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Propagation d'ondes acoustiques dans les réseaux cristallins anharmoniques

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We study the propagation and evolution of acoustic waves in anharmonic crystals on the basis of a semi-infinite discrete monoatomic model with nonlinear interactions between first and second nearest neighbors. In the quasi-continuum approximation the dynamical behavior of the chain is described by Boussinesq or Korteweg-de-Vries equations which admit exact nonlinear propagative solution of the soliton type. By means of two types of excitation in velocity as end conditions we study on the discrete model, both by analytical way and numerical simulation, the competing influence of various parameters (amplitude, rise time of perturbing signal, anharmonicity,…) on the formation of shock and acceleration waves.

Sommaire

Nous étudions la propagation et l'évolution d'ondes acoustiques dans les cristaux anharmoniques sur la base d'un modèle discret monoatomique et semi-infini, avec interactions non linéaires entre premiers et seconds voisins. Dans l'approximation quasi-continue le comportement dynamique de la chaîne est modèlisé par des équations du type Boussinesq ou Korteweg-de- Vries qui admettent des solutions du type soliton. En utilisant deux formes d'excitation en vitesse comme conditions de bord, nous étudions par voie analytique et simulation numérique sur le modèle discret les influences des différents paramètres introduits (amplitude et temps caractéristique du signal perturbateur, anharmonicité, …) sur la formation d'ondes de choc et d'accélération.

Zusammenfassung

Es wird die Ausbreitung und Entwicklung von Schallwellen in anharmonischen Kristallen auf der Grundlage eines diskreten, halbunendlichen Modells mit nichtlinearen Wechselwirkungen zwischen den nächsten und den zweitnächsten Nachbarn untersucht. In der quasikontinuierlichen Approximation kann das dynamische Verhalten der Kette durch Boissinesq- oder Korteweg-de- Fries-Gleichungen dargestellt werden, welche auf Solitonenlösungen führen. Unter Benutzung von zwei Formen der Schnelleanregung als Randbedingungen werden am diskreten Modell auf analytischem Weg und durch numerische Simulation die Einflüsse der verschiedenen Parameter (Amplitude und Anstiegszeit des Störsignals, Anharmonizität, usw.) auf die Bildung von Stoßund Beschleunigungswellen untersucht.
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Document Type: Research Article

Publication date: June 1, 1987

More about this publication?
  • 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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