Applications of bloch expansion to periodic elastic and viscoelastic media

DOI10.1002/mma.1670040128zbMath0495.73014OpenAlexW1994755587MaRDI QIDQ3959526

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Publication date: 1982

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.1670040128

zbMATH Keywords

boundary-value problemBloch expansionfirst term of exact solution expansion is solution of equations obtained in homogenization theorylong memory linear viscoelastic materiallong wave-length compared to period of structuresolution of equations of motion expanded in eigenfunctions of periodic operatorsunbounded, elastic nonhomogeneous material with periodic structure

Mathematics Subject Classification ID

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

Related Items (9)

Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity ⋮ Bloch expansion in generalized thermoelasticity ⋮ On asymptotic elastodynamic homogenization approaches for periodic media ⋮ Large scale modulation of high frequency waves in periodic elastic composites ⋮ Ondes élastiques dans une bande périodique ⋮ Bloch waves for a solid-fluid mixture ⋮ Bloch wave homogenization of linear elasticity system ⋮ On the Maxwell's system in composite media ⋮ Rayleigh scattering in elastic composite materials

Cites Work

• Non-homogeneous media and vibration theory
• Scattering theory for the d'Alembert equation in exterior domains
• Justification de la méthode des echelles multiples pour une classe d'équations aux dérivées partielles
• Theory of Bloch waves
• On the two-scales method for a class of integro-differential equations appearing in viscoelasticity
• An abstract Volterra equation with applications to linear viscoelasticity
• Thermoelastic waves in a periodically laminated medium

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