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Wave Resonance in Media with Modular, Quadratic and Quadratically-Cubic Nonlinearities Described by Inhomogeneous Burgers-Type Equations
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.ORCID iD: 0000-0001-8739-4492
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. Vol. 64, no 4, p. 422-431
Keywords [en]
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
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Other Mathematics
Identifiers
URN: urn:nbn:se:bth-16906DOI: 10.1134/S1063771018040127ISI: 000439751800005Scopus ID: 2-s2.0-85050096276OAI: oai:DiVA.org:bth-16906DiVA, id: diva2:1240182
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2018-08-21Bibliographically approved

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Rudenko, OlegHedberg, Claes

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