Nonlinear Dynamics–2016
Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/24522
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Документ Perturbed Rotations of a Rigid Body Close to the Lagrange Case under the Action of Unsteady Perturbation Torques(NTU "KhPI", 2016) Akulenko, L. D.; Kozachenko, T. A.; Leshchenko, D. D.; Zinkevich, Ya. S.Perturbed rotations of a rigid body close to the Lagrange case under the action of perturbation torques slowly varying in time are investigated. Conditions are presented for the possibility of averaging the equations of motion with respect to the nutation angle and the averaged system of equations of motion is obtained. In the case of the rotational motion of the body in the linear-dissipative medium the numerical integration of the averaged system of equations is conducted.Документ Taking Account of Nonlinear Properties of Subsystems in Problems of Dynamic Interaction of Structures with Loads, Bases and Flows(NTU "KhPI", 2016) Kulyabko, Vladimir; Chaban, Vyacheslav; Makarov, Andrey; Yaroshenko, DenisThis paper describes the additional features of discrete models of various DOF systems to solve nonlinear dynamical problems of complex-compound buildings and structures including elements of significant flexibility (bridges, pylons and supports of power transmission lines, pipe line crossings, guyed masts etc.). Qualitative and quantitative differences between linear solutions (which are popular among FEM designers) and nonlinear solutions (depending on geometrical, physical and constructive nonlinearities) are discussed. It is analyzed the time-history models of different combinations of mention structures with the adjacent subsystems, damping devices (well-known and the most-recently-used), static and dynamic loads and effects (including moving loads). There is also presented experimental and theoretical approach of damages determination for rod elements in the spatial structure by the dynamic diagnosis method (e.g. for bridges crane with the big span).Документ Some Stationary Deformation Problems for Compound Shells of Revolution(NTU "KhPI", 2016) Grigorenko, Yaroslav; Bespalova, Elena; Yaremchenko, NataliaA common approach to solving stationary deformation problems for compound systems composed of shells of revolution with different geometry and structure is developed. The approach is based on the use of shell models with different level of rigor and of the general numerical-analytical technique for solving corresponding problems. The examples of studying the subcritical stress-strain state, vibrations, and dynamical instability of complex form systems are presented, features of their deformation are noted.Документ Numerical Analysis of Stress-Strain State of Orthotropic Plates in the Form of Arbitrary Convex Quadrangle(NTU "KhPI", 2016) Grigorenko, A. Ya.; Pankratiev, S. A.; Yaremchenko, S. N.A numerical and analytical approach to solving problems of the stress-strain state of quadrangular orthotropic plates of complex shape has been proposed. Two-dimensional boundary value problem was solved using spline collocation and discrete orthogonalization methods after applying the appropriate domain transform. The influence of geometric shape of plate in different cases of boundary conditions on the displacement and stress fields is considered according to the refined theory. The results were compared with available data from other authors.Документ Nonlinear Analysis of Gas Flow in Compressors Stage Based on CFD-Method(NTU "KhPI", 2016) Karpik, A.; Vorobiev, Yu.The numerical simulation of a three-dimensional viscous flow in cascade of the axial compressor of low pressure of the gas-turbine engine is presented. The results of a flow in the first stage o f the compressor in nonstationary three-dimensional statement are obtained in the solver F. Velocity and pressure fields are received as a result.Документ Nonlinear Sonic Vacua(NTU "KhPI", 2016) Vakakis, AlexanderWe will present recent results on a special class of dynamical systems designated as nonlinear sonic vacua. These systems are non-linearizable, and have zero speed of sound (in the sense of classical acoustics). Accordingly, their dynamics and acoustics are highly degenerate and tunable with energy, enabling new and highly complex nonlinear phenomena. Two examples of sonic vacua will be discussed. The first is uncompressed ordered granular media, which, depending on their local state, behave either as strongly nonlinear and non-smooth dynamical systems (in the absence of strong local compression), or as almost linear coupled oscillators (under strong local compression, e.g., in the primary fronts of propagating solitary pulses) [1,2]. The second example concerns a spring-mass lattice in the plane. In the small energy limit this seemingly simple system is 'transformed' by geometric nonlinearity to a nonlinear sonic vacuum with surprising properties, such as strong nonlocality (despite o f only next-neighbor interactions in the lattice!), orthogonal nonlinear normal modes, and accelerating propagating fronts [3,4]. Interesting applications of nonlinear sonic vacua will be discussed, including intense energy cascading from low-to-high frequencies and long-to-short wavelengths, resembling “mechanical turbulence ”. We will discuss the implications of these findings on the design of dynamical systems for predictive passive energy management.Документ Analyzing Parallel Computation of the Functions Created with R-operations in CUDA(NTU "KhPI", 2016) Uvarov, Roman A.Brief overview of the recent general tasks for parallel computation on graphics processing units is represented. Adequacy of the parallel computation approach for single analytic function constructed with R-operations is carried out. Brief overview of ray tracing technique and its connection with constructive apparatus of R-functions is considered. Sample comparison calculations to show the benefits of CUDA are provided.Документ Algorithms and JavaScript Programs in Calculation of R-Functions and Producing Their Two- and Three-Dimensional Charts(NTU "KhPI", 2016) Uvarov, Roman A.Usage of HTML5 canvas element suitable for two- and three-dimensional charts of the function is unveiled. Appliance of JavaScript dynamics to this element is implemented. R-functions and level curves construction details are specified. Two- and three-dimension function charts are represented.Документ Application of Solution Structure Method to Modeling Dynamic Response of Mechanical Structures(NTU "KhPI", 2016) Tsukanov, IgorTransient nature of the loading conditions applied to the structural components makes dynamic analysis one of the important components in the design-analysis cycle. Time-varying forces and accelerations can substantially change stress distributions and cause a premature failure of the mechanical structures. In addition, it is also important to determine dynamic response of the structural elements to the frequency of the applied loads. In this paper we describe an application of the meshfree Solution Structure Method to the structural dynamics problems. Solution Structure Method is a meshfree method which enables construction of the solutions to the engineering problems that satisfy exactly all prescribed boundary conditions. This method is capable of using spatial meshes that do not conform to the shape of a geometric model. Instead of using the grid nodes to enforce boundary conditions, it employs distance fields to the geometric boundaries and combines them with the basis functions and prescribed boundary conditions at run time. This defines unprecedented geometric flexibility of the Solution Structure Method as well as the complete automation of the solution procedure.Документ Parameter Analysis of Vibroimpact Machines Dynamics With Variable Mass and Stiffness(NTU "KhPI", 2016) Tkachuk, M. M.; Kostenko, Iurii; Grabovsky, Andriy; Tkachuk, M. A.Vibroimpact machines operate under high repeated loadings. This poses certain requirements with regards to the strength and durability of their components that have to be met by the design. In order to predict the magnitude and time distribution of the acting forces the dynamics of the vibroimpact systems need to be studied. A two-body mechanical system is considered as a model of a shake-out machine designed for Azovmash company and used for extraction of steel casts from the mold. The first body is the suspended frame with the shake-out grid driven by an unbalanced vibrator, while the second one is the cast. Its sand mold is damaged at every impact with the shake-out grid, which results in the gradual loss of mass. The previously developed rigid body dynamics model is extended in order to account for the variable mass factor. Two approaches for the time evolution of the cast mass has been taken. The first one suggests that mass is a predefined linear or piecewise linear function of time. Alternatively the mass is treated as an unknown variable and was determined in the course of solving the equations of motion. A constitutive law for the mass reduction based on the energy dissipated at each impact is proposed. It has been shown that this model results in more adequate description of the shake-out process compared to the fixed-law mass evolution. In addition to the variable mass the influence of stiffness characteristics has been investigated. Nonlinear double springs with variable stiffness and length difference suspending the shake-out platform are considered. The survey on the combined effect of mass and stiffness parameters on the dynamics of the modelled shake-out machine allowed to determine the loads sustained by its structural elements and to make the rational design with the required strength. In particular, it has been shown how to detune the machine from resonance frequencies, in particular from the discovered dangerous subharmonic regimes due to variable mass and stiffness.