# Bloch wave homogenization of linear elasticity system

Sista Sivaji Ganesh; Muthusamy Vanninathan

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 4, page 542-573
- ISSN: 1292-8119

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topGanesh, Sista Sivaji, and Vanninathan, Muthusamy. "Bloch wave homogenization of linear elasticity system." ESAIM: Control, Optimisation and Calculus of Variations 11.4 (2010): 542-573. <http://eudml.org/doc/90777>.

@article{Ganesh2010,

abstract = {
In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three
dimensions. The Bloch wave method for homogenization relies on the regularity of the
lower Bloch spectrum. For the three dimensional linear elasticity system,
the first eigenvalue is degenerate of multiplicity three and hence
existence of such a regular Bloch spectrum is not guaranteed. The
aim here is to develop all necessary spectral tools to overcome these
difficulties. The existence of a directionally regular Bloch spectrum is
proved and is
used in the homogenization. As a consequence an interesting relation between
homogenization process and wave propagation in the homogenized medium is
obtained. Existence of a spectral gap for the directionally regular Bloch spectrum is established and as a consequence
it is proved that higher modes apart from the first three do not contribute to the homogenization process.
},

author = {Ganesh, Sista Sivaji, Vanninathan, Muthusamy},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Bloch waves; homogenization; linear elasticity.; directionally regular Bloch spectrum; spectral gap},

language = {eng},

month = {3},

number = {4},

pages = {542-573},

publisher = {EDP Sciences},

title = {Bloch wave homogenization of linear elasticity system},

url = {http://eudml.org/doc/90777},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Ganesh, Sista Sivaji

AU - Vanninathan, Muthusamy

TI - Bloch wave homogenization of linear elasticity system

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 4

SP - 542

EP - 573

AB -
In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three
dimensions. The Bloch wave method for homogenization relies on the regularity of the
lower Bloch spectrum. For the three dimensional linear elasticity system,
the first eigenvalue is degenerate of multiplicity three and hence
existence of such a regular Bloch spectrum is not guaranteed. The
aim here is to develop all necessary spectral tools to overcome these
difficulties. The existence of a directionally regular Bloch spectrum is
proved and is
used in the homogenization. As a consequence an interesting relation between
homogenization process and wave propagation in the homogenized medium is
obtained. Existence of a spectral gap for the directionally regular Bloch spectrum is established and as a consequence
it is proved that higher modes apart from the first three do not contribute to the homogenization process.

LA - eng

KW - Bloch waves; homogenization; linear elasticity.; directionally regular Bloch spectrum; spectral gap

UR - http://eudml.org/doc/90777

ER -

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