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  • 1.
    Broman, Göran
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Rudenko, Oleg
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Instability of water jet: Aerodynamically induced acoustic and capillary waves2012In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 58, no 5, p. 537-541Article in journal (Refereed)
    Abstract [en]

    High-speed water jet cutting has important industrial applications. To further improve the cutting performance it is critical to understand the theory behind the onset of instability of the jet. In this paper, instability of a water jet flowing out from a nozzle into ambient air is studied. Capillary forces and compressibility of the liquid caused by gas bubbles are taken into account, since these factors have shown to be important in previous experimental studies. A new dispersion equation, generalizing the analogous Rayleigh equation, is derived. It is shown how instability develops because of aerodynamic forces that appear at the streamlining of an initial irregularity of the equilibrium shape of the cross-section of the jet and how instability increases with increased concentration of gas bubbles. It is also shown how resonance phenomena are responsible for strong instability. On the basis of the theoretical explanations given, conditions for stable operation are indicated.

  • 2. Broman, Göran
    et al.
    Rudenko, Oleg
    Submerged Landau jet: exact solutions, their meaning and application2010In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 53, no 1, p. 91-98Article, review/survey (Refereed)
    Abstract [en]

    Exact hydrodynamic solutions generalizing the Landau submerged jet solution are reviewed. It is shown how exact inviscid solutions can be obtained and how boundary layer viscosity can be included by introducing parabolic coordinates. The use of exact solutions in applied hydrodynamics and acoustics is discussed. A historical perspective on the discovery of a class of exact solutions and on the analysis of their physical meaning is presented.

  • 3. Demin, I.Yu.
    et al.
    Pronchatov-Rubtsov, N.V.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Gurbatov, S.N.
    Krainov, A.
    The numerical simulation of propagation of intensive acoustic noise2013Conference paper (Refereed)
    Abstract [en]

    The propagation of intensive acoustic noise is of fundamental interest in nonlinear acoustics. Some of the simplest models describing such phenomena are generalized Burgers’ equations for finite amplitude sound waves. An important problem in this field is to find the wave’s behavior far from the emitting source for stochastic initial waveforms. The method of numerical solution of generalized Burgers equation proposed is step-by-step calculation supported on using Fast Fourier Transform of the considered signal. The general idea is to keep only Fourier image of concerned signal and update it recursively (in space). For simulating the wave evolution we used 4096 (212) point realizations and took averaging over 1000 realizations. Also the object of the present study is a numerical analysis of the spectral and bispectral functions of the intense random signals propagating in nondispersive nonlinear media. The possibility of recovering the input spectrum from the measured spectrum and bispectrum at the output of the nonlinear medium is discusses. The analytical estimations are supported by numerical simulation. For two different types of primary spectrum evolution of jet noise were numerically simulates at a short distance and assayed bispectrum and a spectrum analysis of the signals.

  • 4. Dubkov, Alexander
    et al.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Gurbatov, Sergey
    Probability characteristics of nonlinear dynamical systems driven by delta -pulse noise2016In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 93, no 6, article id 062125Article in journal (Refereed)
    Abstract [en]

    For a nonlinear dynamical system described by the first-order differential equation with Poisson white noise having exponentially distributed amplitudes of δ pulses, some exact results for the stationary probability density function are derived from the Kolmogorov-Feller equation using the inverse differential operator. Specifically, we examine the "effect of normalization" of non-Gaussian noise by a linear system and the steady-state probability density function of particle velocity in the medium with Coulomb friction. Next, the general formulas for the probability distribution of the system perturbed by a non-Poisson δ-pulse train are derived using an analysis of system trajectories between stimuli. As an example, overdamped particle motion in the bistable quadratic-cubic potential under the action of the periodic δ-pulse train is analyzed in detail. The probability density function and the mean value of the particle position together with average characteristics of the first switching time from one stable state to another are found in the framework of the fast relaxation approximation. © 2016 American Physical Society.

  • 5. Dvoesherstov, M.Yu.
    et al.
    Cherednik, V.I.
    Bosov, S.I.
    Orlov, I.Ya.
    Rudenko, Oleg
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Numerical and experimental analysis of the parameters of an electroacoustic thin-film microwave resonator2013In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 59, no 5, p. 513-520Article in journal (Refereed)
    Abstract [en]

    The results of numerical and experimental analysis of the parameters of a singlefrequency micro wave thinfilm electroacoustic resonator based on an (0001)AlN piezofilm with an acoustic reflector operat ing at a frequency of 10 GHz are presented. The effect of the reflector design on the resonator characteristics is considered. Using the modified Butterworth–Van Dyke model, it was shown that the ohmic resistance of electrodes and entrance paths substantially decreases the Qfactor at the resonance frequency of series and the acoustic losses in the resonator deteriorate the Qfactor at the parallel resonance frequency

  • 6. Enflo, Bengt
    et al.
    Hedberg, Claes
    Rudenko, Oleg
    Nonlinear standing waves in a closed tub2002Conference paper (Refereed)
    Abstract [en]

    Simplified nonlinear evolution equations describing nonsteady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach is used based on a nonlinear functional equation. This approach is shown to be equivalent to the version of the successive approximation method developed in 1964 by Chester. It is explained how the acoustic field in the cavity is described as a sum of counterpropagating waves with no cross-interaction. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. Some results from a perturbation calculation of the wave profile are given.

  • 7. Enflo, Bengt
    et al.
    Hedberg, Claes
    Rudenko, Oleg
    Resonant properties of a nonlinear dissipative layer excited by a vibrating boundary: Q-factor and frequency response2005In: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 117, no 2, p. 601-612Article in journal (Refereed)
    Abstract [en]

    Simplified nonlinear evolution equations describing non-steady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach based on a nonlinear functional equation is used. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. The process of development of a standing wave is described analytically on the base of exact nonlinear solutions for different laws of periodic motion of the wall. For harmonic excitation the wave profiles are described by Mathieu functions, and their mean energy characteristics by the corresponding eigenvalues. The sawtooth-shaped motion of the boundary leads to a similar process of evolution of the profile, but the solution has a very simple form. Some possibilities to enhance the Q-factor of a nonlinear system by suppression of nonlinear energy losses are discussed. (C) 2005 Acoustical Society of America.

  • 8. Enflo, Bengt
    et al.
    Hedberg, Claes
    Rudenko, Oleg
    Standing and propagating waves in cubically nonlinear media2006In: Proceedings of the International Conference Mathematical Modelling / [ed] Nilsson, Börje, American Institute of Physics , 2006, p. 187-195Chapter in book (Other academic)
    Abstract [en]

    The paper has three parts. In the first part a cubically nonlinear equation is derived for a transverse finite-amplitude wave in an isotropic solid. The cubic nonlinearity is expressed in terms of elastic constants. In the second part a simplified approach for a resonator filled by a cubically nonlinear medium results in functional equations. The frequency response shows the dependence of the amplitude of the resonance on the difference between one of the resonator's eigenfrequencies and the driving frequency. The frequency response curves are plotted for different values of the dissipation and differ very much for quadratic and cubic nonlinearities. In the third part a propagating N-wave is studied, which fulfils a modified Burgers' equation with a cubic nonlinearity. Approximate solutions to this equation are found for new parts of the wave profile.

  • 9. Enflo, Bengt
    et al.
    Rudenko, Oleg
    Hedberg, Claes
    Nonlinear Standing Waves in a Layer Excited by the Periodic Motion of its Boundary2002Conference paper (Refereed)
    Abstract [en]

    Simplified nonlinear evolution equations describing nonsteady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach is used based on a nonlinear functional equation. This approach is shown to be equivalent to the version of the successive approximation method developed in 1964 by Chester. It is explained how the acoustic field in the cavity is described as a sum of counterpropagating waves with no cross-interaction. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. The process of development of a standing wave is described analytically for three different types of periodic motion of the wall: harmonic excitation, sawtooth-shaped motion and "inverse saw motion".

  • 10. Gazizov, Rafail
    et al.
    Ibragimov, Nail
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Effect of resonant absorption in viscous and dry vibrating contact: Mathematical models and theory connected with slow dynamics and friction welding2014In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 19, no 2, p. 337-344Article in journal (Refereed)
    Abstract [en]

    Process of heating of thin layer located between two vibrating surfaces is studied. Energy loss goes on due to viscous or dry friction. Optimal quantities of shear viscosity and friction corresponding to maximum energy loss are determined. Resonant behavior of loss must be taken into account in the description of "slow dynamics" of rocks and materials exposed to high-intensity seismic or acoustic irradiation as well as in various technologies. Bonding of materials by linear friction welding, widely used in propulsion engineering, can exemplify such a technology.

  • 11.
    Gray, Amber
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    An Intense Wave in Defective Media Containing Both Quadratic and Modular Nonlinearities: Shock Waves, Harmonics, and Nondestructive Testing2018In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 64, no 4, p. 402-407Article in journal (Refereed)
    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.

  • 12.
    Gurbatov, S. N.
    et al.
    NI Lobachevsky State Univ Nizhny Novgorod, Nizhnii Novgorod, Russia..
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. NI Lobachevsky State Univ Nizhny Novgorod, Nizhnii Novgorod, Russia.;Moscow MV Lomonosov State Univ, Moscow, Russia.;AM Prokhorov Inst Gen Phys, Moscow, Russia.;Russian Acad Sci, OYu Shmidt Inst Terr Phys, Moscow, Russia.;Blekinge Inst Technol, Karlskrona, Sweden..
    On the Inverse Problems of Nonlinear Acoustics and Acoustic Turbulence2015In: Radiophysics and Quantum Electronics, ISSN 0033-8443, E-ISSN 1573-9120, Vol. 58, no 7, p. 463-476Article in journal (Refereed)
    Abstract [en]

    We consider the problem of retrieval of the radiated acoustic signal parameters from the measured wave field in some cross section of the nonlinear medium. The possibilities of solving regular and statistical inverse problems are discussed on the basis of the solution of the Burgers equation for zero and infinitesimal viscosities.

  • 13.
    Gurbatov, S. N.
    et al.
    Nizhnii Novgorod State Univ, RUS.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Tyurina, A. V.
    Nizhnii Novgorod State Univ, RUS.
    Transformation of High-Frequency Noise in the Field of a Shockwave2018In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 64, no 5, p. 555-562Article in journal (Refereed)
    Abstract [en]

    We study the interaction of noise and regular signals with a front whose steepness increases or decreases owing to nonlinear distortion of the profile of an intense pumping wave. Projective transformation is used, which is a result of one of the Burgers equation symmetries. Signal interaction with the pumping wave at its leading edge results in an increase in signal amplitude, a decrease in its time scale, an increase in the signal evolution rate, and earlier merging of discontinuities. At the trailing edge, an increase in signal amplitude, an increase in the time scale, and deceleration of the evolution rate occur. Formulas are obtained that describe the transformation of the spectrum and the correlation function of noise. Laws of the change in noise energy for both small and large Reynolds numbers are found. We study the interaction of weak noise with a nonstationary shock front in a medium with a finite viscosity. It is shown that, owing to competition between amplification at the shock front and high-frequency attenuation, the dependence on the noise intensity on distance has a nonmonotonic character, and at large distances, the intensity tends to zero, while the correlation time tends to a finite value.

  • 14. Gusev, V. A.
    et al.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Nonlinear sound in a gas-saturated sediment layer2015In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 61, no 2, p. 152-164Article in journal (Refereed)
    Abstract [en]

    Wave propagation in a near-bottom layer containing gas bubbles is analyzed. Evolution equations are derived for intense acoustic waves and wave beams in a medium with an inhomogeneous bubble distribution. The field of an intense beam along the axis of the focusing sound channel is calculated. The coefficients of reflection and passage of sound from a homogeneous medium into a bubble layer and back again are calculated. It is shown that the near-bottom layer can effectively trap rays incident on it and ensure a waveguide propagation character. The presence of bubbles increases both the interval of angles at which the wave penetrates the layer and the interval of angles at which rays undergo total internal reflection and do not depart the layer. The acoustic field in the layer from a point source is calculated.

  • 15. Gusev, V.A.
    et al.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Intensification of the impact of high-intensity focused ultrasound (HIFU) with special spatiotemporal modulation2013In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 59, no 1, p. 45-50Article in journal (Refereed)
    Abstract [en]

    The principle of forming a special form of powerful acoustic signals is proposed, which makes it possible to ensure precise spatiotemporal beam focusing. The introduction of a transverse-coordinate-dependent local wave frequency is suggested, due to which the equality of the formation lengths of a discontinuity for all rays is achieved. This thereby ensures an increase in nonlinear absorption; as a result, the temperature and radiation action of focused ultrasound on the medium increase.

  • 16. Gusev, V.A.
    et al.
    Rudenko, Oleg
    The Field of Radiative Forces and the Acoustic Streaming in a Liquid Layer on a Solid Half-Space2010In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 56, no 6, p. 861-870Article in journal (Refereed)
    Abstract [en]

    The acoustic field and the field of radiative forces that are formed in a liquid layer on a solid substrate are calculated for the case of wave propagation along the interface. The calculations take into account the effects produced by surface tension, viscous stresses at the boundary, and attenuation in the liquid volume on the field characteristics. The dispersion equations and the velocities of wave propagation are determined. The radiative forces acting on a liquid volume element in a standing wave are calculated. The structure of streaming is studied. The effect of streaming on small size particles is considered, and the possibilities of ordered structure formation from them are discussed.

  • 17. Haller, Kristian
    et al.
    Hedberg, Claes
    Rudenko, Oleg
    Slow variations of mechanical and electrical properties of dielectrics and nonlinear phenomena at ultrasonic irradiation2010In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 56, no 5, p. 660-664Article in journal (Refereed)
    Abstract [en]

    The interconnection between variations of elasticity and dielectric permittivity of mesoscopic solid systems under exposure to ultrasound is experimentally observed. A phenomenological theory generalizing Debye’s approach for polar fluids is developed to explain the measured data. The substitution of acoustic measurements by dielectric ones not only simplifies the procedure, but offers new possibilities to remotely evaluate the mechanical properties of materials and natural media.

  • 18.
    Hedberg, Claes
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Collisions, mutual losses and annihilation of pulses in a modular nonlinear medium2017In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 90, no 3, p. 2083-2091Article in journal (Refereed)
    Abstract [en]

    One of the most important sections of nonlinear wave theory is related to the collisions of single pulses. These often exhibit corpuscular properties. For example, it is well known that solitons described by the Korteweg–de Vries equation and a few other conservative model equations exhibit properties of elastic particles, while shock waves described by dissipative models like Burgers’ equation stick together as absolutely inelastic particles when colliding. The interactions of single pulses in media with modular nonlinearity considered here reveal new physical features that are still poorly understood. There is an analogy between the single pulses collision and the interaction of clots of chemical reactants, such as fuel and oxidant, where the smaller component disappears and the larger one decreases after a reaction. At equal “masses” both clots can be annihilated. In this work various interactions of two and three pulses are considered. The conditions for which a complete annihilation of the pulses occurs are indicated. © 2017 The Author(s)

  • 19. Hedberg, Claes
    et al.
    Rudenko, Oleg
    Dissipative and hysteresis loops as images of irreversible processes in nonlinear acoustic fields2011In: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 110, no 5Article in journal (Refereed)
    Abstract [en]

    Irreversible processes taking place during nonlinear acoustic wave propagation are considered using a representation by loops in a thermodynamic parameter space. For viscous and heat conducting media, the loops are constructed for quasi-harmonic and sawtooth waves and the descriptive equations are formulated. The linear and nonlinear absorptions are compared. For relaxing media, the processes are frequency-dependent. The loops broadens, narrows, and bends. The linear and nonlinear relaxation losses of wave energy are shown. Residual stresses and irreversible strains appear for hysteretic media, and here, a generalization of Rayleigh loops is pictured which takes into account the nonlinearly frequency-dependent hereditary properties. These describe the dynamic behavior, for which new equations are derived.

  • 20. Hedberg, Claes
    et al.
    Rudenko, Oleg
    Interaction between low and high-frequency Modes in a Nonlinear System: Gas-Filled Cylinder Covered by a movable Piston2003In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 32, no 4, p. 405-416Article in journal (Refereed)
    Abstract [en]

    A simple mechanical system containing a low-frequency vibration mode and set of high-frequency acoustic modes is considered. The frequency response is calculated. Nonlinear behaviour and interaction between modes is described by system of functional equations. Two types of nonlinearities are taken into account. The first one is caused by the finite displacement of a movable boundary, and the second one is the volume nonlinearity of gas. New mathematical models based on nonlinear equations are suggested. Some examples of nonlinear phenomena are discussed on the base of derived solutions.

  • 21.
    Hedberg, Claes
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Nonlinear acoustics of structurally complex materials described by non-analytic nonlinearities2018In: 25th International Congress on Sound and Vibration 2018, ICSV 2018: Hiroshima Calling, International Institute of Acoustics and Vibration, IIAV , 2018, p. 1993-1998Conference paper (Refereed)
    Abstract [en]

    Everybody is accustomed to that nonlinear effects amplify with increasing amplitude or intensity of a wave. When the amplitude becomes small, the nonlinearity disappears and the wave enters a linear regime. Instead, we shall consider here so-called strong nonlinearity of the first type (according to a classification introduced earlier by the authors) where the effects of nonlinearity do not disappear even for infinitesimal amplitudes. Among these nonlinearities are modular (M) and quadratically-cubic (QC). When these nonlinearities are included in partial differential equations, they form new mathematical models describing new physical effects. Such equations have been proposed over the past few years and a review of these models is given here. They are interesting because of two reasons: (i) the equations admit exact analytic solutions, and (ii) the solutions describe real physical phenomena. Among them are M- and QC-equations of Hopf, Burgers, Korteveg-de Vries, Khokhlov-Zabolotskaya and Ostrovsky-Vakhnenko types. Media with non-analytic nonlinearities exist among composites, meta-materials, and inhomogeneous and multiphase systems. Some of the physical phenomena manifested in such media are described, e.g. stable shock fronts of compression and rarefaction in QC-media. The last cannot exist in usual media and the periodic wave consists of a series of trapezoidal teeth, rather than usual triangular. In an M-nonlinear medium collision, mutual losses and annihilation of pulses are studied. These pulses exhibit corpuscular properties and, in contrast to solitons (elastic particles) and shock waves (absolutely inelastic collisions), they behave like clots of chemical reagents (fuel and oxidizer). As result of an reaction, the smaller component disappears, and the larger decreases. At equal "masses", these clots disappear or annihilate. In M-media a new stable wave - a modular soliton - exists. Other interesting physical phenomena occur for focused waves in M-media and a review of these is also included in the presentation. Copyright © (2018) by International Institute of Acoustics & Vibration.All rights reserved.

  • 22. Hedberg, Claes
    et al.
    Rudenko, Oleg
    Pulse response of a nonlinear layer2001In: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 110, no 5, p. 2340-2350Article in journal (Refereed)
    Abstract [en]

    A simple analytical theory is developed for the description of non-steady state response of a thin nonlinear layer, which differs markedly in its linear properties from the surrounding medium. Such a layer can model the behavior of real inhomogeneities like a cloud of gas bubbles in a liquid, a crack or split plane in a solid, or the contact between two slightly tighted rough surfaces. Both weakly nonlinear pulse and harmonic responses are calculated and the general properties of the spectral and temporal structure of the scattered field are discussed. The exact strongly nonlinear solutions are derived for a special type of stress-strain relationship corresponding to the behavior of real condensed media under strong load. Profiles and spectra shown are in conformity with experimental results. The pulse response on the short delta-pulse shaped incident wave is calculated for arbitrary nonlinear properties of the layer. The possibilities to apply the sets of data on measured characteristics of pulse response in the solution of inverse problems are briefly discussed.

  • 23. Ibragimov, Nail H.
    et al.
    Meleshko, Sergey
    Rudenko, Oleg
    Group analysis of evolutionary integro-differential equations describing nonlinear waves: General model2011In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 44, no 31Article in journal (Refereed)
    Abstract [en]

    The paper deals with an evolutionary integro-differential equation describing nonlinear waves. Particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov-Zabolotskaya equation, the Kadomtsev-Petviashvili equation and others. Since solutions of these equations describe many physical phenomena, analysis of the general model studied in the paper equation is important. One of the methods for obtaining solutions differential equations is provided by the Lie group analysis. However, this method is not applicable to integro-differential equations. Therefore we discuss new approaches developed in modern group analysis and apply them to the general model considered in the present paper. Reduced equations and exact solutions are also presented.

  • 24. Ibragimov, Nail H.
    et al.
    Rudenko, Oleg
    Principle of an a priori use of symmetries in the theory of nonlinear waves.2004In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 50, no 4, p. 406-419Article in journal (Refereed)
    Abstract [en]

    The principle of an a priori use of symmetries is proposed as a new approach to solving nonlinear problems on the basis of a reasonable complication of mathematical models. This approach often provides additional symmetries, and hence opens possibilities to find new analytical solutions. The potentialities of the proposed approach are illustrated by applying to problems of nonlinear acoustics.

  • 25. Lebedev-Stepanov, P. V.
    et al.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Acoustic microfluidics: Capillary waves and vortex flows in the cylindrical volume of a fluid drop2015In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 61, no 2, p. 173-177Article in journal (Refereed)
    Abstract [en]

    We calculate the field of radiation forces in a cylindrical fluid layer on a solid substrate formed as a result of the action on a fluid of a capillary wave propagating from the axis along a free surface. We study the structure of acoustic flows excited by the radiation forces. We discuss the action of flows on small-sized particles and the possibilities of these particles to form ordered structures. © 2015, Pleiades Publishing, Ltd.

  • 26. Lebedev-Stepanov, P.V.
    et al.
    Rudenko, Oleg
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Acoustic Flows in a Fluid Layer on a Vibrating Substrate2013In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 59, no 6, p. 640-643Article in journal (Refereed)
    Abstract [en]

    The field of radiation forces in a fluid layer on a solid substrate is calculated. This field is formed during propagation of surface capillary wave along a free surface. The wave is excited by substrate vibrations as a result of instability development. The structure of acoustic flows is studied. Their effect on small size particles and the possibilities of generating ordered structures from these particles are discussed.

  • 27. Mfoumou, Etienne
    et al.
    Rudenko, Oleg
    Hedberg, Claes
    Kao-Walter, Sharon
    Acoustical measurement accompanying tensile test: new modality for non-destructive testing and characterization of sheet materials2006Conference paper (Refereed)
    Abstract [en]

    A series of uniaxial tensile tests was performed for sheet materials like paperboard, polyethylene and packing layered composites. These sheets can be considered as membranes. In parallel with a tensile test, the natural frequency was measured through an acoustical excitation. Firstly, it was shown both theoretically and experimentally that, at a given load, the frequency is sensitive to the local deviation in the standard thickness or to the presence of cracks inside the material. It means that this acoustic measurement can be used as one of the methods of damage assessment, or nondestructive testing in general. Secondly, the resonance frequency shift was continuously monitored for increasing strain on polyethylene and paperboard, and the curves obtained were compared to the stress-strain curves for material characterization. They were not the same and showed a non-monotonic stiffness variation for the polyethylene. It was shown that the resonance frequency shift measurement can successfully replace the stress-strain curve for material characterization under tensile test. During a long time under load an irreversible plastic deformation of the sample takes place, and the frequency shift can also serve as a new method for evaluating the residual strain of the material.

  • 28.
    Mikhailov, S. G.
    et al.
    Lomonosov Moscow State University, RUS.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    A Simple Bimodular Nonlinear Element2018In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 64, no 3, p. 293-298Article in journal (Refereed)
    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.

  • 29.
    Mikhailov, S. G.
    et al.
    Moscow MV Lomonosov State Univ, RUS.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    A simple nonlinear element model2017In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 63, no 3, p. 270-274Article in journal (Refereed)
    Abstract [en]

    We study experimentally the behavior of a nonlinear element, a light plate pressed to the opening in the cavity of an acoustic resonator. Measurements of field oscillations inside and outside the cavity have shown that for large amplitudes, they become essentially anharmonic. The time dependences of displacement of the plate with increasing amplitude of the exciting voltage demonstrates a gradual change in the shape of vibrations from harmonic to half-period oscillation. A constant component appears in the cavity: rarefaction or outflow of the medium through the orifice. We construct a theory for nonlinear oscillations of a plate taking into account its different elastic reactions to compression and rarefaction with allowance for monopole radiation by the small-wave-size plate or radiation of a plane wave by the plate. We calculate the amplitudes of the harmonics and solve the problem of low-frequency stationary noise acting on the plate. We obtain expressions for the correlation function and mean power at the output given a normal random process at the input.

  • 30.
    Nefedov, N. N.
    et al.
    Moscow MV Lomonosov State Univ, RUS.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification2018In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 99-103Article in journal (Refereed)
    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.

  • 31. Ostrovsky, L. A.
    et al.
    Rudenko, Oleg
    What Problems of Nonlinear Acoustics Seem to be Important and Interesting Today2008Conference paper (Refereed)
    Abstract [en]

    The purpose of this presentation is to briefly outline the progress and achievements that have occurred in some areas of nonlinear acoustics during recent years. © 2008 American Institute of Physics.

  • 32.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    A nonlinear screen as an element for sound absorption and frequency conversion systems2016In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 62, no 1, p. 46-50Article in journal (Refereed)
    Abstract [en]

    The paper discusses a model for a screen with dissipative and nonlinear elastic properties that can be used in acoustic sound absorption and frequency conversion systems. Calculation and estimation schemes are explained that are necessary for understanding the functional capabilities of the device. Examples of the nonlinear elements in the screen and promising applications are described.

  • 33.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities2016In: Doklady Mathematics, ISSN 1064-5624, Vol. 94, no 3, p. 703-707Article in journal (Refereed)
    Abstract [en]

    A second-order partial differential equation admitting exact linearization is discussed. It contains terms with nonlinearities of three types—modular, quadratic, and quadratically cubic—which can be present jointly or separately. The model describes nonlinear phenomena, some of which have been studied, while others call for further consideration. As an example, individual manifestations of modular nonlinearity are discussed. They lead to the formation of singularities of two types, namely, discontinuities in a function and discontinuities in its derivative, which are eliminated by dissipative smoothing. The dynamics of shock fronts is studied. The collision of two single pulses of different polarity is described. The process reveals new properties other than those of elastic collisions of conservative solitons and inelastic collisions of dissipative shock waves.

  • 34.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Exact solutions of an integro-differential equation with quadratically cubic nonlinearity2016In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 94, no 1, p. 468-471Article in journal (Refereed)
    Abstract [en]

    Exact solutions of a nonlinear integro-differential equation with quadratically cubic nonlinear term are found. The equation governs, in particular, stationary shock wave propagation in relaxing media. For the exponential kernel the shapes of both compression and rarefaction shocks having a finite width of the front are calculated. For media with limited "memorizing time" the difference relation permitting the construction of wave profile by the mapping method is derived. The initial equation is rather general. It governs the evolution of nonlinear waves in real distributed systems, for example, in biological tissues, structurally inhomogeneous media and in some meta-materials.

  • 35.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    «exotic» models of high-intensity wave physics: Linearizing equations, exactly solvable problems and non-analytic nonlinearities2018In: Izvestiya Vysshikh Uchebnykh Zavedeniy. Prikladnaya Nelineynaya Dinamika, ISSN 0869-6632, Vol. 26, no 3, p. 7-34Article in journal (Refereed)
    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.

  • 36. Rudenko, Oleg
    Giant nonlinearities in structurally inhomogeneous media and the fundamentals of nonlinear acoustic diagnostic techniques2006In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 49, no 1, p. 69-87Article, review/survey (Refereed)
  • 37.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Modular solutions2016In: Doklady Mathematics, ISSN 1064-5624, Vol. 94, no 3, p. 708-711Article in journal (Refereed)
    Abstract [en]

    Solutions to a partial differential equation of the third order containing the modular nonlinearity are studied. The model describes, in particular, elastic waves in media with weak high-frequency dispersion and with different response to tensile and compressive stresses. This equation is linear for solutions preserving their sign. Nonlinear phenomena only manifest themselves to alternating solutions. Stationary solutions in the form of solitary waves or solitons are found. It is shown how the linear periodic wave becomes nonlinear after exceeding a certain critical value of the amplitude, and how it transforms into a soliton with further increase in the amplitude.

  • 38.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Nonlinear dynamics of quadratically cubic systems2013In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 56, no 7, p. 683-690Article, review/survey (Refereed)
    Abstract [en]

    We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg-de Vries, and nonlinear Schrodinger partial differential equations. Some problems are solved exactly in the space-time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed.

  • 39.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Nonlinear integro-differential models for intense waves in media like biological tissues and geostructures with complex internal relaxation-type dynamics2014In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 60, no 4, p. 398-404Article in journal (Refereed)
    Abstract [en]

    The paper discusses a universal scheme for constructing nonlinear integro-differential models to describe intense waves in media with a complex internal relaxation-type dynamics. Examples of such media are presented. Various forms of kernels are described. Situations are shown in which the models can be simplified by reducing them to differential or differential-difference equations with partial derivatives. Integral relations for the linear momentum and energy transferred by the wave are obtained. Exact solutions are found. The mapping method is used to obtain approximate solutions and analyze them in the form of difference relations.

  • 40.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Nonlinear Oscillators with "Modulus" Potentials: Dynamic and Stochastic Solutions2015In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 92, no 2, p. 268-271Article in journal (Refereed)
    Abstract [en]

    Two models of an anharmonic oscillator that have exact solutions are considered. The equationsdescribe motion in a “modulus” potential well with a singularity at the minimum and in a double symmetricwell with a singularity at the vertex of the potential barrier. The forms and spectra of the oscillations are computed. Forced oscillations caused by a random force are analyzed on the basis of equations with Langevinsources. Nonstationary solutions of the corresponding Fokker–Planck equations are constructed. Thesesolutions describe

  • 41.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    One-dimensional model of KZ-type equations for waves in the focal region of cubic and quadratically-cubic nonlinear media2017In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 96, no 1, p. 399-402Article in journal (Refereed)
    Abstract [en]

    Solutions of the equation describing the high-intensity wave profile within the focal region are derived. This equation is similar to the previously studied models with quadratic and modular nonlinearities, but it is adapted for cubic and quadratically-cubic (QC) nonlinear media, where other physical processes are realized. This simplified one-dimensional equation can be regarded as a "projection" of a three-dimensional equation of Khokhlov-Zabolotskaya type (KZ) onto the axis of the wave beam. Stationary profiles at high intensities of focused waves turn out to be periodic sequences of half-periods of triangular shape with singularities of the derivative at extremum points. Such profiles are typical for nonlinear systems with low-frequency dispersion. There is shown to exist a saturation effect-the amplitude of the wave in the focus cannot exceed a certain maximum value, which does not depend on the initial amplitude.

  • 42. Rudenko, Oleg
    The 40th Anniversary of the Khokhlov-Zabolotskaya Equation2010In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 56, no 4, p. 452-462Article in journal (Refereed)
    Abstract [en]

    The 40th anniversary of the Khokhlo-Zabolotskaya equation was marked by a special session of the 158th Meeting of the Acoustical Society of America (October 2009, San Antonio, Texas, United States). A response on the part of Acoustical Physics to this date is also quite appropriate, all the more so because Russian scientists were the main players involved in formulating and using this equation during the period of time between the middle 1960s and middle 1980s. In this article, the author—a participant and witness of those events—presents his view of the dramatic history of the formulation of this equation and related models in the context of earlier and independent work in aerodynamics and nonlinear wave theory. The main problems and physical phenomena described by these mathematical models are briefly considered.

  • 43. Rudenko, Oleg
    V.A.Robsman: Nonlinear Testing and Building Industry2006Conference paper (Refereed)
    Abstract [en]

    This talk is devoted to the memory of outstanding scientist and engineer Vadim A. Robsman who died in January 2005. Dr.Robsman was the Honored Builder of Russia. He developed and applied new methods of nondestructive testing of buildings, bridges, power plants and other building units. At the same time, he published works on fundamental problems of acoustics and nonlinear dynamics. In particular, he suggested a new equation of the 4-th order continuing the series of basic equations of nonlinear wave theory (Burgers Eq.: 2-nd order, Korteveg - de Vries Eq.: 3-rd order) and found exact solutions for high-intensity waves in scattering media. © 2006 American Institute of Physics.

  • 44.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Moscow MV Lomonosov State Univ, Phys Fac, Moscow 119991, Russia.;Russian Acad Sci, Prokhorov Gen Phys Inst, Moscow, Russia.;Russian Acad Sci, Schmidt Inst Phys Earth, Moscow, Russia.;Blekinge Inst Technol, Karlskrona, Sweden..
    Wave Excitation in a Dissipative Medium with a Double Quadratically-Modular Nonlinearity: a Generalization of the Inhomogeneous Burgers Equation2018In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 3, p. 279-282Article in journal (Refereed)
    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.

  • 45.
    Rudenko, Oleg
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Оn strongly nonlinear waves and waves with strongly displayed weak nonlinearity2013In: Nonlinear Waves – 2012 / [ed] Gurbatov, S.N., Nizhny Novgorod: Institute of Applied Physics , 2013Chapter in book (Refereed)
  • 46.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering. Moscow MV Lomonosov State Univ, Phys Fac, Moscow 119991, Russia.;Nizhnii Novgorod State Univ, Radiophys Fac, Nizhn Novgorod, Russia.;Russian Acad Sci, Prokhorov Gen Phys Inst, Moscow, Russia.;Russian Acad Sci, Schmidt Inst Phys Earth, Moscow, Russia.;Blekinge Inst Technol, Karlskrona, Sweden..
    Gurbatov, S. N.
    Nizhnii Novgorod State Univ, RUS.
    Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems2018In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 97, no 1, p. 95-98Article in journal (Refereed)
    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.

  • 47. Rudenko, Oleg
    et al.
    Gurbatov, Sergey
    Hedberg, Claes
    Nonlinear Acoustics Through Problems and Examples2010Book (Other academic)
    Abstract [en]

    The fundamentals of nonlinear acoustics are presented in form of problems followed by solutions, explanations and answers. As distinct from existing textbooks, this book of problems not only helps the reader to become familiar with nonlinear wave processes and the methods of their description, but contributes to mastering calculation procedures and obtaining numerical estimates of the most significant parameters. Thereby, skills are acquired which are indispensable for carrying out original scientific research. This book can be useful to undergraduate and postgraduate students and researchers working in the field of nonlinear wave physics and acoustics.

  • 48. Rudenko, Oleg
    et al.
    Gurbatov, Sergey
    Hedberg, Claes
    Nonlinear Acoustics through Problems and Examples (in Russian)2006Book (Other academic)
  • 49.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Gurbatov, Sergey N.
    Lobachevsky State University of Nizhni Novgorod, RUS.
    Tyurina, A. V.
    Lobachevsky State University of Nizhni Novgorod, RUS.
    Evolution of weak noise and regular waves on dissipative shock fronts described by the Burgers model2018In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, p. 20-29Article in journal (Refereed)
    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.

  • 50.
    Rudenko, Oleg
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Gurbatov, S.N.
    Inverse problem of nonlinear acoustics: Synthesizing intense signals to intensify the thermal and radiation action of ultrasound2016In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 62, no 4, p. 418-428Article in journal (Refereed)
    Abstract [en]

    Inverse problems of nonlinear acoustics have important applied significance. On the one hand, they are necessary for nonlinear diagnostics of media, materials, manufactured articles, building units, and biological and geological structures. On the other hand, they are needed for creating devices that ensure optimal action of acoustic radiation on a target. However, despite the many promising applications, this direction remains underdeveloped, especially for strongly distorted high-intensity waves containing shock fronts. An example of such an inverse problem is synthesis of the spatiotemporal structure of a field in a radiating system that ensures the highest possible energy density in the focal region. This problem is also related to the urgent problems of localizing wave energy and the theory of strongly nonlinear waves. Below we analyze some quite general and simple inverse nonlinear problems. © 2016, Pleiades Publishing, Ltd.

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