Institute for Problems in Mechanical Engineering

Saint Petersburg, Russia

Institute for Problems in Mechanical Engineering

Saint Petersburg, Russia
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Kiselev A.P.,Saint Petersburg State University | Kiselev A.P.,Institute for Problems in Mechanical Engineering | Plachenov A.B.,Moscow Technological University | Plachenov A.B.,St. Petersburg State University of Aerospace Instrumentation | Dyakova G.N.,St. Petersburg State University of Aerospace Instrumentation
Journal of Electromagnetic Waves and Applications | Year: 2017

We consider two classes of exact solutions of the wave equation, which play an important role in the linear theory of localized wave propagation. These are the complexified spherical wave, known as the “complex source wavefield”, and the complexified Bateman solution. Both involve an arbitrary analytic function of a complex argument, known as the waveform. We explore a possibility of considering non-analytical waveforms and establish that in the both cases the analyticity is unavoidable. © 2017 Informa UK Limited, trading as Taylor & Francis Group

Argatov I.,Institute for Problems in Mechanical Engineering | Butcher E.A.,New Mexico State University
Journal of Sound and Vibration | Year: 2011

The problem of detecting localized large-scale internal damage in structures with imperfect bolted joints is considered. The proposed damage detection strategy utilizes the structural damping and an equivalent linearization of the bolted lap joint response to separate the combined boundary damage from localized large-scale internal damage. The frequencies are found approximately using asymptotic analysis and a perturbation technique. The proposed approach is illustrated on an example of longitudinal vibrations in a slender elastic bar with both ends clamped by bolted lap joints with different levels of damage. It is found that while the proposed method allows for the estimation of internal damage severity once the crack location is known, it gives multiple possible crack locations so that other methods (e.g., mode shapes) are required to obtain a unique crack location. © 2011 Elsevier Ltd.

Argatov I.,Institute for Problems in Mechanical Engineering | Sevostianov I.,New Mexico State University
International Journal of Engineering Science | Year: 2011

The contribution of a rigid toroidal inhomogeneity to the overall elastic properties is addressed. The method of asymptotic extension is applied to derive asymptotic approximations for the polarization matrix of a rigid toroidal inclusion embedded in an elastic media. © 2010 Elsevier Ltd. All rights reserved.

Argatov I.I.,Institute for Problems in Mechanical Engineering | Sabina F.J.,National Autonomous University of Mexico
Wave Motion | Year: 2010

The scattering problem of an incident plane sound wave by a finite number of small sound-soft arbitrarily shaped obstacles is considered. First, we study the case of multiple scattering in the long wave limit. By analogy with Greenwood's approximation for the electrical constriction resistance of a circular cluster of microcontacts, we obtain an approximation for the harmonic capacity of a system of a large number of small sound-soft obstacles grouped into a spherical cluster. We generalize Greenwood's approach for the case of an arbitrary convex cluster and, as a by-product of our analysis, we elicit an approximate formula for the harmonic capacity of a convex solid. The study of the general case of multiple scattering by a cluster of small soft-sound obstacles is based on the first order asymptotic model obtained in our previous paper. We use the method of artificial small parameter for constructing Padé approximants of the scattering amplitude. Explicit formulas are derived and illustrated on several examples. © 2010 Elsevier B.V.

Blekhman I.I.,Institute for Problems in Mechanical Engineering | Sorokin V.S.,Technical University of Denmark
Nonlinear Dynamics | Year: 2016

A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics equations). The approach is named as the oscillatory strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that capture the averaged effect of oscillations. The method of direct separation of motions appears to be an efficient and simple tool to derive these equations. A modification of the method applicable to study problems that do not imply restrictions on the spectrum of excitation frequencies is proposed. It allows also to abandon other restrictions usually introduced when employing the classical asymptotic methods, e.g., the requirement for the involved nonlinearities to be weak. The approach is illustrated by several relevant examples from various fields of science, e.g., mechanics, physics, chemistry and biophysics. © 2015, Springer Science+Business Media Dordrecht.

Argatov I.I.,Aberystwyth University | Fadin Yu.A.,Institute for Problems in Mechanical Engineering
Tribology Letters | Year: 2011

The article presents asymptotic modeling of the running-in wear process with fixed contact zone under a prescribed constant normal load or an imposed contact displacement. The wear contact problem is formulated within the framework of the two-dimensional theory of elasticity in conjunction with Archard's law of wear. The running-in process is considered at the macro-scale level, while the micro-processes associated with roughness changes, tribomaterial evolution, and microstructural alteration in the subsurface layers as a first approximation are neglected. The setting of the steady-state regime for the macro-contact pressure evolution is chosen as the criterion to characterize the completion of running-in. Simple closed-form approximations are derived for the running-in period and running-in sliding distance. The obtained results can be used for estimating the running-in period in wear processes where the evolution of the macro-shape deviations at the contact interface plays a dominant role. © 2011 Springer Science+Business Media, LLC.

Argatov I.I.,Institute for Problems in Mechanical Engineering | Fadin Y.A.,Institute for Problems in Mechanical Engineering
International Journal of Engineering Science | Year: 2010

Different aspects of the long-period oscillations of tribological parameters in the wear process of metals under constant heavy duty sliding conditions are theoretically investigated on the basis of the previously constructed mathematical model. The obtained asymptotic formula for the period of oscillations agrees with the quantitative predictions known in the literature. The period of oscillations is suggested as a diagnostic parameter in assessing the health of operating tribosystem. An approximate formula for the phase of oscillations of relaxation type in the Lotka-Volterra nonlinear mathematical model is derived by the relaxation oscillation method. © 2010 Elsevier Ltd. All rights reserved.

Argatov I.,Institute for Problems in Mechanical Engineering
Mechanics of Materials | Year: 2010

Widely used the Bulychev-Alekhin-Shorshorov relation for analyzing nanoindentation load-displacement data to determine elastic modulus of a thin specimen does not account for the size of specimen since the BASh relation is based on analytical solutions of the contact problems for an elastic half-space. In order to model the substrate effect, the unilateral contact problem for a spherical indenter pressed against an elastic layer on an elastic half-space is analyzed for different types of boundary conditions imposed at the interface between the specimen and the substrate. Approximate (asymptotically exact) solutions are obtained in explicit form. The influence of the substrate effect on the incremental contact stiffness is described in terms of the asymptotic constants possessing information about the thickness of the specimen and depending on the relative stiffness of the substrate. © 2010 Elsevier Ltd.

Sorokin V.S.,Institute for Problems in Mechanical Engineering | Blekhman I.I.,Institute for Problems in Mechanical Engineering | Vasilkov V.B.,Institute for Problems in Mechanical Engineering
Nonlinear Dynamics | Year: 2012

This paper is concerned with the analysis of motion of a gas bubble in a uniformly oscillating incompressible fluid. A theoretical model explaining the effect of sinking of gas bubbles in the absence of a standing pressure wave is validated experimentally. The conditions under which this effect occurs are determined, and a simple formula is derived for the average velocity of a gas bubble in the fluid. © 2011 Springer Science+Business Media B.V.

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