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Nonlinear acoustics of structurally complex materials described by non-analytic nonlinearities
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.ORCID iD: 0000-0001-8739-4492
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
2018 (English)In: 25th International Congress on Sound and Vibration 2018, ICSV 2018: Hiroshima Calling, International Institute of Acoustics and Vibration, IIAV , 2018, p. 1993-1998Conference paper, Published 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.

Place, publisher, year, edition, pages
International Institute of Acoustics and Vibration, IIAV , 2018. p. 1993-1998
Keywords [en]
Annihilation, Bi-modular media, Modular nonlinearity, Nonlinear partial differential equations, Strongly nonlinear systems), Acoustics, Control nonlinearities, Nonlinear optics, Nonlinear systems, Partial differential equations, Shock waves, Solitons, Analytic nonlinearities, Exact analytic solutions, New mathematical model, Non-linear acoustics, Strongly nonlinear system, Nonlinear equations
National Category
Other Mechanical Engineering
Identifiers
URN: urn:nbn:se:bth-17460Scopus ID: 2-s2.0-85058697135ISBN: 9781510868458 (print)OAI: oai:DiVA.org:bth-17460DiVA, id: diva2:1276850
Conference
25th International Congress on Sound and Vibration 2018: Hiroshima Calling, ICSV 2018; Hiroshima; Japan; 8 July 2018 through 12 July 2018
Available from: 2019-01-09 Created: 2019-01-09 Last updated: 2019-01-09Bibliographically approved

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Hedberg, ClaesRudenko, Oleg

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