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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 dimensionreduction, normresolvent estimates for the plate, under different energy scalings with respect to the plate thickness.
Original language  English 

Pages (fromto)  16341680 
Number of pages  47 
Journal  Journal of the London Mathematical Society 
Volume  105 
Issue number  3 
Early online date  7 Feb 2022 
DOIs  
Publication status  Published  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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Dive into the research topics of 'Sharp operatornorm asymptotics for thin elastic plates with rapidly oscillating periodic properties'. Together they form a unique fingerprint.Projects
 2 Finished

Support of collaborative research with Dr I Velcic (University of Zagreb) Croatia
8/09/19 → 21/09/19
Project: UK charity

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council