Vibration analysis of foam plates based on cell volume distribution

doi:10.1007/s10483-012-1639-7

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (12): 1493-1504.doi: https://doi.org/10.1007/s10483-012-1639-7

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Vibration analysis of foam plates based on cell volume distribution

Yu-li MA^1,2, Ji-wei CHEN¹, Yong-quan LIU¹, Xian-yue SU¹

1. The State Key Laboratory for Turbulence and Complex Systems LTCS and Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, P. R. China;
2. Chinalco Research Institute of Science and Technology, Beijing 100082, P. R. China

Received:2012-03-14 Revised:2012-04-12 Online:2012-12-10 Published:2012-12-10
Supported by:
Project supported by the National Natural Science Foundation of China (No. 90916007)

Abstract

Abstract: In this paper, vibration analysis of irregular-closed-cell foam plates is per-formed. 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 pa-rameters 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: uniformly smooth real Banach spaces, Ishikawa iteration with Errors, strongly accretive operator

2010 MSC Number:

O322

Yu-li MA;Ji-wei CHEN;Yong-quan LIU;Xian-yue SU. Vibration analysis of foam plates based on cell volume distribution. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1493-1504.

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Vibration analysis of foam plates based on cell volume distribution

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