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Rudenko, Oleg
Publications (10 of 74) Show all publications
Mikhailov, S. G. & Rudenko, O. (2018). A Simple Bimodular Nonlinear Element. Acoustical Physics, 64(3), 293-298
Open this publication in new window or tab >>A Simple Bimodular Nonlinear Element
2018 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 64, no 3, p. 293-298Article in journal (Refereed) Published
Abstract [en]

We have studied the dynamics of an artificial nonlinear element representing a flexible membrane with oscillation limiters and a static pressing force. Such an element has the property of “bimodularity” and demonstrates “modular” nonlinearity. We have constructed a mathematical model that describes these oscillations. Their shapes have been calculated. We follow the analogy with a classical object—Galileo’s pendulum. We demonstrate that for a low-frequency excitation of the membrane, the level of the harmonics in the spectrum is higher than in the vicinity of the resonance frequency. We have established a strong dependence of the level of the harmonics on the magnitude of the pressing force for a weak perturbation. We propose a design scheme for a device in the quasi-static approximation possessing the property of bimodularity. We perform an experiment that confirms its operability. We show a qualitative coincidence of the experimental results and calculations when detecting an amplitude-modulated signal. © 2018, Pleiades Publishing, Ltd.

Place, publisher, year, edition, pages
Pleiades Publishing, 2018
Keywords
artificial nonlinear element, detection of acoustic oscillations, generation of harmonics, modular nonlinearity, Acoustics, Physics, Acoustic oscillation, Amplitude modulated signals, Nonlinear elements, Quasistatic approximations, Resonance frequencies, Strong dependences, Harmonic analysis
National Category
Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-16633 (URN)10.1134/S1063771018020112 (DOI)000434472200005 ()2-s2.0-85048219221 (Scopus ID)
Available from: 2018-06-27 Created: 2018-06-27 Last updated: 2018-06-29Bibliographically approved
Gray, A. & Rudenko, O. (2018). An Intense Wave in Defective Media Containing Both Quadratic and Modular Nonlinearities: Shock Waves, Harmonics, and Nondestructive Testing. Acoustical Physics, 64(4), 402-407
Open this publication in new window or tab >>An Intense Wave in Defective Media Containing Both Quadratic and Modular Nonlinearities: Shock Waves, Harmonics, and Nondestructive Testing
2018 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 64, no 4, p. 402-407Article in journal (Refereed) Published
Abstract [en]

The observed nonclassical power-law dependence of the amplitude of the second harmonic wave on the amplitude of a harmonic pump wave is explained as a phenomenon associated with two types of nonlinearity in a structurally inhomogeneous medium. An approach to solving the inverse problem of determining the nonlinearity parameters and the exponent in the above-mentioned dependence is demonstrated. To describe the effects of strongly pronounced nonlinearity, equations containing a double nonlinearity and generalizing the Hopf and Burgers equations are proposed. The possibility of their exact linearization is demonstrated. The profiles, spectral composition, and average wave intensity in such doubly nonlinear media are calculated. The shape of the shock front is found, and its width is estimated. The wave energy losses that depend on both nonlinearity parameters—quadratic and modular—are calculated. © 2018, Pleiades Publishing, Ltd.

Place, publisher, year, edition, pages
Pleiades Publishing, 2018
Keywords
diagnostics, Hopf–Burgers type equations, nonlinear losses, nonlinearity parameters, quadratic modular nonlinearity, shock front, Energy dissipation, Harmonic analysis, Inverse problems, Nondestructive examination, Nonlinear equations, Plasma diagnostics, Shock testing, Shock waves, Wave energy conversion, Inhomogeneous medium, Non-linearity parameter, Nonlinear loss, Power-law dependences, Second harmonic waves, Shock fronts, Spectral composition, Control nonlinearities
National Category
Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-16907 (URN)10.1134/S1063771018040048 (DOI)000439751800002 ()2-s2.0-85050124455 (Scopus ID)
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2018-08-21Bibliographically approved
Rudenko, O., Gurbatov, S. N. & Tyurina, A. V. (2018). Evolution of weak noise and regular waves on dissipative shock fronts described by the Burgers model. Wave motion, 82, 20-29
Open this publication in new window or tab >>Evolution of weak noise and regular waves on dissipative shock fronts described by the Burgers model
2018 (English)In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, p. 20-29Article in journal (Refereed) Published
Abstract [en]

The interaction of weak noise and regular signals with a shock wave having a finite width is studied in the framework of the Burgers equation model. The temporal realization of the random process located behind the front approaches it at supersonic speed. In the process of moving to the front, the intensity of noise decreases and the correlation time increases. In the central region of the shock front, noise reveals non-trivial behaviour. For large acoustic Reynolds numbers the average intensity can increase and reach a maximum value at a definite distance. The behaviour of statistical characteristics is studied using linearized Burgers equation with variable coefficients reducible to an autonomous equation. This model allows one to take into account not only the finite width of the front, but the attenuation and diverse character of initial profiles and spectra as well. Analytical solutions of this equation are derived. Interaction of regular signals of complex shape with the front is studied by numerical methods. Some illustrative examples of ongoing processes are given. Among possible applications, the controlling the spectra of signals, in particular, noise suppression by irradiating it with shocks or sawtooth waves can be mentioned. © 2018 Elsevier B.V.

Place, publisher, year, edition, pages
Elsevier B.V., 2018
Keywords
Burgers equation, Dissipation, Noise, Nonlinearity, Shock front, Control nonlinearities, Energy dissipation, Numerical methods, Partial differential equations, Random processes, Reynolds number, Autonomous equations, Burgers equations, Noise suppression, Shock fronts, Statistical characteristics, Variable coefficients, Shock waves, numerical model, shock wave
National Category
Other Mathematics
Identifiers
urn:nbn:se:bth-16903 (URN)10.1016/j.wavemoti.2018.06.007 (DOI)000444790500003 ()2-s2.0-85050081319 (Scopus ID)
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2018-10-04Bibliographically approved
Rudenko, O. (2018). «exotic» models of high-intensity wave physics: Linearizing equations, exactly solvable problems and non-analytic nonlinearities. Izvestiya Vysshikh Uchebnykh Zavedeniy. Prikladnaya Nelineynaya Dinamika, 26(3), 7-34
Open this publication in new window or tab >>«exotic» models of high-intensity wave physics: Linearizing equations, exactly solvable problems and non-analytic nonlinearities
2018 (English)In: Izvestiya Vysshikh Uchebnykh Zavedeniy. Prikladnaya Nelineynaya Dinamika, ISSN 0869-6632, Vol. 26, no 3, p. 7-34Article in journal (Refereed) Published
Abstract [en]

Topic and aim. A brief review of publications and discussion of some mathematical models are presented, which, in the author's opinion, are well-known only to a few specialists. These models are not well studied, despite their universality and practical significance. Since the results were published at different times and in different journals, it is useful to summarize them in one article. The goal is to form a general idea of the subject for the readers and to interest them with mathematical, physical or applied details described in the cited references. Investigated models. Higher-order dissipative models are discussed. Precisely linearizable equations containing nonanalytic nonlinearities -quadratically-cubic (QC) and modular (M) -are considered. Equations like Burgers, KdV, KZ, Ostrovsky-Vakhnenko, inhomogeneous and nonlinear integro-differential equations are analyzed. Results. The appearance of dissipative oscillations near the shock front is explained. The formation in the QC-medium of compression and rarefaction shocks, which are stable only for certain parameters of the «jump», as well as the formation of periodic trapezoidal sawtooth waves and self-similar N-pulse signals are described. Collisions of single pulses in the M-medium are discussed, revealing new corpuscular properties (mutual absorption and annihilation). Collisions are similar to inter-actions of clusters of chemically reacting substances, for example, fuel and oxidizer. The features of the behavior of «modular» solitons are described. The phenomenon of nonlinear wave resonance in media with QC-, Q-and M-nonlinearities is studied. Precisely linearizable inhomogeneous equations with external sources are used. The shift of maximum of resonance curves relative to the linear position, which is determined by the equality of velocities of freely propagating and forced waves, is indicated. Simplified models for diffracting beams obtained by projecting 3D equations onto the beam axis are analyzed. Strongly nonlinear waves in systems with holonomic constraints are discussed. Integro-differential equations with relaxation type kernel, and the possibility of reducing them to differential and differential-difference equations are considered. Discussion. The material is outlined on a popular level. Apparently, these studies can be continued if the readers find them interesting enough. © 2018 Saratov State University. All rights reserved.

Place, publisher, year, edition, pages
Saratov State University, 2018
Keywords
Dissipative models, Linearizing equations, Q-and M-non-linearities, QC-, Shock fronts
National Category
Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-16914 (URN)10.18500/0869-6632-2018-26-3-7-34 (DOI)2-s2.0-85050114272 (Scopus ID)
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2018-08-20Bibliographically approved
Nefedov, N. N. & Rudenko, O. (2018). On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification. Doklady. Mathematics, 97(1), 99-103
Open this publication in new window or tab >>On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification
2018 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 99-103Article in journal (Refereed) Published
Abstract [en]

A singularly perturbed initial-boundary value problem for a parabolic equation known in applications as a Burgers-type or reaction-diffusion-advection equation is considered. An asymptotic approximation of solutions with a moving front is constructed in the case of modular and quadratic nonlinearity and nonlinear amplification. The influence exerted by nonlinear amplification on front propagation and blowing- up is determined. The front localization and the blowing-up time are estimated.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER, 2018
National Category
Other Mathematics Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-16079 (URN)10.1134/S1064562418010143 (DOI)000427590400026 ()
Available from: 2018-04-06 Created: 2018-04-06 Last updated: 2018-04-06Bibliographically approved
Rudenko, O. & Hedberg, C. (2018). SINGLE SHOCK AND PERIODIC SAWTOOTH-SHAPED WAVES IN MEDIA WITH NON-ANALYTIC NONLINEARITIES. Mathematical Modelling of Natural Phenomena, 13(2), Article ID UNSP 18.
Open this publication in new window or tab >>SINGLE SHOCK AND PERIODIC SAWTOOTH-SHAPED WAVES IN MEDIA WITH NON-ANALYTIC NONLINEARITIES
2018 (English)In: Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, E-ISSN 1760-6101, Vol. 13, no 2, article id UNSP 18Article in journal (Refereed) Published
Abstract [en]

The review of new mathematical models containing non-analytic nonlinearities is given. These equations have been proposed recently, over the past few years. The models describe strongly nonlinear waves of the first type, according to the classification introduced earlier by the authors. These models are interesting because of two reasons: (i) equations admit exact analytic solutions, and (ii) solutions describe the real physical phenomena. Among these models are modular and quadratically cubic equations of Hopf, Burgers, Korteveg-de Vries, Khokhlov-Zabolotskaya and Ostrovsky-Vakhnenko type. Media with non-analytic nonlinearities exist among composites, meta-materials, inhomogeneous and multiphase systems. Some physical phenomena manifested in the propagation of waves in such media are described on the qualitative level of severity.

Place, publisher, year, edition, pages
EDP SCIENCES S A, 2018
Keywords
Equations of Hopf, Burgers, KdV, KZ and Ostrovsky-Vakhnenko types, exact solutions, modular solutions, quadratically-cubic nonlinearity, shocks of rarefaction, triangular and trapezoidal saw
National Category
Other Mathematics Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-17017 (URN)10.1051/mmnp/2018028 (DOI)000443894600003 ()
Available from: 2018-09-20 Created: 2018-09-20 Last updated: 2018-09-20Bibliographically approved
Rudenko, O. & Gurbatov, S. N. (2018). Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems. Doklady. Mathematics, 97(1), 95-98
Open this publication in new window or tab >>Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems
2018 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 95-98Article in journal (Refereed) Published
Abstract [en]

A one-dimensional equation is presented that generalizes the Burgers equation known in the theory of waves and in turbulence models. It describes the nonlinear evolution of waves in pipes of variable cross section filled with a dissipative medium, as well as in ray tubes, if the approximation of geometric acoustics of an inhomogeneous medium is used. The generalized equation is reduced to the common Burgers equation with a dissipative parameter-the "Reynolds-Goldberg number," depending on the coordinate. The method for solving statistical problems corresponding to specified characteristics of a noise signal at the input of the system is described. Integral expressions for exact solutions are given for the correlation function and the noise intensity spectrum experiencing nonlinear distortions during propagation in a waveguide. For waves in a dissipative medium, an approximate method of calculating statistical characteristics is given, consisting in finding an auxiliary correlation function and the subsequent nonlinear functional transformation. Solutions have a complicated form, so physical analysis of phenomena requires the numerical methods. For some correlation functions of stationary noise with initial Gaussian statistics and some waveguide systems, it is possible to obtain simple results.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER, 2018
National Category
Other Mathematics Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-16078 (URN)10.1134/S1064562418010040 (DOI)000427590400025 ()
Available from: 2018-04-06 Created: 2018-04-06 Last updated: 2018-04-06Bibliographically approved
Rudenko, O. (2018). Wave Excitation in a Dissipative Medium with a Double Quadratically-Modular Nonlinearity: a Generalization of the Inhomogeneous Burgers Equation. Doklady. Mathematics, 97(3), 279-282
Open this publication in new window or tab >>Wave Excitation in a Dissipative Medium with a Double Quadratically-Modular Nonlinearity: a Generalization of the Inhomogeneous Burgers Equation
2018 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 3, p. 279-282Article in journal (Refereed) Published
Abstract [en]

Solutions of a forced (inhomogeneous) partial differential equation of the second order with two types of nonlinearity: power (quadratic) and nonanalytic (modular) are found. Equations containing each of these nonlinearities separately were studied earlier. A natural continuation of these studies is the development of the theory of wave phenomena in a medium with a double nonlinearity, which have recently been observed in experiments. Here solutions describing the profiles of intense waves are derived. Shapes of freely propagating stationary perturbations in the form of shock waves with a finite front width are found. The profiles of forced waves excited by external sources are calculated.

Place, publisher, year, edition, pages
MAIK NAUKA/INTERPERIODICA/SPRINGER, 2018
National Category
Other Mechanical Engineering
Identifiers
urn:nbn:se:bth-16902 (URN)10.1134/S1064562418030110 (DOI)000438890200021 ()
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2018-08-20Bibliographically approved
Rudenko, O. & Hedberg, C. (2018). Wave Resonance in Media with Modular, Quadratic and Quadratically-Cubic Nonlinearities Described by Inhomogeneous Burgers-Type Equations. Acoustical Physics, 64(4), 422-431
Open this publication in new window or tab >>Wave Resonance in Media with Modular, Quadratic and Quadratically-Cubic Nonlinearities Described by Inhomogeneous Burgers-Type Equations
2018 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 64, no 4, p. 422-431Article in journal (Refereed) Published
Abstract [en]

The phenomenon of “wave resonance” which occurs at excitation of traveling waves in dissipative media possessing modular, quadratic and quadratically-cubic nonlinearities is studied. The mathematical model of this phenomenon is the inhomogeneous (or “forced”) equation of Burgers type. Such nonlinearities are of interest because the corresponding equations admit exact linearization and describe real physical objects. The presence of “accompanying sources” (traveling with the wave) on the right-hand side of the inhomogeneous equations ensures the inflow of energy into the wave, which thereafter spreads throughout the wave profile, flows to emerging shock fronts, and then dissipates due to linear and nonlinear losses. As an introduction, the phenomenon of wave resonance in ideal and dissipative media is described and physical examples are given. Exact expressions for nonlinear steady-state wave profiles are derived. Non-stationary processes of wave generation, spatial “beating” of amplitudes with different relationship between the speed of motion of the sources and the natural wave velocity in the medium are studied. Resonance curves are constructed that contain a nonlinear shift of the absolute maxima to the “supersonic” region. The features of the resonance in each of the three types of nonlinearity are discussed. © 2018, Pleiades Publishing, Ltd.

Place, publisher, year, edition, pages
Pleiades Publishing, 2018
Keywords
excitation of nonlinear wave, inhomogeneous Burgers-type equation, modular, quadratic, quadratically cubic nonlinearity, wave resonance, Nonlinear equations, Resonance, Wave propagation, Cubic nonlinearities, Nonlinear waves, Wave resonances, Control nonlinearities
National Category
Other Mathematics
Identifiers
urn:nbn:se:bth-16906 (URN)10.1134/S1063771018040127 (DOI)000439751800005 ()2-s2.0-85050096276 (Scopus ID)
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2018-08-21Bibliographically approved
Rudenko, O. & Hedberg, C. (2017). A new equation and exact solutions describing focal fields in media with modular nonlinearity. Nonlinear dynamics, 89(3), 1905-1913
Open this publication in new window or tab >>A new equation and exact solutions describing focal fields in media with modular nonlinearity
2017 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 89, no 3, p. 1905-1913Article in journal (Refereed) Published
Abstract [en]

Brand-new equations which can be regarded as modifications of Khokhlov–Zabolotskaya–Kuznetsov or Ostrovsky–Vakhnenko equations are suggested. These equations are quite general in that they describe the nonlinear wave dynamics in media with modular nonlinearity. Such media exist among composites, meta-materials, inhomogeneous and multiphase systems. These new models are interesting because of two reasons: (1) the equations admit exact analytic solutions and (2) the solutions describe real physical phenomena. The equations model nonlinear focusing of wave beams. It is shown that inside the focal zone a stationary waveform exists. Steady-state profiles are constructed by the matching of functions describing the positive and negative branches of exact solutions of an equation of Klein–Gordon type. Such profiles have been observed many times during experiments and numerical studies. The non-stationary waves can contain singularities of two types: discontinuity of the wave and of its derivative. These singularities are eliminated by introducing dissipative terms into the equations—thereby increasing their order. © 2017 The Author(s)

Place, publisher, year, edition, pages
Springer Netherlands, 2017
Keywords
Bimodular media, Exact solution, Focusing, HIFU, High-intensity focused ultrasound, Modified KZ–OV, Modular nonlinearity, Nonlinear partial differential equation, Control nonlinearities, Partial differential equations, High intensity focused ultrasound, Nonlinear partial differential equations, Nonlinear equations
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:bth-14471 (URN)10.1007/s11071-017-3560-8 (DOI)000405962800025 ()2-s2.0-85019632379 (Scopus ID)
Available from: 2017-06-13 Created: 2017-06-13 Last updated: 2017-08-22Bibliographically approved
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