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Article Dans Une Revue Journal of Mathematics and Mechanics Année : 1963

Continuum dynamics of elastic plates and multilayered solids under initial stress

Résumé

General solutions are developed for the continuum dynamics of elastic plates and multilayered media under initial stress. By the use of specially suited analytical devices they are obtained in a remarkably simple form which brings out their mathematical structure and their physical significance. The results are derived for orthotropic materials and include the special case of a material isotropic in finite strain. They provide basic solutions, incorporating the effect of initial stress, in problems of vibrations and acoustics of sandwich plates and seismic propagation in stratified rock. The problem of elastic stability of plates and multilayered media is solved as a particular case by putting the frequency equal to zero. This extends to compressible media the analysis of internal, interfacial, and surface instability and other related phenomena developed earlier by the writer in the context of incompressibility. By viscoelastic correspondence the result also provides complete solutions for the dynamics of viscoelastic plates and multilayered viscoelastic media under initial stress.
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Dates et versions

hal-01371473 , version 1 (26-09-2016)

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  • HAL Id : hal-01371473 , version 1

Citer

Maurice A. Biot. Continuum dynamics of elastic plates and multilayered solids under initial stress. Journal of Mathematics and Mechanics, 1963, 12 (3), pp.793-810. ⟨hal-01371473⟩
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