caa a22 4500 467949484 CHVBK 20180405193740.0 cr unu---uuuuu 170328e20041201xx s 000 0 eng 10.1007/s00419-003-0310-9 doi (NATIONALLICENCE)springer-10.1007/s00419-003-0310-9 (NATIONALLICENCE)springer-10.1007/BF02637194 On the modelling of dynamic problems for plates with a periodic structure [Elektronische Daten] [K. Mazur-Śniady, Cz. Woźniak, E. Wierzbicki] 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. Springer-Verlag Berlin Heidelberg, 2004 plate nationallicence 2D-modelling nationallicence dynamics nationallicence periodic structure nationallicence inhomogeneity nationallicence Mazur-Śniady K. Institute of Civil Engineering, Wroclaw University of Technology, Poland aut Woźniak Cz Institute of Mathematics and Computer Sciences, Częstochowa University of Technology, Dabrowskiego 73, PL-42200, Częstochowa, Poland aut Wierzbicki E. Institute of Mathematics and Computer Sciences, Częstochowa University of Technology, Dabrowskiego 73, PL-42200, Częstochowa, Poland aut Archive of Applied Mechanics Springer-Verlag 74/3-4(2004-12-01), 179-190 0939-1533 74:3-4<179 2004 74 419 https://doi.org/10.1007/s00419-003-0310-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-003-0310-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Woźniak Cz Institute of Mathematics and Computer Sciences, Częstochowa University of Technology, Dabrowskiego 73, PL-42200, Częstochowa, Poland aut NATIONALLICENCE 700 1- Wierzbicki E. Institute of Mathematics and Computer Sciences, Częstochowa University of Technology, Dabrowskiego 73, PL-42200, Częstochowa, Poland aut NATIONALLICENCE 700 1- Mazur-Śniady K. Institute of Civil Engineering, Wroclaw University of Technology, Poland aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 74/3-4(2004-12-01), 179-190 0939-1533 74:3-4<179 2004 74 419 NATIONALLICENCE 700 1- Woźniak Cz Institute of Mathematics and Computer Sciences, Częstochowa, University of Technology, Dabrowskiego 73, PL-42200, Częstochowa, Poland aut NATIONALLICENCE 700 1- Wierzbicki E. Institute of Mathematics and Computer Sciences, Częstochowa, University of Technology, Dabrowskiego 73, PL-42200, Częstochowa, Poland aut NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02637194 text/html Onlinezugriff via DOI Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE NATIONALLICENCE NL-springer