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


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


2010 Mathematics Subject Classification



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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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