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General variational methods for waves in elastic composites

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Abstract

General variational theorems in which the displacement, the stress, and the strain in one case, and the displacement and the stress in another case, are given independent variations, and which include appropriate general bondary and discontinuity conditions, are developed with a view toward the application to harmonic waves in elastic composites with periodic structures. The one-dimensional case is first developed in detail, and in order to demonstrate the effectiveness of the results, especially their accuracy in providing the dispersion curve, waves propagating normal to layers in a layered composite are discussed, and numerical results are presented; see Tables I and II. Then the general three-dimensional case is considered, and the results are applied to waves propagating normal to the fibers in a fiber-reinforced composite.

Résumé

Les théorèmes généraux variationels, dans lesquels on varie indépendemment le déplacement, la contrainte et la déformation, dans le premier cas, et le déplacement et la contrainte, dans le second cas, et qui fournissent de même les conditions aux limites et les conditions de discontinuité, sont dévelopés dans le but d'application aux ondes harmoniques dans les matériaux composites à structure périodique. Le cas d'une seule dimension est d'abord exposé en détail, et pour démontrer l'efficacité des résultats, en particulier la précision avec laquelle la courbe de dispersion peut être determinée, le cas d'ondes se propageant normalement aux couches du matériel composite est discuté et des résultats numériques sont présentés (voir Tables I et II). Par suite, le cas géneral en trois dimensions est considéré et les résultats sont appliqués aux ondes qui se propagent normalement aux fibres dans un matériel renforcé par fibres.

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Authors and Affiliations

  1. The Technological Institute, Northwestern University, Evanston, Illinois

    S. Nemat-Nasser (Professor)

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  1. S. Nemat-Nasser
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Additional information

This work was partly completed while the author was at the University of California, San Diego, La Jolla, California, as a consultant to Grant AF-AFOSR 70-1957, sponsored by the Air Force Office of Aerospace Research, United States Air Force, Washington, D.C.

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Nemat-Nasser, S. General variational methods for waves in elastic composites. J Elasticity 2, 73–90 (1972). https://doi.org/10.1007/BF00046056

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  • DOI: https://doi.org/10.1007/BF00046056

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