层状复合材料周期结构的超声传播频散特性及均匀化模拟
Ultrasonic Dispersion and Structure Homogenization Simulation of Layered Periodic Structures Composites
摘 要
首先采用改进全局矩阵算法, 研究了层状复合材料周期结构的频散特性。当层数足够大时, 在特定方向上结构表现出类似均匀各向异性材料的性质, 可采用均匀化方法求解频散曲线。其次, 给出了层状复合材料周期结构均匀化的计算方法, 并研究了其适用范围。发现在低频段和高频高相速度段范围内可以采用等效模量计算频散特性; 而高频低相速度范围内不能采用均匀化方法, 该范围内波的性质有待进一步研究。
复合材料
全局矩阵
等效模量
Layered periodic structure
Composites
Global matrix
Effective modules
Abstract
The dispersive property of layered periodic composites structure was researched by improved global matrix approach, firstly. It was found that the structure represented characterization of the homogenous anisotropic materials when the number of layer was large enough. Then the effective modules algorithm was developed and its applicability was discussed. The effective modules could be accepted in two ranges including the lower frequency band as well as the higher frequency and phase velocity band. However, the dispersive curves could not be calculated using effective modules in situation of higher frequency band with lower phase velocity below the longitudinal wave velocity, and the characterization of waves needed further investigation.
中图分类号 TG115.28
所属栏目 科研成果与学术交流
基金项目
收稿日期 2009/10/13
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备注常新龙(1965- ), 男, 教授, 博士生导师, 研究方向为火箭发动机失效物理与可靠性, 复合材料无损检测。
引用该论文: CHANG Xin-Long,NI Tao,AI Chun-An,LIU Yu. Ultrasonic Dispersion and Structure Homogenization Simulation of Layered Periodic Structures Composites[J]. Nondestructive Testing, 2010, 32(10): 780～784
常新龙,尼 涛,艾春安,刘 瑜. 层状复合材料周期结构的超声传播频散特性及均匀化模拟[J]. 无损检测, 2010, 32(10): 780～784
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参考文献
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【2】张海燕, 他得安, 刘镇清.层状各向异性复合板中的兰姆波[M].北京: 科学出版社, 2008.
【3】Karunasena W, Shah A H, Datta S K. Wave propagation in a multilayered laminated cross-ply composite plate[J]. Journal of Applied Mechanics, 1991, 58(10): 1028-1032.
【4】Lee J. Plate waves in multi-directional composite laminates[J]. Composite Structures, 1999, 46(4): 289-297.
【5】Wang L, Rokhlin S I. Floquet wave homogenization of periodic anisotropic media[J]. Journal of the Acoustical Society of America, 2002, 112(1): 38-45.
【6】Rokhlin S I, Wang L. Stable recursive algorithm for elastic wave propagation in layered anisotropic media: stiffness matrix method[J]. Journal of the Acoustical Society of America, 2002, 112(3): 822-834.
【7】Rokhlin S I, Wang L. Ultrasonic waves in layered anisotropic media: characterization of multidirectional composites[J]. Solids and Structures, 2002, 39(9): 5529-5545.
【8】Liu G R, Tani J, Watanabe K, et al. Lamb wave propagation in anisotropic laminates[J]. Journal of Applied Mechanics, 1990, 57(6): 923-929.
【9】Michel J C, Moulinec H, Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach[J]. Computer Methods in Applied Mechanics and Engineering, 1999, 172(2): 109-143.
【10】Cohen I, Bergman D J. Effective elastic properties of periodic composite medium[J]. Journal of the Mechanics and Physics of Solids, 2003, 51(9): 1433-1457.
【11】Pastukhova S E. Homogenization of elasticity problems on periodic composite structures[J]. Sbornic: Mathematics, 2005, 196(7): 1033-1073.
【12】曹礼群, 崔俊芝.复合材料拟周期结构的均匀化方法[J].计算数学, 1999, 21(3): 331-344.
【13】胡更开, 郑泉水, 黄筑平.复合材料有效弹性性质分析方法[J].力学进展, 2001, 31(3): 361-392.
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