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An Intense Wave in Defective Media Containing Both Quadratic and Modular Nonlinearities: Shock Waves, Harmonics, and Nondestructive Testing
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
2018 (English)In: Acoustical Physics, ISSN 1063-7710, E-ISSN 1562-6865, Vol. 64, no 4, p. 402-407Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Pleiades Publishing , 2018. Vol. 64, no 4, p. 402-407
Keywords [en]
diagnostics, Hopf–Burgers type equations, nonlinear losses, nonlinearity parameters, quadratic modular nonlinearity, shock front, Energy dissipation, Harmonic analysis, Inverse problems, Nondestructive examination, Nonlinear equations, Plasma diagnostics, Shock testing, Shock waves, Wave energy conversion, Inhomogeneous medium, Non-linearity parameter, Nonlinear loss, Power-law dependences, Second harmonic waves, Shock fronts, Spectral composition, Control nonlinearities
National Category
Other Mechanical Engineering
Identifiers
URN: urn:nbn:se:bth-16907DOI: 10.1134/S1063771018040048ISI: 000439751800002Scopus ID: 2-s2.0-85050124455OAI: oai:DiVA.org:bth-16907DiVA, id: diva2:1240193
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2018-08-21Bibliographically approved

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Gray, AmberRudenko, Oleg

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