Result: Nonlinear kinematic wave mechanics of elastic solids

Title:
Nonlinear kinematic wave mechanics of elastic solids
Authors:
MAUGIN, Gérard A
Source:
Selected papers presented at the International Symposium on Mechanical Waves in SolidsWave motion. 44(6):472-481
Publisher Information:
Amsterdam: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 34 ref
Original Material:
INIST-CNRS
Subject Terms:
Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Approximation et analyse numériques, Numerical approximation and analysis, Equations différentielles et équations aux dérivées partielles, problèmes aux valeurs limites, Ordinary and partial differential equations, boundary value problems, Domaines classiques de la physique (y compris les applications), Fundamental areas of phenomenology (including applications), Mécanique des solides, Solid mechanics, Mécanique des structures et des milieux continus, Structural and continuum mechanics, Elasticité statique (thermoélasticité...), Static elasticity (thermoelasticity...), Vibration, onde mécanique, stabilité dynamique (aéroélasticité, contrôle vibration...), Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...), Approximation asymptotique, Asymptotic approximation, Aproximación asintótica, Calcul variationnel, Variational calculus, Cálculo de variaciones, Cinématique, Kinematics, Cinemática, Cristal élastique, Elastic crystals, Cristal elástico, Dispersion onde, Wave dispersion, Dispersión onda, Effet non linéaire, Non linear effect, Efecto no lineal, Elastodynamique, Elastodynamics, Elastodinámico, Loi conservation, Conservation law, Ley conservación, Matériau hétérogène, Heterogeneous material, Material heterogéneo, Modélisation, Modeling, Modelización, Mécanique ondulatoire, Wave mechanics, Mecánica ondulatoria, Méthode moyenne, Averaging method, Método medio, Onde contrainte, Stress wave, Onda tensión, Onde non linéaire, Non linear wave, Onda no lineal, Onde surface, Surface wave, Onda superficie, Onde volume, Bulk wave, Onda volumen, Onde élastique, Elastic wave, Onda elástica, Propriété mécanique, Mechanical properties, Propiedad mecánica, Quantité mouvement, Momentum, Cantidad movimiento, Relation contrainte déformation, Stress strain relation, Relación tensión deformación, Relation dispersion, Dispersion relation, Ecuación dispersión, Tenseur Eshelby, Eshelby tensor, Tensor Eshelby, Théorie cinématique, Kinematic theory, Teoría cinemática, Dispersion, Elastic solids, Nonlinear waves, Variational principle, Wave kinematics
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Université Pierre et Marie Curie (Paris 6). Institut Jean Le Rond d'Alembert, UMR CNRS 7190. Case 162, 4 place Jussieu, 75252 Paris, France
ISSN:
0165-2125
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=18892790
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Physics: solid mechanics

Theoretical physics
Accession Number:
edscal.18892790
Database:
PASCAL Archive

Further Information

The kinematic wave theory due essentially to M.J. Lighthill, G.B. Whitham and W.D. Hayes has rarely been applied to the case of elastic waves, an exception being works by Maugin and Hadouaj on nonlinear surface waves on covered crystal elastic substrates in 1989-1992. Here, basing on the canonical projection of continuum mechanics onto the material manifold (theory of so-called material inhomogeneities and of material or configurational forces) it is first shown that the kinematic wave theory develops in parallel with that materials mechanics but in terms of frequency and material wave vector instead of time and material coordinates. A conservation law of material wave momentum is thus deduced involving a material wave Eshelby stress in addition to the conservation of wave action. This formalism and the Whitham-Newell averaging method are then used in an illustration to the case of nonlinear dispersive bulk waves in elastic crystals. A nonlinear (i.e., amplitude dependent), dispersive (i.e., dependent on space and time derivatives of the amplitude) dispersion relation is thus constructed by means of asymptotics, which allows one to obtain slowly varying small amplitude, almost monochromatic dynamical solutions such as envelope solitons.