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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.


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.


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.


Slyn'ko V.I.,Timoshenko Institute of Mechanics | Denisenko V.S.,Khmelnitsky National University
Automation and Remote Control | Year: 2012

We give sufficient robust stability conditions for matrix polytopes of linear systems with impulsive influence. The methods of our study are based on logarithmic matrix measure theory and linear operator theory in Banach spaces. Our results reduce the robust stability problem to the feasibility problem for a system of linear matrix inequalities in the class of positive definite matrices. © Pleiades Publishing, Ltd., 2012.


Zhuk Y.A.,Timoshenko Institute of Mechanics | Guz I.A.,University of Aberdeen | Sands C.M.,University of Aberdeen
Archive of Applied Mechanics | Year: 2011

A coupled dynamic problem of electromechanics for thin wall multilayer elements is formulated based on the Kirchhoff-Love hypotheses. In the case of harmonic loading, a simplified formulation is given using the monoharmonic approach and the concept of complex moduli to characterize the cyclic properties of the material. The problem of forced vibrations of three-layer beam, whose outer layers are made of a viscoelastic piezoactive material, and, the inner layer of a passive physically nonlinear material, is considered as an example to demonstrate the possibility of the technique elaborated. The possibility of damping the forced vibrations of a structure with the help of harmonic voltages applied to the external piezoactive layers is studied. Results obtained for the transient response of the beam using the complete model are compared with data found using the simplified model. Limitations on the simplified model application are specified. © 2010 Springer-Verlag.

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