Перегляд Автор "Bazhenov, V. A."

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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.
An estimation of residual lifetime of spatial structural elements under continual fracture condition
(КНУБА, 2014) Bazhenov, V. A.; Gulyar, O. I.; Pyskunov, S. O.
The techniques of modeling of continual fracture process for space circular and prismatic bodies under prolonged load condition and some results of determining of the estimated lifetime (up to local loss of material bearing capacity) and the residual (additional) lifetime (time of continual fracture zone growth) is presented in this paper. The Kachanov-Rabotnov’s scalar damage parameter to describe the continual fracture of the material and the semianalytic finite element method (SFEM) as numerical method of boudary problem solution is used. It‘s shown, that the value of residual lifetime could be differ significantly for different loading condition and object configuration.
Application of parameter continuation method for investigation of vibroimpact systems dynamic behaviour. problem state. short survey of world scientific literature
(КНУБА, 2014) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.
Authors in their works study vibroimpact system dynamic behaviour by numerical parametric continuation technique combined with shooting and Newton-Raphson’s methods. The technique is adapted to two-mass two-degree-of-freedom vibroimpact system under periodic excitation. Impact is simulated by nonlinear contact interaction force based on Hertz’s contact theory. Stability or instability of obtained periodic solutions is determined by monodromy matrix eigenvalues (multipliers) based on Floquet’s theory. In the present paper we describe the state of problem of parameter continuation method using for nonlinear tasks solution. Also we give the short survey of numerous contemporary literature in English and Russian about parameter continuation method application for nonlinear problems. This method is applied for vibroimpact problem solving more rarely because of the difficulties connected with repeated impacts.
Buckling and vibrations of the shell with the hole under the action of thermomechanical loads
(КНУБА, 2020) Bazhenov, V. A.; Krivenko, O. P.
The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and vibrations of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, under complex thermomechanical loading. The technique is based on the geometrically nonlinear equations of three-dimensional thermoelasticity, the finite element formulation of the problem in increments, and the use of the moment finite-element scheme. A thin shell is considered by this method as a threedimensional body. We approximate a shell by one spatial universal finite element (FE) throughout the thickness. The universal FE is based on an isoparametric spatial FE with polylinear shape functions for coordinates and displacements. The universal element has additional variable parameters introduced to expand its capabilities. The method of modal analysis of the shell is based on an approach that at each current stage of thermomechanical loading takes into account the stresses accumulated at the previous stages. The developed algorithm allows one to study geometric nonlinear deformation and buckling of elastic shells of an inhomogeneous structure with a thin and medium thickness, as well as to study small vibrations of the shells relative to the reference deformed state caused by static loading, taking into account large displacements and a prestressed state. An analysis of the stability and vibration of the spherical panel with the hole is carried out. The effect on the frequencies and mode shapes of the shell of the sequential action of thermal and mechanical loads is investigated.
Creation of mathematical model of platformvibrator with shock, designed for concrete products compaction and molding
(КНУБА, 2020) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.
Platform-vibrators are the main molding equipment in the production of precast concrete elements. Shock-vibration technology for the precast concrete production on low-frequency resonant platform-vibrators significantly improves the quality of the products front surfaces and the degree of their factory readiness. This technology is used to produce large elements. We describe the creation of a mathematical model for platform-vibrator that uses shock to produce asymmetric oscillations. The values of the upper and lower accelerations of the mold with concrete have different values with shock-vibration technology. The created mathematical model corresponds to the two-body 2-DOF vibro-impact system. It is strongly nonlinear non-smooth discontinuous system. It has some peculiar properties, namely: the upper body with very large mass breaks away from the lower body during vibrational motion; both bodies move separately; the upper body falls down onto the soft constraint; the impact that occurs is soft one due to the softness and flexibility of the constraint. The soft impact simulation requires special discussion. In this paper, we simulate a soft impact by a nonlinear contact force in accordance with the Hertz quasistatic contact law. The numerical parameters for this system were chosen in such a way that: firstly they provide the fulfillment of requirements for real machine, and secondly they allow analyzing its dynamic behavior by nonlinear dynamics tools. The created model is well enough to fulfill a number of requirements, namely: T-periodic steady-state movement after passing the transient process; the appropriate value of mold oscillations amplitude; the satisfactory value of the asymmetry coefficient that is the ratio of lower acceleration to the upper acceleration. We believe that the created model meets all the necessary requirements.
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.
Influence of system stiffness parameters at contact softness in vibroimpact system
(КНУБА, 2014) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.
The possibility of contact character changing by system parameters changing is researching. It is investigated the contact between two bodies in two-degree-of-freedom vibroimpact system. We show which parameters changing can transform the rigid impact in system into the soft one. In the main these parameters are the Young’s modulus and geometrical characteristics of the contact zone for both bodies.
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.
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.
Modeling of nonlinear deformation and buckling of elastic inhomogeneous shells
(КНУБА, 2014) Bazhenov, V. A.; Solovei, N. A.; Krivenko, O. P.
The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped mid-surface, geometrical features throughout the thickness, and multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finiteelement scheme. The method is justified numerically. Comparing solutions with those obtained by other authors and by software LIRA and SCAD is conducted.
“Nonlinear Dynamics - 2016” Conference
(КНУБА, 2016) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.
There is short description of problem state on nonlinear dynamics in this paper. Information about some contemporary journals and recent Conferences on this subject is given. Information about 5th International Conference on Nonlinear Dynamics which was holding in National Technical University “Kharkov Polytechnic Institute” in September 2016 and impression about it are presented.
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.
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.