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

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...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2022-04, Vol.105 (3), p.1634-1680
Main Authors: Cherednichenko, Kirill, Velčić, Igor
Format: Article
Language:English
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Summary: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.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.12543