shortened during deformation, a straight segment along the thickness remains straight. This segment is not necessarily normal to the mid-surface of the shell. The displacements are assumed distributed linearly along the thickness, which is conventional in the theory of thin shells. The static hypothesis compressive assumes that the stresses in the fibers are constant throughout the thickness of the shell. Modal analysis of a shallow ribbed panel demonstrates the effectiveness of the developed method. The natural frequencies and mode shapes are determined at each increment of static loading.Документ Dynamic behaviour of nonlinear nonsmooth discontinuous vibroimpact system(КНУБА, 2015) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.Authors shortly describe the problem state about studying of discontinuous vibroimpact systems dynamical behaviour. Recently the investigations of such systems are developed rapidly. There is survey of world scientific literature about this problem. Information and description of an International Conference on Nonlinear Dynamics Complexity is given. Authors show owns the most spectacular results demonstrating the phenomena unique for nonsmooth systems describing by differential equations with discontinuous right-hand side. These results were obtained by numerical parameter continuation method.Документ Lyapunov exponents estimation for strongly nonlinear nonsmooth discontinuous vibroimpact system(КНУБА, 2017) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.Lyapunov exponents are ones of the most important characteristics for the definition of the dynamical system state. Their estimation for nonsmooth discontinuous system that is vibroimpact system has got certain difficulties. We study their calculation by following the evolution of two nearby orbits in phase space and use three formulas for such estimation. We check this calculation for three different oscillatory regimes: periodic, quasi-periodic and chaotic. We also define the largest Lyapunov exponent by Benettin’s algorithm and compare obtained results.Документ Effectiveness of semi-analytical finite element method in the numeric analysis of deformation of non-homogeneous 3d constructions subject to initial deviation of form(КНУБА, 2015) Solodei, I. I.; Vabishchevych, M. O.; Sіzevych, B. I.; Chepurna, O. O.Static and dynamic numeric models to analyze stress-strain state of 3D uncanonical form bodies are considered in the range of semi-analytical finite element method. Effectiveness and simulation veracity analysis are provided on the base of specific test cases.