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Second-gradient homogenized model for wave propagation in heterogeneous periodic media

Bacigalupo, Andrea and Gambarotta, Luigi Second-gradient homogenized model for wave propagation in heterogeneous periodic media. International Journal of Solids and Structures, 51 (5). 1052 - 1065. ISSN 0020-7683 (2014)

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Abstract The paper is focused on a homogenization procedure for the analysis of wave propagation in materials with periodic microstructure. By a reformulation of the variational-asymptotic homogenization technique recently proposed by Bacigalupo and Gambarotta (2012a), a second-gradient continuum model is derived, which provides a sufficiently accurate approximation of the lowest (acoustic) branch of the dispersion curves obtained by the Floquet–Bloch theory and may be a useful tool for the wave propagation analysis in bounded domains. The multi-scale kinematics is described through micro-fluctuation functions of the displacement field, which are derived by the solution of a recurrent sequence of cell {BVPs} and obtained as the superposition of a static and dynamic contribution. The latters are proportional to the even powers of the phase velocity and consequently the micro-fluctuation functions also depend on the direction of propagation. Therefore, both the higher order elastic moduli and the inertial terms result to depend by the dynamic correctors. This approach is applied to the study of wave propagation in layered bi-materials with orthotropic phases, having an axis of orthotropy parallel to the direction of layering, in which case, the overall elastic and inertial constants can be determined analytically. The reliability of the proposed procedure is analysed by comparing the obtained dispersion functions with those derived by the Floquet–Bloch theory.

Item Type: Article
Identification Number: 10.1016/j.ijsolstr.2013.12.001
Uncontrolled Keywords: Dispersive waves; Periodic materials; Second-gradient continuum; Non-local homogenization
Subjects: T Technology > TJ Mechanical engineering and machinery
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 21 Jan 2015 09:02
Last Modified: 21 Jan 2015 09:02
URI: http://eprints.imtlucca.it/id/eprint/2539

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