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Nonlinear Two-Dimensional Longitudinal and Shear Waves in Solids

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The two-dimensional (2D) problem of propagating nonlinear longitudinal and shear waves in solids by a bounded input is considered. Using appropriate scaling of dependent and independent variables, the 2D evolution equations are derived. The solutions to these nonlinear model equations are comparatively analysed and the differences between the distortion of longitudinal and shear waves are explained. The novelty of the 2D evolution equation for shear waves is an integral-type term accounting for the nonlinear coupling effects. Both asymptotic and numerical solutions to the evolution equations under consideration are presented with an explanation of the simplified 1 D models.

Zusammenfassung

Es wird das zweidimensionale (2 D-) Problem der Ausbreitung nichtlinearer Longitudinal- und Scherwellen in Festkörpern betrachtet, die von einer begrenzten Quelle ausgehen. Mittels einer geeigneten Skalierung der abhängigen und unabhängigen Variablen werden die zweidimensionalen Evolutionsgleichungen abgeleitet. Die Lö- sungen dieser nichtlinearen Modellgleichungen werden vergleichend analysiert, und es werden die Unterschiede zwischen der Verzerrung der Longitudinal- und Scherwellen erklärt. Neu an der Gleichung für Scherwellen ist ein Integralterm, der die nichtlinearen Kopplungseffekte berücksichtigt. Es werden sowohl asymptotische als auch umerische Lösungen der Evolutionsgleichungen vorgestellt, zusammen mit einer Erklärung des vereinfachten 1 D-Modells.

Sommaire

On a étudié la propagation à deux dimensions (2 D) dans les solides, d'ondes non linéaires longitudinales et de cisaillement produites par une excitation d'amplitude finie. A partir d'une transformation appropriée des variables dépendantes et indépendantes, on aboutit aux équations du mouvement à deux dimensions. Une analyse comparée des solutions de ces équations non linéaires permet d'interpréter les différences de distorsion entre ondes longitudinales et ondes de cisaillement. L'originalité de l'équation 2 D du mouvement pour les ondes de cisaillement est un terme de type intégrate qui rend compte des effets de couplage non linéaire. On présente des solutions asymptotiques et numériques des équations en question, avec interprétation des modèles simplifiés unidimensionnels.
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Document Type: Research Article

Publication date: March 1, 1992

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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