Engineering Transactions, 46, 1, pp. 73–87, 1998
10.24423/engtrans.659.1998

On Dynamics of Thin Plates with a Periodic Structure

J. Jędrysiak
Łódź Univesity of Technology
Poland

A new modelling approach to thin elastic Kirchhoff plates with a periodic structure along the midplane based on that given in [7] is shown. The main feature of this model is that it describes the length-scale effect on the plate dynamics, which is neglected in the known asymptotic theories of periodic composite plates. The structural model, which takes into account also the effect of the rotational inertia, and the comparison between this model and the local models without the length-scale effect are presented.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

J.D. ACHENBACH and G. HERRMANN, Wave motions in solids with lamellar structuring, Dynamics of Structured Solids, G. HERMANN [Ed.], Am. Soc. of Mech. Engng., New York 1968.

E. BARON and C. WOZNIAK, On the micro-dynamics of composite plates, Arch. Appl. Mech., 66, 126–133, 1995.

A. BENSOUSSAN, J.L. LIONS and G. PAPANICOLAOU, Asymptotic analysis for periodic structures, North Holland, Amsterdam 1978.

D. CAILLERIE, Thin elastic and periodic plates, Math. Meth. in the Appl. Sci., 6, 159–191, 1984.

M.T. HUBER, Theory of orthotropic plates [in Polish], Arch. Tow. Nauk., Lwow 1921.

M.T. HUBER, Probleme der Statik technisch wichtiger orthotroper Flatten, PWN, Warszawa 1956.

J. JĘDRYSIAK and C. WOŹNIAK, On the elasto-dynamics of thin microperiodic plates, J. Theor. Appl. Mech., 33, 337–349, 1995.

V.V. JIKOV, S.M. KOZLOV and O.A. OLEINIK, Homogenization of differential operators and integral functionals, Springer Verlag, Berlin–Heidelberg–New York 1994.

R.V. KOHN and M. VOGELIUS, A new model for thin plates with rapidly varying thickness, Int. J. Solids Structures, 20, 333–350, 1984.

T. LEWINSKI, Homogenizing stiffnesses of plates with periodic structure, Int. J. Solids Structures, 21, 309–326, 1992.

S.J. MATYSIAK and W. NAGÓRKO, Microlocal parameters in the modelling of micro–periodic plates, Ing. Arch., 59, 434–444, 1989.

B. MICHALAK, C. WOŹNIAK and M. WOŹNIAK, The dynamic modelling of elastic wavy plates, Arch. Appl. Mech., 66, 177–186, 1995.

B.A. SCHREFLER and M. LEFIK, Use of homogenization method to build a beam element with thermo–mechanical microscale properties, Structural Engineering and Mech., 4, 6, 613–630, 1996.

C. WOŹNIAK, Refined macrodynamics of periodic structures, Arch. Mech., 45, 295–304, 1993.

C. WOŹNIAK, Microdynamics: Continuum modelling the simple composite materials, J.Theor. Appl. Mech., 33, 267–289, 1995.

C. WOŹNIAK and M. WOŹNIAK, Modelling in dynamics of composites. Theory and applications [in Polish], Prace IPPT, 25, Warszawa 1995.

C. WOŹNIAK, M. WOŹNIAK and S. KONIECZNY, A note on dynamic modelling of periodic composites, Arch. Mech., 45, 779–783, 1993.

J. JĘDRYSIAK, Free vibrations of thin periodic plates [to appear].




DOI: 10.24423/engtrans.659.1998