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Dynamic Modelling of Annular Plates of Functionally Graded Structure Resting on Elastic Heterogeneous Foundation with Two Modules

Published online by Cambridge University Press:  18 May 2015

A. Wirowski ,
B. Michalak  and
M. Gajdzicki
A. Wirowski*
Affiliation:
Department of Structural Mechanics Lodz University of Technology Lodz, Poland
B. Michalak
Affiliation:
Department of Structural Mechanics Lodz University of Technology Lodz, Poland
M. Gajdzicki
Affiliation:
Department of Structural Mechanics Lodz University of Technology Lodz, Poland
*
* Corresponding author (artur.wirowski@p.lodz.pl)
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Abstract

The contribution is devoted to formulate an averaged mathematical model describing the dynamic behaviour of the composite annular plates resting on elastic heterogeneous foundation with two foundation modules. The plates are made of two-phased, functionally graded — type composites. In contrast to most of the papers in which material properties vary through the plate thickness, in the presented study we have dealt with the plate and foundation in which effective properties vary in a radial direction of the plate. The formulation of the macroscopic mathematical model for the analysis of the dynamic behaviour of these plates will be based on the tolerance averaging technique (Woźniak, Michalak, Jędrysiak, [ed]). This averaging method is an alternative to known asymptotic homogenization. The general results of the contribution will be illustrated by the analysis of free vibrations of the composite plates on heterogeneous foundation. The results obtained from the tolerance model were compared with the results obtained from FEM. There were compared the first four natural frequencies. A good consistency of the results from both methods was obtained.

Keywords

Tolerance averaging techniqueComposite plateHeterogeneous foundationFunctionally graded thin plates
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 5 , October 2015 , pp. 493 - 504
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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References

1.Suresh, S. and Mortensen, A., Fundamentals of Functionally Graded Materials, the University Press, Cambridge (1998).Google Scholar
2.Chen, C. S., Chen, T. J. and Chien, R. D., “Nonlinear Vibration of Initially Stressed Functionally Graded Plates,” Thin-Walled Structures, 44, pp. 844–851 (2006).Google Scholar
3.Batra, R. C. and Jin, J., “Natural Frequencies of a Functionally Graded Rectangular Plate,” Journal of Sound and Vibration, 282, pp. 509–516 (2005).CrossRefGoogle Scholar
4.Oradöğe, E., Küçükarslan, S., Sofiyev, A., Omurtag, M. H., “Finite Element Analysis of Functionally Graded Plates for Coupling Effect of Extension and Bending,” Meccanica, 45, pp. 63–72 (2010).Google Scholar
5.Malezadeh, P., Golbahar Haghighi, M. R. and Atashi, M. M., “Free Vibration Analysis of Elastically Supported Functionally Graded Annular Plates Subjected to Thermal Environment,” Meccanica, DOI 10.1007/s11012-010-9345-5 (2010).Google Scholar
6.Prakash, T. and Ganapathi, M., “Asymmetric Flexural Vbration and Thermoelastic Stability of FGM Circular Plates Using Finite Element Method,” Composites Part B: Engineering, 37, pp. 642–649 (2006).Google Scholar
7.Tylikowski, A., “Dynamic Stability of Functionally Graded Plate Under In-Plane Compression,” Mathematical Problems in Engineering, 4, pp. 411–424 (2005).Google Scholar
8.You, L. H., Wang, J. X., Tang, B. P., “Deformations and Stresses in Annular Disks Made of Functionally Graded Materials Subjected to Internal and/or External Pressure,” Meccanica, 44, pp. 283–292 (2009).CrossRefGoogle Scholar
9.Woźniak, C., Michalak, B., Jędrysiak, J., Thermo-mechanics of Microheterogeneous Solids and Structures, Wydawnictwo Politechniki Łódzkiej, Łódź (2008).Google Scholar
10.Woźniak, C., et al.Mathematical Modelling and Analysis in Continuum Mechanics of Microstructured Media, Silesian Technical University Press, Gliwice (2010).Google Scholar
11.Baron, E., “On Dynamic Behaviour of Medium Thickness Plates with Uniperiodic Structure,” Archive of Applied Mechanics, 73, pp. 505–516 (2003).CrossRefGoogle Scholar
12.Cielecka, I. and Jędrysiak, J., “A Non-Asymptotic Model of Dynamics of Honeycomb Lattice-Type Plates,” Journal of Sound and Vibration, 296, pp. 130–149 (2006).Google Scholar
13.Jędrysiak, J., “Free Vibrations of Thin Periodic Plates Interacting with an Elastic Periodic Foundation,” International Journal of Mechanical Sciences, 45, pp. 1411–1428 (2003).Google Scholar
14.Matysiak, S. J. and Nagórko, W., “On the Wave Propagation in Periodically Laminated Composites. Bulletin De l’Académie Polonais Des Sciences,” Série des Sciences Techniques, 43, pp. 1–12 (1995).Google Scholar
15.Michalak, B., “Vibrations of Plates with Initial Geometrical Periodical Imperfections Interacting with a Periodic Elastic Foundation,” Archive of Applied Mechanics, 70, pp. 508–518 (2000).CrossRefGoogle Scholar
16.Michalak, B., Woźniak, C. and Woźniak, M., “The Dynamic Modelling of Elastic Wavy Plates,” Archive of Applied Mechanics, 66, pp. 177–186 (1996).Google Scholar
17.Tomczyk, B., “On the Modelling of Thin Uniperiodic Cylindrical Shells,” Journal of Theoretical and Applied Mechanics, 41, pp. 755–774 (2003).Google Scholar
18.Wierzbicki, E. and Woźniak, C., “On the Dynamic Behaviour of Honeycomb Based Composite Solids,” Acta Mechanica, 141, pp. 161–172 (2000).Google Scholar
19.Jęrysiak, J. and Woźniak, C., “Elastic Shallow Shells with Functionally Graded Structure,” PAMM 9, pp. 357–358 (2009).Google Scholar
20.Michalak, B., Woźniak, C., Woźniak, M., “Modelling and Analysis of Certain Functionally Graded Heat Conductor,” Archive of Applied Mechanics, 77, pp. 823–834 (2007).Google Scholar
21.Michalak, B. and Wirowski, A., “Dynamic Modelling of Thin Plate Made of Certain Functionally Graded Materials,” Meccanica, 47, pp. 1487–1498 (2012).CrossRefGoogle Scholar
22.Rychlewska, J. and Woźniak, C., “Boundary Layer Phenomena in Elastodynamics of Functionally Graded Laminates,” Archives of Mechanics, 58, pp. 1–14 (2006).Google Scholar
23.Wirowski, A., “Self-Vibration of Thin Plate Band with Non-Linear Functionally Graded Material,” Archives of Mechanics, 64, pp. 603–615 (2012).Google Scholar
24.Gomuliński, A., “Determination of Eigenvalues for Circular Plates Resting on Elastic Foundation with Two Moduli,” Archives of Civil Engineering, 2, pp. 183–203 (1967).Google Scholar
25.Jikov, V. V., Kozlov, C. M. and Oleinik, O. A., Homogenization of Differential Operators and Integral Functionals, Heidelberg, Springer (1994).Google Scholar
26.Jędrysiak, J., “A Contribution to the Modeling of Dynamic Problems for Periodic Plates,” Engineering Transactions, 49, pp. 65–87 (2001).Google Scholar
27.Jędrysiak, J. and Michalak, B., “Some Remarks on Dynamic Results for Averaged and Exact Models of Thin Periodic Plates,” Journal of Theoretical and Applied Mechanics, 43, pp. 405–425 (2005).Google Scholar