Turbe, N. Application of Bloch expansion to periodic elastic and viscoelastic media. (English) Zbl 0495.73014 Math. Methods Appl. Sci. 4, 433-449 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 9 Documents 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 Keywords:Bloch expansion; unbounded, elastic nonhomogeneous material with periodic structure; solution of equations of motion expanded in eigenfunctions of periodic operators; long wave-length compared to period of structure; first term of exact solution expansion is solution of equations obtained in homogenization theory; long memory linear viscoelastic material; boundary-value problem × Cite Format Result Cite Review PDF Full Text: DOI 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 · doi:10.1016/0022-0396(70)90101-4 [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 · doi:10.1007/BF02413873 [8] Sve, Time harmonic waves travelling obliquely in a periodically laminated medium, J. Appl. Mech. 93 pp 477– (1971) · Zbl 0224.73018 · doi:10.1115/1.3408800 [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 · doi:10.1016/0020-7225(79)90015-6 [11] Wilcox, Scattering theory for the d’Alembert equation in exterior domains (1975) · Zbl 0299.35002 · doi:10.1007/BFb0070581 [12] Wilcox, Theory of Bloch waves, J. Anal. Math. 33 pp 146– (1978) · Zbl 0408.35067 · doi:10.1007/BF02790171 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.