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On free vibrations of thin functionally graded plate bands resting on an elastic foundation

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this note free vibrations of plate bands with functionally graded properties, resting on an elastic foundation, are investigated. On the micro-level, these plate bands have a tolerance- -periodic structure. It can be shown that in dynamic problems of those objects, the effect of the microstructure size plays a role. This effect can be described in the framework of the tolerance model, which is presented here for these bands. Obtained results are evaluated introducing the asymptotic model. Both fundamental and higher free vibration frequencies of these plate bands are calculated using the Ritz method. The effects of differences of material plate properties in the cell on the microlevel and of the foundation are shown.
Rocznik
Strony
629--642
Opis fizyczny
Bibliogr. 45 poz., rys.
Twórcy
  • Lodz University of Technology, Department of Structural Mechanics, Łódź, Poland
  • Lodz University of Technology, Department of Structural Mechanics, Łódź, Poland
Bibliografia
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  • 3. Domagalski Ł., Jędrysiak J., 2012, On the elastostatics of thin periodic plates with large deflections, Meccanica, 47, 1659-1671
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  • 5. Jędrysiak J., 1999, Dynamics of thin periodic plates resting on a periodically inhomogeneous Winkler foundation, Archive of Applied Mechanics, 69, 345-356.
  • 6. Jędrysiak J., 2003, Free vibrations of thin periodic plates interacting with an elastic periodic foundation, International Journal of Mechanical Sciences, 45, 1411-1428
  • 7. Jędrysiak J., 2010, Thermomechanics of Laminates, Plates and Shells with Functionally Graded Structure (in Polish), Wyd. PŁ Łódź
  • 8. Jędrysiak J., 2013, Modelling of dynamic behaviour of microstructured thin functionally graded plates, Thin-Walled Structures, 71, 102-107
  • 9. Jędrysiak J., 2014, Free vibrations of thin functionally graded plates with microstructure, Engineering Structures, 75, 99-112
  • 10. Jędrysiak J., Michalak B., 2011, On the modelling of stability problems for thin plates with functionally graded structure, Thin-Walled Structures, 49, 627-635
  • 11. Jędrysiak J., Paś A., 2005, On the modelling of medium thickness plates interacting with a periodic Winkler’s subsoil, Electronic Journal of Polish Agricultural Universities, 8, www.ejpau.media.pl
  • 12. Jędrysiak J., Paś A., 2014, Dynamics of medium thickness plates interacting with a periodic Winkler’s foundation: non-asymptotic tolerance modelling, Meccanica, 49, 1577-1585
  • 13. Jędrysiak J., Pazera E., 2014, Free vibrations of thin microstructured plates, Journal of Vibrations in Physical Systems, 26, 93-98
  • 14. Jha D.K., Kant Tarun, Singh R.K., 2013, Free vibration response of functionally graded thick plates with shear and normal deformations effects, Composite Structures, 96, 799-823
  • 15. Kaźmierczak M., Jędrysiak J., 2010, Free vibrations of transversally graded plate bands, Electronic Journal of Polish Agricultural Universities, 13, 4, www.ejpau.media.pl
  • 16. Kaźmierczak M., Jędrysiak J., 2011, Tolerance modelling of vibrations of thin functionally graded plates, Thin-Walled Structures, 49, 1295-1303
  • 17. Kaźmierczak M., Jędrysiak J., 2013, A new combined asymptotic-tolerance model of vibrations of thin transversally graded plates, Engineering Structures, 46, 322-331
  • 18. Kaźmierczak-Sobińska M., Jędrysiak J., 2014, Vibrations of thin functionally graded plates with tolerance-periodic microstructure, Journal of Vibrations in Physical Systems, 26, 99-104
  • 19. Kohn R.V., Vogelius M., 1984, A new model for thin plates with rapidly varying thickness, International Journal of Solids and Structures, 20, 333-350
  • 20. Kołakowski Z., 2009, Some aspects of the axial extension mode in an elastic thin-walled beam- -column, Journal of Theoretical and Applied Mechanics, 50, 147-168
  • 21. Kołakowski Z., 2012, Static and dynamic interactive buckling of composite columns, Journal of Theoretical and Applied Mechanics, 47, 177-192
  • 22. Królak M., Kowal-Michalska K., Mania R.J., Świniarski J., 2009, Stability and load carrying capacity of multi-cell thin-walled columns of rectangular cross-sections, Journal of Theoretical and Applied Mechanics, 47, 435-456
  • 23. Kubiak T., 2006, Interactive buckling in thin-walled beam-columns with widthwise varying orthotropy, Journal of Theoretical and Applied Mechanics, 44, 75-90
  • 24. Magnucka-Blandzi E., 2011, Mathematical modelling of a rectangular sandwich plate with a metal foam core, Journal of Theoretical and Applied Mechanics, 49, 439-455
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  • 26. Marczak J., Jędrysiak J., 2014, Analysis of vibrations of plate strip with concentrated masses using tolerance averaging technique, Journal of Vibrations in Physical Systems, 26, 161-168
  • 27. Michalak B., 2002, On the dynamic behaviour of a uniperiodic folded plates, Journal of Theoretical and Applied Mechanics, 40, 113-128
  • 28. Michalak B., 2012, Dynamic modeling of thin skeletonal shallow shells as 2D structures with nonuniform microstructures, Archive of Applied Mechanics, 82, 949-961
  • 29. Michalak B., Wirowski A., 2012, Dynamic modelling of thin plate made of certain functionally graded materials, Meccanica, 47, 1487-1498
  • 30. Nagórko W., 1998, Two methods of modelling of periodic nonhomogeneous elastic plates, Journal of Theoretical and Applied Mechanics, 36, 291-303
  • 31. Nagórko W., Woźniak C., 2002, Nonasymptotic modelling of thin plates reinforced by a system of stiffeners, Electronic Journal of Polish Agricultural Universities, 5, 2, www.ejpau.media.pl
  • 32. Oktem A.S., Mantari J.L., Guedes Soares C., 2012, Static response of functionally graded plates and doubly-curved shells based on a higher order shear deformation theory, European Journal of Mechanics – A/Solids, 36, 163172
  • 33. Ostrowski P., Michalak B., 2011, Non-stationary heat transfer in a hollow cylinder with functionally graded material properties, Journal of Theoretical and Applied Mechanics, 49, 385-397
  • 34. Roque C.M.C., Ferreira A.J.M., Jorge R.M.N., 2007, A radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory, Journal of Sound and Vibration, 300, 1048-1070
  • 35. Suresh S., Mortensen A., 1998, Fundamentals of Functionally Graded Materials, The University Press Cambridge
  • 36. Tahouneh V., Naei M.H., 2014, A novel 2-D six-parameter power-law distribution for threedimensional dynamic analysis of thick multi-directional functionally graded rectangular plates resting on a two-parameter elastic foundation, Meccanica, 49, 91-109
  • 37. Tomczyk B., 2007, A non-asymptotic model for the stability analysis of thin biperiodic cylindrical shells, Thin-Walled Structures, 45, 941-944
  • 38. Tomczyk B., 2013, Length-scale effect in dynamics and stability of thin periodic cylindrical shells, Scientific Bulletin of the Lodz University of Technology, 1166, series: Scientific Transactions, 466, Wyd. PŁ, Łódź
  • 39. Tornabene F., Liverani A., Caligiana G., 2011, FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: A 2-D GDQ solution for free vibrations, International Journal of Mechanical Sciences, 53, 443-470
  • 40. Wierzbicki E., Woźniak C., 2000, On the dynamics of combined plane periodic structures, Archive of Applied Mechanics, 70, 387-398
  • 41. Wirowski A., 2012, Self-vibration of thin plate band with non-linear functionally graded material, Archives of Mechanics, 64, 603-615
  • 42. Woźniak C., et al. (Eds.), 2010, Mathematical Modeling and Analysis in Continuum Mechanics of Microstructured Media, Wyd. PŚl, Gliwice
  • 43. Woźniak C., Michalak B., Jędrysiak J. (Eds.), 2008, Thermomechanics of Heterogeneous Solids and Structures, Wyd. PŁ, Łódź
  • 44. Woźniak C., Wierzbicki E., 2000, Averaging Techniques in Thermomechanics of Composite Solids, Wyd. PCz, Częstochowa
  • 45. Yajuvindra Kumar, Lal R., 2012, Vibrations of nonhomogeneous orthotropic rectangular plates with bilinear thickness variation resting on Winkler foundation, Meccanica, 47, 893-915
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b5c50e96-89c9-4940-b325-6654585b883b
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