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Applied Mathematics and Mechanics

, Volume 33, Issue 12, pp 1493–1504 | Cite as

Vibration analysis of foam plates based on cell volume distribution

  • Yu-li Ma (马宇立)
  • Ji-wei Chen (陈继伟)
  • Yong-quan Liu (刘咏泉)
  • Xian-yue Su (苏先樾)Email author
Article

Abstract

In this paper, vibration analysis of irregular-closed-cell foam plates is performed. A cell volume distribution coefficient is introduced to modify the original Gibson-Ashby equations of effective Young’s modulus of foam materials. A Burr distribution is imported to describe the cell volume distribution situation. Three Burr distribution parameters are obtained and related to the cell volume range and the diversity. Based on the plate theory and the effective modulus theory, the natural frequency of foam plates is calculated with the change of the cell volume distribution parameters. The relationship between the frequencies and the cell volumes are derived. The scale factor of the average cell size is introduced and proved to be an important factor to the performance of the foam plate. The result is shown by the existing theory of size effects. It is determined that the cell volume distribution has an impact on the natural frequency of the plate structure based on the cell volume range, the diversity, and the average size, and the impact can lead to optimization of the synthesis procedure.

Key words

closed-cell foam plate vibration natural frequency cell volume distribution effective Young’s modulus scale factor 

Chinese Library Classification

O322 

2010 Mathematics Subject Classification

70K60 

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References

  1. [1]
    Gibson, L. J. and Ashby, M. F. Cellular Solids: Structure and Properties, 2nd ed., Press Syndicate of University of Cambridge, Cambridge (1997)Google Scholar
  2. [2]
    Hausherr, J. M., Krenkel, W., Fischer, F., and Altstadt, V. Nondestructive characterization of high-performance C/SiC-ceramics using X-ray-computed tomography. International Journal of Applied Ceramic Technology, 7(3), 361–368 (2010)CrossRefGoogle Scholar
  3. [3]
    Marmottant, A., Salvo, L., Martin, C. L., and Mortensen, A. Coordination measurements in compacted NaCl irregular powders using X-ray microtomography. Journal of the European Ceramic Society, 28(13), 2441–2449 (2008)CrossRefGoogle Scholar
  4. [4]
    Guo, L. W. and Yu, J. L. Bending behavior of aluminum foam-filled double cylindrical tubes. Acta Mechanica, 222(3–4), 233–244 (2011)zbMATHCrossRefGoogle Scholar
  5. [5]
    Elliott, J. A., Windle, A. H., Hobdell, J. R., Eeckhaut, G., Oldman, R. J., Ludwig, W., Boller, E., Cloetens, P., and Baruchel, J. In-situ deformation of an open-cell flexible polyurethane foam characterised by 3D computed microtomography. Journal of Materials Science, 37(8), 1547–1555 (2002)CrossRefGoogle Scholar
  6. [6]
    Viot, P., Plougonven, E., and Bernard, D. Microtomography on polypropylene foam under dynamic loading: 3D analysis of bead morphology evolution. Composites Part A: Applied Science and Manufacturing, 39(8), 1266–1281 (2008)CrossRefGoogle Scholar
  7. [7]
    Van Dommelen, J. A. W., Wismans, J. G. F., and Govaert, L. E. X-ray computed tomographybased modeling of polymeric foams: the effect of finite element model size on the large strain response. Journal of Polymer Science Part B: Polymer Physics, 48(13), 1526–1534 (2010)CrossRefGoogle Scholar
  8. [8]
    Ashby, M. F. Materials Selection in Mechanical Design, 2nd ed., Butterworth Heinemann, Oxford (1999)Google Scholar
  9. [9]
    Ashby, M. F. Designing hybrid materials. Acta Materialia, 51, 5801–5821 (2003)CrossRefGoogle Scholar
  10. [10]
    Jeon, I., Asahina, T., Kang, K. J., Im, S., and Lu, T. J. Finite element simulation of the plastic collapse of closed-cell aluminum foams with X-ray computed tomography. Mechanics of Materials, 42(3), 227–236 (2010)CrossRefGoogle Scholar
  11. [11]
    Jeon, I., Katou, K., Sonoda, T., Asahina, T., and Kang, K. J. Cell wall mechanical properties of closed-cell Al foam. Mechanics of Materials, 41(1), 60–73 (2009)zbMATHCrossRefGoogle Scholar
  12. [12]
    Teixeira, S., Rodriguez, M. A., Pena, P., de Aza, A. H., de Aza, S., Ferraz, M. P., and Monteiro, F. J. Physical characterization of hydroxyapatite porous scaffolds for tissue engineering. Materials Science and Engineering C: Biomimetic and Supramolecular Systems, 29(5), 1510–1514 (2009)CrossRefGoogle Scholar
  13. [13]
    Ma, Y., Pyrz, R., Rodriguez-Perez, M. A., Escudero, J., Rauhe, J. C., and Su, X. X-ray microtomographyic study of nanoclay-polypropylene foams. Cellular Polymers, 30(3), 95–110 (2011)Google Scholar
  14. [14]
    Dai, G. M. and Zhang, W. H. Size effects of basic cell in static analysis of sandwich beams. International Journal of Solids and Structures, 45(9), 2512–2533 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Chen, J. W., Liu, W., and Su, X. Y. Vibration and buckling of truss core sandwich plates on an elastic foundation subjected to biaxial in-plane loads. Computers, Materials and Continua, 24(2), 163–181 (2011)Google Scholar
  16. [16]
    Mindlin, R. D. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics, 18, 31–38 (1951)zbMATHGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yu-li Ma (马宇立)
    • 1
    • 2
  • Ji-wei Chen (陈继伟)
    • 1
  • Yong-quan Liu (刘咏泉)
    • 1
  • Xian-yue Su (苏先樾)
    • 1
    Email author
  1. 1.The State Key Laboratory for Turbulence and Complex Systems (LTCS) and Department of Mechanics and Aerospace Engineering, College of EngineeringPeking UniversityBeijingP. R. China
  2. 2.Chinalco Research Institute of Science and TechnologyBeijingP. R. China

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