Mechanics of Generalized Continua, Holm Altenbach; G?rard A. Maugin; Vladimir Erofeev

Автор: Slawinski M. A.
Название: Waves and Rays in Elastic Continua
ISBN: 9814641758 ISBN-13(EAN): 9789814641753
Издательство: World Scientific Publishing
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Описание: The present book — which is the third, significantly revised edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.

Автор: Gurtin
Название: The Mechanics and Thermodynamics of Continua
ISBN: 1107617065 ISBN-13(EAN): 9781107617063
Издательство: Cambridge Academ
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Описание: A consolidated treatment of continuum mechanics and thermodynamics that stresses the universal status of the basic balances and the entropy imbalance. The Mechanics and Thermodynamics of Continua is written for engineers, physicists and mathematicians.

Автор: G?rard A. Maugin; Andrei V. Metrikine
Название: Mechanics of Generalized Continua
ISBN: 1441956948 ISBN-13(EAN): 9781441956941
Издательство: Springer
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Описание: In their 1909 publication Theorie des corps deformables, Eugene and Francois Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers.

Автор: Géry de Saxcé, Claude Valleé
Название: Galilean Mechanics and Thermodynamics of Continua
ISBN: 1848216424 ISBN-13(EAN): 9781848216426
Издательство: Wiley
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Описание: This title proposes a unified approach to continuum mechanics which is consistent with Galilean relativity.

Автор: Angela Madeo
Название: Generalized Continuum Mechanics and Engineering Applications
ISBN: 1785480324 ISBN-13(EAN): 9781785480324
Издательство: Elsevier Science
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Описание:

The new concept of metamaterial is increasingly attracting the interest of physicists and mechanical engineers. Such materials are obtained by suitably assembling multiple individual elements but usually arranged in (quasi-)periodic substructures in order to show exotic global mechanical properties. Indeed, the particular shape, geometry, size, orientation and arrangement of their constituting elements can affect, the propagation of waves of light or sound in a manner not observed in natural materials, creating material properties which may give rise to unexpected engineering applications. Particularly promising in the design and description of metamaterials are those micro-structures which present high contrasts in their mechanical properties: these micro-structures, once homogenized, may produce generalized continuum media, for example, second gradient or micromorphic.