On the modelling of dynamic problems for plates with a periodic structure |
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Authors: | K Mazur-?niady Cz Wo?niak E Wierzbicki |
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Institution: | (1) Institute of Civil Engineering, Wroclaw University of Technology, Poland;(2) Institute of Mathematics and Computer Sciences, Częstochowa, University of Technology, Dabrowskiego 73, PL-42200 Częstochowa, Poland |
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Abstract: | Summary The subject of analysis is the bending of elastic plates exhibiting a nonhomogeneous periodic structure and/or a periodically
variable thickness in a certain direction parallel to the plate's midplane. The fundamental modelling problem is how to obtain
an effective 2D-model of a plate under consideration, i.e., a 2D-model represented by PDEs with constant coefficients. This
problem for periodic plates has been solved independently in 5] and 10], using asymptotic homogenization. However, homogenization
neglects dynamic phenomena related to the plate's rotational inertia and cannot be applied to the analysis of higher-order
vibration frequences. The main aim of this contribution is to formulate a new non-asymptotic effective 2D-model of a periodic
plate which is free from the mentioned drawbacks and describes the dynamic behaviour of plates having the thickness of the
order of the period length. The proposed model is applied to the analysis of some vibration problems. |
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Keywords: | plate 2D-modelling dynamics periodic structure inhomogeneity |
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