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  • 1.
    Enflo, Bengt O.
    et al.
    KTH, Superseded Departments, Mechanics.
    Hedberg, C. M.
    Theory of nonlinear acoustics in fluids2004In: Fluid Mechanics and its Applications, ISSN 0926-5112, p. 251-282Article in journal (Refereed)
  • 2.
    Enflo, Bengt O.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hedberg, Claes M.
    A standing acoustic wave with shocks in a cubically nonlinear medium2008In: NONLINEAR ACOUSTICS FUNDAMENTALS AND APPLICATIONS / [ed] Enflo, BO; Hedberg, CM; Kari, L, 2008, Vol. 1022, p. 263-266Conference paper (Refereed)
    Abstract [en]

    It is well known that transversal elastic waves in homogeneous solids satisfy a wave equation with a cubic nonlinearity. This equation with resonator boundary conditions can be transformed into a functional equation, which can be reduced to a second order partial differential equation with a cubic nonlinearity. From this equation, by specializing to steady state and integrating one step, we obtain a first order ordinary differential equation with three terms in addition to the derivative: a cubic and a linear term in the dependent variable and a known term (sinus). The coefficient of the derivative is proportional to the dissipation and assumed to be small. Among several cases the most complicated case, the coefficient of the linear term lying between zero and (0.5) (2/3) = 0.63, is treated in this paper. In each period the solution has two shocks. At one side of each shock it is necessary to introduce an intermediate boundary layer between the outer region and the inner region next to the shock. The intermediate solution is matched both outwards and inwards. The actual first order ordinary differential equation is also solved numerically both in the outer region and in the neighborhood of the shocks.

  • 3.
    Enflo, Bengt O.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hedberg, Claes M.
    Blekinge Institute of Technology, Sweden.
    On the evolution of a spherical short pulse in nonlinear acoustics2012In: Nonlinear Acoustics: State-Of-The-Art And Perspectives (ISNA 19) / [ed] Kamakura, T; Sugimoto, N, American Institute of Physics (AIP), 2012, p. 48-51Conference paper (Refereed)
    Abstract [en]

    Planar wave propagation in nonlinear acoustics is modeled by the Burgers equation, which is exactly soluble. Spherical wave propagation is modeled by a generalized Burgers equation, in which the dissipative parameter of the plane wave Burgers equation is replaced by an exponentially growing function of the variable symbolizing the travelled length of the wave. A procedure previously used in 1998 by B.O. Enflo [1] on cylindrical short pulses is now used on spherical short pulses, which are originally N-waves. The procedure consists of the four steps: 1) A shock solution of the generalized Burgers equation is found by asymptotic matching. The shock fades in the region where the nonlinear term in the equation can be neglected. 2) The linear equation in step 1) is rescaled. It is identically solved by an integral representation containing an unknown function. 3) The integral representation found in step 2) is evaluated by the steepest descent method in the fading shock region introduced in step 1). The unknown function introduced in step 2) is determined by comparing the result of this evaluation with the fading shock solution found in step 1). 4) The integral representation with the unknown function determined is evaluated approximately asymptotically for large values of the original length (or time) variables in the original generalized Burgers equation (old-age regime). The result of this procedure is an old-age solution, controlled by numerical calculations. Curves of analytical and numerical solutions are given.

  • 4.
    Enflo, Bengt O.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hedberg, Claes M.
    Rudenko, Oleg V.
    Standing and propagating waves in cubically nonlinear media2006In: Mathematical Modeling of Wave Phenomena / [ed] Nilsson, B; Fishman, L, MELVILLE, NY: AMER INST PHYSICS , 2006, Vol. 834, p. 187-195Conference paper (Refereed)
    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.

  • 5.
    Enflo, Bengt O.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hedberg, Claes M.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Rudenko, Oleg V.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Standing waves in quadratic and cubic nonlinear resonators: Q-factor and frequency response2006In: Innovations in Nonlinear Acoustics / [ed] Atchley, AA; Sparrow, VW; Keolian, RM, MELVILLE, NY: AMER INST PHYSICS , 2006, Vol. 838, p. 457-460Conference paper (Refereed)
    Abstract [en]

    High-Q acoustic resonators are used to significantly increase the wave energy volume density. For high-intensity waves the magnitude of Q-factor is determined not only by the design of the resonator, but by the strength of internal field as well. Methods to calculate the Q-factor and both the spatio-temporal and spectral structure of this field are described. Results are given for quadratic and cubic nonlinear resonators demonstrating quite different physical properties.

  • 6.
    Enflo, Bengt Olof
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hedberg, C M
    Rudenko, O V
    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.

  • 7.
    Enflo, Bengt Olof
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Hedberg, Claes M.Blekinge Institute of Technology.Kari, LeifKTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
    Non-Linear Acoustics: Fundamentals and Applications2008Conference proceedings (editor) (Refereed)
  • 8. Gurbatov, S.
    et al.
    Demin, I.
    Pronchatov-Rubtsov, N.
    Enflo, Bengt O.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    The nonlinear decay of complex acoustical signals and burgers turbulence2008In: AIP Conf. Proc., 2008, p. 103-106Conference paper (Refereed)
  • 9. Gurbatov, S. N.
    et al.
    Demin, I. Yu.
    Cherepennikov, Val. V.
    Enflo, Bengt Olof
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Behavior of intense acoustic noise at large distances2007In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 53, no 1, p. 48-63Article in journal (Refereed)
    Abstract [en]

    Propagation of intense acoustic noise waves is investigated in the case of a nonplanar geometry. It is shown that, at large distances from the source, where the nonlinear effects become negligible, the spectrum of such waves has a universal self-similar shape. The amplitude of the spectrum is determined by a single constant D-infinity= D-infinity(epsilon, R-0) (the spectrum steepness at zero-valued argument) whose value depends on two dimensionless parameters: the inverse acoustic Reynolds number epsilon and the dimensionless radius R-0. It is shown that the plane of dimensionless parameters (epsilon, R-0) can be divided into four regions, so that, within each of them, the quantity D-infinity is described by a universal function of these parameters. The numerical factors of these parameters are found from numerical simulations.

  • 10. Rudenko, O. V.
    et al.
    Hedberg, C. M.
    Enflo, Bengt Olof
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Finite-amplitude standing acoustic waves in a cubically nonlinear medium2007In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 53, no 4, p. 455-464Article in journal (Refereed)
    Abstract [en]

    The acoustic field in a resonator filled with a cubically nonlinear medium is investigated. The field is represented as a linear superposition of two strongly distorted counterpropagating waves. Unlike the case of a quadratically nonlinear medium, the counterpropagating waves in a cubically nonlinear medium are coupled through their mean (over a period) intensities. Free and forced standing waves are considered. Profiles of discontinuous oscillations containing compression and expansion shock fronts are constructed. Resonance curves, which represent the dependences of the mean field intensity on the difference between the boundary oscillation frequency and the frequency of one of the resonator modes, are calculated. The structure of the profiles of strongly distorted "forced" waves is analyzed. It is shown that discontinuities are formed only when the difference between the mean intensity and the detuning takes certain negative values. The discontinuities correspond to the jumps between different solutions to a nonlinear integro-differential equation, which, in the case of small dissipation, degenerates into a third-degree algebraic equation with an undetermined coefficient. The dependence of the intensity of discontinuous standing waves on the frequency of oscillations of the resonator boundary is determined. A nonlinear saturation is revealed: at a very large amplitude of the resonator wall oscillations, the field intensity in the resonator ceases depending on the amplitude and cannot exceed a certain limiting value, which is determined by the nonlinear attenuation at the shock fronts. This intensity maximum is reached when the frequency smoothly increases above the linear resonance. A hysteresis arises, and a bistability takes place, as in the case of a concentrated system at a nonlinear resonance.

  • 11. Sachdev, P L
    et al.
    Rao, C S
    Enflo, Bengt Olof
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Large-time asymptotics for periodic solutions of the modified burgers equation2005In: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590, Vol. 114, no 3, p. 307A-323Article in journal (Refereed)
    Abstract [en]

    In this paper, we construct large-time asymptotic solution of the modified Burgers equation with sinusoidal initial conditions by using a balancing argument. These asymptotics are validated by a careful numerical study.

1 - 11 of 11
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