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Application of Bloch expansion to periodic elastic and viscoelastic media. (English) Zbl 0495.73014


MSC:

74E05 Inhomogeneity in solid mechanics
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
47F05 General theory of partial differential operators
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References:

[1] Bensoussan, Asymptotic Analysis for Periodic Structures (1978)
[2] Broutman, Composite Materials 2 (1975)
[3] Dafermos, An abstract Volterra equation with application to linear viscoelasticity, J. Diff. Eqn. 7 pp 554– (1970) · Zbl 0212.45302
[4] Dafermos, Asymptotic stability in viscoelasticity, A. R. M. A. 37 pp 297– (1970)
[5] Germain, Cours de Mécanique des Milieux Continus (1973)
[6] Sanchez-Palencia, Non-homogeneous media and vibration theory (1980) · Zbl 0432.70002
[7] Sanchez-Palencia, Justification de la méthode des échelles multiples pour une classe d’équations aux dérivées partielles, Annal. Mat. Pura Appl. 116 pp 159– (1978) · Zbl 0405.35007
[8] Sve, Time harmonic waves travelling obliquely in a periodically laminated medium, J. Appl. Mech. 93 pp 477– (1971) · Zbl 0224.73018
[9] Turbe, Justification de la méthode des échelles multiples pour un type d’équations intégro-différentielles, Actes du Congrès de Florence, Equa. diff. 78 pp 287– (1978)
[10] Turbe, On the two-scale method for a class of integro-differential equations appearing in viscoelasticity, Int. J. Engng. Sc. 17 pp 857– (1979) · Zbl 0412.73002
[11] Wilcox, Scattering theory for the d’Alembert equation in exterior domains (1975) · Zbl 0299.35002
[12] Wilcox, Theory of Bloch waves, J. Anal. Math. 33 pp 146– (1978) · Zbl 0408.35067
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