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

Vibration analysis of foam plates based on cell volume distribution

马宇立^1,2, 陈继伟¹, 刘咏泉¹, 苏先樾¹

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

收稿日期:2012-03-14 修回日期:2012-04-12 出版日期:2012-12-10 发布日期:2012-12-10
通讯作者: Xian-yue SU, Professor, Ph.D., E-mail: xyswsk@pku.edu.cn E-mail:xyswsk@pku.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 90916007)

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)

摘要/Abstract

摘要： 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.

关键词: uniformly smooth real Banach spaces, Ishikawa iteration with Errors, strongly accretive operator

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

中图分类号:

O322

马宇立;陈继伟;刘咏泉;苏先樾. Vibration analysis of foam plates based on cell volume distribution[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1493-1504.

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

参考文献

[1] Gibson, L. J. and Ashby, M. F. Cellular Solids: Structure and Properties, 2nd ed., Press Syndicateof University of Cambridge, Cambridge (1997)
[2] Hausherr, J. M., Krenkel, W., Fischer, F., and Altstadt, V. Nondestructive characterization ofhigh-performance C/SiC-ceramics using X-ray-computed tomography. International Journal ofApplied Ceramic Technology, 7(3), 361-368 (2010)
[3] Marmottant, A., Salvo, L., Martin, C. L., and Mortensen, A. Coordination measurements in com-pacted NaCl irregular powders using X-ray microtomography. Journal of the European CeramicSociety, 28(13), 2441-2449 (2008)
[4] Guo, L. W. and Yu, J. L. Bending behavior of aluminum foam-filled double cylindrical tubes. ActaMechanica, 222(3-4), 233-244 (2011)
[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 foamcharacterised by 3D computed microtomography. Journal of Materials Science, 37(8), 1547-1555(2002)
[6] Viot, P., Plougonven, E., and Bernard, D.Microtomography on polypropylene foam under dynamicloading: 3D analysis of bead morphology evolution. Composites Part A: Applied Science andManufacturing, 39(8), 1266-1281 (2008)
[7] Van Dommelen, J. A. W., Wismans, J. G. F., and Govaert, L. E. X-ray computed tomography-based modeling of polymeric foams: the effect of finite element model size on the large strainresponse. Journal of Polymer Science Part B: Polymer Physics, 48(13), 1526-1534 (2010)
[8] Ashby, M. F. Materials Selection in Mechanical Design, 2nd ed., Butterworth Heinemann, Oxford(1999)
[9] Ashby, M. F. Designing hybrid materials. Acta Materialia, 51, 5801-5821 (2003)
[10] Jeon, I., Asahina, T., Kang, K. J., Im, S., and Lu, T. J. Finite element simulation of the plasticcollapse of closed-cell aluminum foams with X-ray computed tomography. Mechanics of Materials,42(3), 227-236 (2010)
[11] Jeon, I., Katou, K., Sonoda, T., Asahina, T., and Kang, K. J. Cell wall mechanical properties ofclosed-cell Al foam. Mechanics of Materials, 41(1), 60-73 (2009)
[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. MaterialsScience and Engineering C: Biomimetic and Supramolecular Systems, 29(5), 1510-1514 (2009)
[13] Ma, Y., Pyrz, R., Rodriguez-Perez, M. A., Escudero, J., Rauhe, J. C., and Su, X. X-ray microto-mographyic study of nanoclay-polypropylene foams. Cellular Polymers, 30(3), 95-110 (2011)
[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)
[15] Chen, J. W., Liu, W., and Su, X. Y. Vibration and buckling of truss core sandwich plates on anelastic foundation subjected to biaxial in-plane loads. Computers, Materials and Continua, 24(2),163-181 (2011)
[16] Mindlin, R. D. Influence of rotatory inertia and shear on flexural motions of isotropic, elasticplates. Journal of Applied Mechanics, 18, 31-38 (1951)

Vibration analysis of foam plates based on cell volume distribution

Vibration analysis of foam plates based on cell volume distribution

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价

[1]	谷峰. ITERATIVE PROCESS FOR CERTAIN NONLINEAR MAPPINGS WITH LIPSCHITZ CONDITION[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(12): 1458-1467.
[2]	丁协平;张红琳. ITERATIVE PROCESS TO φ-HEMICONTRACTIVE OPERATOR AND φ-STRONGLY ACCRETIVE OPERATOR EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(11): 1256-1263.
[3]	周海云. ITERATIVE SOLUTION OF NONLINEAR EQUATIONS WITH STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(3): 282-289.
[4]	薛志群;周海云. ITERATIVE APPROXIMATION WITH ERRORS OF FIXED POINT FOR A CLASS OF NONLINEAR OPERATOR WITH A BOUNDER RANGE[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(1): 99-104.