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Self-vibration of thin plate band with non-linear functionally graded material

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Języki publikacji
EN
Abstrakty
EN
The subject of this paper is the analysis of free vibration of a thin plate band made of nonlinear functionally graded material. The considered material has periodic properties in one direction and slow but non-linear functionally graded properties in the other. The main attention is given to description of the effect of the material distribution on the overall response of the composite. The modelling approach is based on the tolerance averaging of the equation of motion. The general results are illustrated by the free vibration analysis of the bracket and the plate band simply supported on both sides.
Rocznik
Strony
603--603
Opis fizyczny
-–615, Bibliogr. 33 poz.
Twórcy
autor
  • Department of Structural Mechanics Technical University of Łodź al. Politechniki 6 90-924 Łodź, Poland, artur.wirowski@p.lodz.pl
Bibliografia
  • 1. T. Reiter, G.J. Dvorak, V. Tvergaard, Micromechanics models for graded composite materials, J. Mech. Phys. Solids, 45, 1281–1302, 1997.
  • 2. S. Suresh, A. Mortensen, Fundamentals of functionally graded materials, Cambridge, The University Press, 1998.
  • 3. I.V. Andrianov, Awrejcewicz, L.I. Manevitch, Asymptotical Mechanics of ThinWalled Structures, A Handbook, Springer, 2004.
  • 4. V.V. Jikov, C.M. Kozlov, O.A. Oleinik, Homogenization of differential operators and integral functional, Berlin-Heidelberg, Springer, 1994.
  • 5. A.L. Kalamkarov, A.G. Kolpakov, Analysis, Design and Optimization of Composite Structures, Wiley, 1997.
  • 6. A. Bensoussan, J.L. Lions, G. Papanicolau, Asymptotic analysis for periodic structures, North-Holland, Amsterdam 1978.
  • 7. A.G. Kolpakov, Stressed Composite Structures: Homogenized Models for Thin-Walled Nonhomogeneous Structures with Initial Stresses, Springer, 2004.
  • 8. Cz. Wozniak, B. Michalak, J. Jedrysiak, [Eds.], Thermomechanics of microheterogeneous solids and structures, Wydawnictwo Politechniki Łódzkiej, Łódź 2008.
  • 9. B. Michalak, A. Wirowski, Dynamic modelling of thin plate made of certain functionally graded materials, Meccanica, 47, 6, 1487–1498, DOI: 10.1007/s11012-011-9532-z, 2012.
  • 10. M. Kazmierczak, J. Jedrysiak, Tolerance modelling of vibrations of thin functionally graded plates, Thin-Walled Structures, 49, 10, 1295–1303, DOI: 10.1016/j.tws.2011.05.001, 2011.
  • 11. B.P. Patel, S.S. Gupta, M.S. Loknath, C.P. Kadu, Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory, Composite Structures, 69, 3, 259–270, 2005.
  • 12. S. Natarajan, P.M. Baiz, S. Bordas, T. Rabczuk, P. Kerfriden, Natural frequencies of cracked functionally graded material plates by the extended finite element method, Composite Structures, 93, 11, 3082–3092, 2011.
  • 13. S. Natarajan, G. Manickam, Bending and vibration of functionally graded material sandwich plates using an accurate theory, Finite Elements in Analysis and Design, 57, 32–42, 2012.
  • 14. K.M. Liew, X. Zhao, A.J.M. Ferreira, A review of meshless methods for laminatem and functionally graded plates and shells, Composite Structures, 2011.
  • 15. H. Nguyen-Xuan, L.V. Tran, C.H. Thai, T. Nguyen-Thoi, Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing, ThinWalled Structures, 54, 1–18, 2012.
  • 16. Y.Y. Lee, X. Zhao, J.N. Reddy, Postbuckling analysis of functionally graded plater subject to compressive and thermal loads, Computer Methods in Applied Mechanics and Engineering, 199, 25, 1645–1653, 2010.
  • 17. J. Yang, H.S. Shen, Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments, Journal of Sound and Vibration, 255, 3, 579–602, 2002.
  • 18. S. Hui-Shen, Functionally graded materials: non-linear analysis of plates and shells, CRC Press, 2009.
  • 19. R.S. Rhee, Multi-scale modelling of functionally graded materials (FGMs) using finie elements methods, University of Southern California, 2007.
  • 20. R. Ahman, A. Bagri, S.P.A. Bordas, T. Rabczuk, Analysis of Thermoelastic Waves in a Two-Dimensional Functionally Graded Materials Domain by the Meshless Local Petrov-Galerkin(MLPG)Method, Computer Modelling in Engineering and Science, 2010.
  • 21. A. Wirowski, The Higher Frequency of Free Vibrations of Thin Annular Plates Made of Functionally Graded Material, PAMM, 10, 1, 231–232, 2010.
  • 22. A. Wirowski, Dynamic behaviour of thin annular plates made from functionally graded material, Shell Structures: Theory and Applications, 2, 207–210, Pietraszkiewicz, Kreja [Eds.], Taylor & Francis Group, London UK, 2010.
  • 23. Cz. Wozniak, E. Wierzbicki, Averaging techniques in thermomechanics solids and structures, Wyd. Naukowe PL, 2000.
  • 24. L. Domagalski, J. Jedrysiak, On the elastostatics of thin periodic plates with large deflections, Meccanica, 47, 7, 1659–1671, 2012.
  • 25. I. Cielecka, J. Jedrysiak, A non-asymptotic model of dynamics of honeycomb lattice-type plates, Journal of Sound and Vibration, 296, 1-2, 130–149, 2006.
  • 26. J. Jedrysiak, Free vibrations of thin periodic plates interacting with an elastic periodic foundation, International Journal of Mechanical Sciences, 45, 8, 1411–1428, 2003.
  • 27. B. Michalak, Dynamic modeling thin skeletonal shallow shells as 2D structures with nonuniform microstructures, Archive of Applied Mechanics, 82, 7, 949–961, 2012.
  • 28. J. Jedrysiak, A. Radzikowska, Tolerance averaging of heat conduction in transversally graded laminates, Meccanica, 47, 1, 95–107, 2012.
  • 29. J. Jedrysiak, A. Radzikowska, Some problems of heat conduction for transversally graded laminates with non-uniform distribution of laminas, Archives of Civil and Mechanical Engineering, 11, 1, 75–87, 2011.
  • 30. P. Ostrowski, B. Michalak, Non-stationary heat transfer in a hollow cylinder with functionally graded material properties, Journal of theoretical and applied mechanics, 49, 2, 385–397, 2011.
  • 31. J. Jedrysiak, The tolerance averaging model of dynamic stability of thin plates with one-directional periodic structure, Thin-Walled Structures, 45, 10-11, 855–860, 2007.
  • 32. J. Jedrysiak, B. Michalak, On the modelling of stability problems for thin plates with functionally graded structure, Thin-Walled Structures, 49, 5, 627, 2011.
  • 33. B. Tomczyk, A non-asymptotic model for the stability analysis of thin biperiodic cylindrical shells, Thin-Walled Structures, 45, 941–944, 2007.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0013-0048
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