Timoshenko Institute of Mechanics

Zhovkva, Ukraine

Timoshenko Institute of Mechanics

Zhovkva, Ukraine
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Efimova T.L.,Timoshenko Institute of Mechanics
Journal of Mathematical Sciences | Year: 2010

With the use of the 3D theory of elasticity, we investigate the problem of free torsional vibrations of an anisotropic hollow cylinder with different boundary conditions at its end faces. We have proposed a numerical-analytic approach for the solution of this problem. The original partial differential equations of the theory of elasticity with the use of spline approximation and collocation are reduced to an eigenvalue problem for a system of ordinary differential equations of high order in the radial coordinate. This system is solved by the stable numerical method of discrete orthogonalization together with the method of step-by-step search. We also present numerical results for the case of orthotropic and inhomogeneous material of the cylinder for some kinds of boundary conditions. © 2010 Springer Science+Business Media, Inc.


Hryhorenko Y.M.,Timoshenko Institute of Mechanics | Rozhok L.S.,Timoshenko Institute of Mechanics
Journal of Mathematical Sciences (United States) | Year: 2015

We study the stress state of a hollow cylinder with cross section in the form of connected convex semicorrugations under certain conditions imposed on the ends and external loading of the lateral surfaces in the 3D statement. For the solution of the problem, we use the approximations of functions by discrete Fourier series. The results of calculations are presented in the form of the plots of dependences of displacements and stresses on the curvature of cross section of the cylinder. © 2015, Springer Science+Business Media New York.


Babich D.V.,Timoshenko Institute of Mechanics | Bezverkhii A.I.,Timoshenko Institute of Mechanics | Dorodnykh T.I.,Timoshenko Institute of Mechanics
Journal of Mathematical Sciences (United States) | Year: 2017

A continual model of deformation of piezoelectric materials weakened by a system of microcracks dispersed over the bulk of the material is constructed with use of the energy method. This method is based on the assumption of equivalence of the strain energy of the cracked electroelastic medium and the strain energy of a continuum modeling the indicated medium. A generalization of the Eshelby principle is used to determine the strain energy of microinhomogeneous media with inclusions. © 2017 Springer Science+Business Media New York


Zakrzhevsky A.E.,Timoshenko Institute of Mechanics
Vibrations in Physical Systems | Year: 2014

Dynamics of the spacecraft with giro-gravitational system of stabilisation, in which the pantograph design deployed in an orbit and containing on the end the concentrated mass is used as the gravitational stabilizer and the carrier of solar batteries, is investigated. The analysis of the obtained information is carried out and graphs that illustrate behaviour of characteristic variables are discussed. © by Poznan University of Technology, Poznan, Poland 2014.


Rushchitsky J.,Timoshenko Institute of Mechanics
Vibrations in Physical Systems | Year: 2014

This paper is devoted to analysis of the surface nonlinear elastic harmonic waves of four types (Rayleigh and Stoneley harmonic waves within the framework of plane strain state; Love and Mozhaev harmonic wave within the framework of anti-plane strain state). The nonlinear model is based on introducing the Murnaghan elastic poten tial, which includes both geometrical and physical nonlinearities. Each type of surface waves is discussed in four steps: statement of the problem, nonlinear wave equations, approximate solution (first two approximations), so-me conclusions. A nonlinear analysis of waves required many novelties: new variants of the Murnaghan poten-tial, new nonlinear wave equations and new nonlinear boundary conditions. The nonlinear wave equations were solved by the method of successive approximations. A new approach to analyze the boundary conditions is offe-red. Some new nonlinear wave effects are observed theoretically: a wave picture is reached by the 2nd harmonic and becomes changing in time of propagation, the wave numbers become depending on the initial amplitude. © by Poznan University of Technology, Poznan, Poland 2014.


Zakrzhevskii A.E.,Timoshenko Institute of Mechanics
Journal of the Astronautical Sciences | Year: 2016

The object of this research is a space tether of two bodies connected by a flexible massless string. The research objective is the development and theoretical justification of a novel approach to the solution of the problem of deployment of the space tether in a circular orbit with its alignment to the local vertical. The approach is based on use of the theorem on the angular momentum change. It allows developing the open-loop control of the tether length that provides desired change of the angular momentum of the tether under the effect of the gravitational torque to the value, which corresponds to the angular momentum of the deployed tether aligned to the local vertical. The given example of application of the approach to a case of deployment of a tether demonstrates the simplicity of use of the method in practice, and also the method of validation of the mathematical model. © 2016, American Astronautical Society.


Nazarenko L.,Timoshenko Institute of Mechanics
ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers | Year: 2012

The problem of deformation and micro-damage in the components of composites with transversally-isotropic components is considered. The mechanism of deformation and damage is investigated on the basis of the methods of mechanics of stochastically nonhomogeneous media and on the assumption that the micro-strength of fibers material is nonhomogeneous. Modeled the dispersed micro-damage by a system of randomly distributed quasi spherical micro-pores, which are empty or filled with "destroyed" material, a porous material of stochastic structure is obtained, whose damage is described as increasing porosity. The corresponding limit value of equivalent stress from the damage criteria is considered as a random function (statistically homogeneous) of coordinates. One-point distribution function of this limit value is described by a Weibull distribution. From definition of distribution function we may have a damage evolution equation. The relations for determining the effective elastic moduli for the case of transversally-isotropic components and the damage evolution equation are taken as basic relations. It allows us to describe the deformation and damage and their mutual influence on the deformation properties of the composite. The influence of damage of fibers material on the relationships between macro-stresses and macrostrains is investigated.


Selivanov M.F.,Timoshenko Institute of Mechanics | Chornoivan Y.O.,Timoshenko Institute of Mechanics
Journal of Engineering Mathematics | Year: 2012

The problem of describing of the viscoelastic properties of composite materials that consist of more than one viscoelastic component is studied. It is supposed that the viscoelastic properties of the components are known. The difficulty in the application of the mixture theory arises in the cases when the properties are described by integral operators with different integral kernels. This difficulty is avoided by the approximations of the viscoelastic operators in the stress-strain relations. A method is proposed to obtain appropriate approximations that reduce all the viscoelastic operators to a general kernel using rational approximations of their Laplace transforms. The proposed method allows for the reduction of the approximation error for related operators. Examples are given for the adjustment of viscoelastic functions in the cases of increase and decrease of functions parameter. © 2011 Springer Science+Business Media B.V.


Zhuk A.P.,Timoshenko Institute of Mechanics | Kubenko V.D.,Timoshenko Institute of Mechanics | Zhuk Y.A.,Timoshenko Institute of Mechanics
Journal of the Acoustical Society of America | Year: 2012

The acoustic pressure and radiation force acting on the spherical rigid particle located in a fluid-filled cylindrical vessel are determined as a function of the primary wave frequency making use of the solution of a problem of plane harmonic wave scattering on a spherical body. The problem is solved by the variables separation method. To satisfy the boundary conditions on cylindrical and spherical surfaces, the mutual expansions of spherical wave functions over the cylindrical ones and vice versa are used. Required constants in the solution are calculated from an infinite system of algebraic equations which is solved by a truncation method. It is established that the value of the radiation force is affected significantly by the presence of the cylindrical boundary surface. Depending on the frequency of the incident wave, the radiation force can change its direction. It is established that there are peak values of the force at some discrete values of the frequency. The mentioned peculiarities can stipulate specific localization effects and influence the motion of the particles in the cylindrical cavity under the influence of an acoustic wave. © 2012 Acoustical Society of America.


Kaminsky A.A.,Timoshenko Institute of Mechanics | Selivanov M.F.,Timoshenko Institute of Mechanics | Chornoivan Y.O.,Timoshenko Institute of Mechanics
International Journal of Solids and Structures | Year: 2013

The general failure of structures is often preceded by the growth and coalescence of intermediate cracks. In this work, a model with process zone is used to study the deformed state of an infinite isotropic body with three collinear cracks. A numerical algorithm is presented to obtain crack opening displacements effectively. The problem is analyzed for all possible cases of mutual location of the cracks and different levels of loading. The numerical solution shows negligible influence of two cracks coalescence process on the opening displacement of the third crack. An example of the results implementation to calculate crack initiation duration in a problem for viscoelastic body is given. © 2013 Elsevier Ltd. All rights reserved.

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