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  • 1. Enflo, Bengt
    et al.
    Hedberg, Claes
    Rudenko, Oleg
    Resonant properties of a nonlinear dissipative layer excited by a vibrating boundary: Q-factor and frequency response2005Inngår i: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 117, nr 2, s. 601-612Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 2. Hedberg, Claes
    Multifrequency plane, nonlinear, and dissipative waves at arbitrary distances1999Inngår i: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 106, nr 6, s. 3150-3155Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A solution for multifrequency plane waves propagating through a dissipative and nonlinear medium is presented. It originates from the well-known Bessel function series ratio for a pure sinusiodal wave, introduced by Cole and Mendousse. The solution is exact. The only limitation, inherited from the single-frequency solution, is the slow convergence of the series when the nonlinearity is very large compared to the dissipation. Otherwise any frequencies, amplitudes and phases can be introduced in the original wave and the solution is valid for any propagated distance.

  • 3. Hedberg, Claes
    et al.
    Rudenko, Oleg
    Pulse response of a nonlinear layer2001Inngår i: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 110, nr 5, s. 2340-2350Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 4.
    Rudenko, Oleg
    et al.
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för maskinteknik.
    Hedberg, Claes
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för maskinteknik.
    The phenomenon of self-trapping of a strongly nonlinear wave.2014Inngår i: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 135, nr 4Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Self means here an effect of a wave on itself. Several self-action phenomena are known in nonlinear wave physics. Among them are self-focusing of beams self-compression of light pulses self-channeling self-reflection (or self-splitting) waves with shock fronts self-induced transparency and self-modulation. These phenomena are known for weakly nonlinear waves of different physical origin. Our presentation at ASA meeting in Montreal [POMA 19 045080 (2013)] was devoted to strongly nonlinear waves having no transition to the linear limit at infinitesimally small amplitudes. Such waves can demonstrate particle-like properties. Self-trapping consists of the arrest of wave propagation and in the formation of a localized state. In particular the model generalizing the Heisenberg' ordinary differential equation to spatially distributed systems predicts periodic oscillations but no traveling waves. Different models for strongly nonlinear waves will be considered and some unusual phenomena will be discussed. Preliminary results were published in Ac. Phys. 59 584 (2013) and Physics-Uspekhi (Adv. Phys. Sci.) 183 683 (2013). [This work was supported by the Megagrant No.11.G34.31.066 (Russia) and the KK Foundation (Sweden).

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