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Bobrovnitskii Yu.I.,RAS Blagonravov Institute of Mechanical Engineering
Acoustical Physics | Year: 2013

It is proven that linear oscillatory systems with hysteretic damping in the form of complex stiffness and/or complex elastic moduli satisfy the causality principle: the response of such a system to an arbitrary external force cannot appear earlier than the onset of the force. The proof, based on a rigorous solution to the problem of forced oscillations, is presented in detail for an oscillator with a complex stiffness, as well as in a brief explanation for a system with N mass. It is also shown that these systems are Lyapunov-unstable. A comparison is made to other linear hysteretic damping models. © 2013 Pleiades Publishing, Ltd. Source


Bobrovnitskii Yu.I.,RAS Blagonravov Institute of Mechanical Engineering
Acoustical Physics | Year: 2013

The general formulas are derived for calculating the kinetic and potential energies and other energy characteristics of linear oscillatory systems, a portion of the degrees of freedom of which are internal, i.e., inaccessible for direct measurements and/or excluded from consideration. The energy characteristics are expressed by means of parameters pertaining only to the part of accessible (or selected for consideration) degrees of freedom. The formulas are derived based on the use of certain novel properties of the so-called Shur matrix complement. The obtained formulas are applicable for calculating the energy characteristics of the elements of acoustic metamaterials by means of their effective inertial-elastic parameters. The main focus is the case of negative values of these parameters. Proceeding from the nonnegativity of the kinetic and potential energies of mechanical structures, limitations on the character of the frequency dependences of the effective parameters are formulated. © 2013 Pleiades Publishing, Ltd. Source


Bobrovnitskii Y.I.,RAS Blagonravov Institute of Mechanical Engineering
Acoustical Physics | Year: 2014

An approach is proposed to describe a general form of acoustic media, in particular, acoustic metamaterials, based on their modeling with the simplest discrete periodic structures. The parameters of the discrete models, determined from the dispersion equation, are taken as the effective parameters of the modeled media. Transfer to an effective continuous medium is achieved by uniform distribution of these parameters over the length of the periodicity cell. It is shown that all of the wave motion characteristics of the medium, including the energy characteristics, are expressed through the effective parameters thus introduced. The necessary formulas are derived. Examples are given. The proposed method is useful for designing acoustic materials with the given wave properties. © 2014 Pleiades Publishing, Ltd. Source


Bobrovnitskii Y.I.,RAS Blagonravov Institute of Mechanical Engineering
Acoustical Physics | Year: 2015

For two-dimensional linear acoustic metamaterials and media represented in the form of periodic structures made of complex cells, a general model is proposed, formulas are derived for the effective parameters and energy characteristics, and the restrictions imposed on such media are formulated. They are divided into four main types, differing in general wave properties; the differentiating features of each type are shown. Several new schemes of negative and hyperbolic types of discrete and continuous metamaterials are presented, for which the dispersion dependences are constructed and the corresponding “wave” equations are written. © 2015, Pleiades Publishing, Ltd. Source


Kovriguine D.A.,RAS Blagonravov Institute of Mechanical Engineering
Archive of Applied Mechanics | Year: 2012

We analyze a classical problem of oscillations arising in an elastic base caused by rotor vibrations of an asynchronous driver near the critical angular velocity. The nonlinear coupling between oscillations of the elastic base and rotor takes place naturally due to unbalanced masses. This provides typical frequency-amplitude patterns, even let the elastic properties of the base be linear one. As the measure of energy dissipation increases, the effect of bifurcated oscillations can disappear. The latter circumstance indicates the efficiency of using vibration absorbers to stabilize the dynamics of the electromechanical system. The second section of this paper presents results of theoretical studies inspired by the problem of reducing the noise and vibrations by using hydraulic absorbers as dampers to dissipate the energy of oscillations in railway electric equipments. The results of experimental trials over this problem and some theoretical calculations, discussed in the text, are demonstrated the ability to customize the damping properties of hydraulic absorbers to save an electric power and to protect the equipment itself due to utilizing the synchronous modes of rotation of the rotors. © Springer-Verlag 2011. Source

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