Bensoussan A.

Berdichevski V. L.

Cremer L.

Graff K. F.

Joannopoulos J. D.

Panasenko G.

Sanchez-Palencia E.

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

We consider microstructured thin elastic plates that have an underlying periodic structure, and develop an asymptotic continuum model that captures the essential microstructural behaviour entirely in a macroscale setting. The asymptotics are based upon a two-scale approach and are valid even at high frequencies when the wavelength and microscale length are of the same order. The general theory is illustrated via one- and two-dimensional model problems that have zero-frequency stop bands that preclude conventional averaging and homogenization theories. Localized defect modes created by material variations are also modelled using the theory and compared with numerical simulations.</jats:p

T. Antonakakis

R. V. Craster

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High-frequency asymptotics for microstructured thin elastic plates and platonics

01/0/8/12 MEB.  Submitted verison attached. Requested the academic to change version for an accepted one

Antonakakis, T

Craster, RV

Spiral - Imperial College Digital Repository

High-frequency asymptotics for microstructured thin elastic plates and platonics

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Spiral - Imperial College Digital Repository