Sharp operator-norm asymptotics for thin elastic plates with rapidly oscillating periodic properties

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Abstract



We analyse a system of partial differential equations describing the behaviour of an elastic plate with periodic moduli in the two planar directions, in the asymptotic regime when the period and the plate thickness are of the same order. Assuming that the displacement gradients of the points of the plate are small enough for the equations of linearised elasticity to be a suitable approximation of the material response, such as the case in, for example, acoustic wave propagation, we derive a class of ‘hybrid’, homogenisation dimension-reduction, norm-resolvent estimates for the plate, under different energy scalings with respect to the plate thickness.
Original languageEnglish
Pages (from-to)1634-1680
Number of pages47
JournalJournal of the London Mathematical Society
Volume105
Issue number3
Early online date7 Feb 2022
DOIs
Publication statusPublished - 30 Apr 2022

Bibliographical note

Funding Information:
KC is grateful for the support of the Engineering and Physical Sciences Research Council (EPSRC): Grant EP/L018802/2 ‘Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory’. IV has been supported by the Croatian Science Foundation under Grant agreement No. 9477 (MAMPITCoStruFl) and Grant agreement No. IP‐2018‐01‐8904 (Homdirestroptcm). KC would also like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme ‘The mathematical design of new materials’, where work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1.

ASJC Scopus subject areas

  • Mathematics(all)

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