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We assume that the thickness of the plate is $h^2$ and that the mid-surface of the plate is given by $(x_1,x_2) \\to (x_1,x_2,h^2\\theta(\\per))$, where $\\theta$ is $[0,1]^2$ periodic function. We also assume that the strain energy of the plate has the order $h^8=(h^2)^4$, which corresponds to the F\\\"oppl-von K\\'arm\\'an model in the case of the ordinary plate. 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