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超声技术可用于对功能梯度材料(FGMs)的性质进行评估. 由于FGMs性质的非均匀性,采用分布函数来描述FGMs弹性常数和密度沿厚度方向的变化趋势,并提出利用Taylor展开的方法来解决分布函数为任意函数时的FGMs中Lamb波的传播问题. 利用本征函数展开法得到了铁基氧化铝FGMs中Lamb波的相速度色散曲线,讨论了材料性质分布对铁基氧化铝FGMs中Lamb波传播特性的影响. 为FGMs性质(沿板厚方向变化)的反演提供了理论依据.
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关键词:
- 功能梯度材料 /
- Lamb波 /
- Legendre多项式 /
- 分布函数
The technology of ultrasound can be used to evaluate properties of functionally graded materials(FGMs). Because of the inhomogeneity of the FGM properties, distribution function is used to describe the FGM elastic constant and density which are assumed to vary in the direction of the thickness. Taylor expansion method is used to solve Lamb wave propagation problems in FGMs, in which the distribution function is an arbitrary function. Phase velocity dispersion curves for Lamb waves in iron-based alumina FGMs are obtained by using an extension of the Legendre polynomial approach, and the effects of the gradient variation of iron-based alumina FGMs properties on Lamb wave propagation characteristics are discussed in detail. The conclusion could be useful for inversing elastic constant and density, which are varied along the thickness direction, of FGMs.-
Keywords:
- functionally gradient materials /
- Lamb waves /
- Legendre polynomial /
- distribution function
[1] Han Q B, Qian M L, Zhu C P 2007 Acta Phys. Sin. 56 313 (in Chinese) [韩庆邦、钱梦禄、朱昌平 2007 物理学报 56 313]
[2] Chona R, Suh C S, Rabroker G A 2003 Optics and Lasers in Engineering 40 371
[3] Dewhurst R J, Edwards C, McKie A D W, Palmer S B 1987 Appl. Phys. Lett. 51 1066
[4] Xu B Q, Shen Z H, Ni X W 2004 Appl. Phys. Lett. 85 6161
[5] Yuan L, Shen Z H, Ni X W 2007 Acta Phys. Sin. 56 7058 (in Chinese) [袁 玲、沈中华、倪晓武 2007 物理学报 56 7058]
[6] Sun H X, Xu B Q, Wang J J, Xu G D, Xu C G, Wang F 2009 Acta Phys. Sin. 58 6344 (in Chinese) [孙宏祥、许伯强、王纪俊、徐晨光、王 峰 2009 物理学报 58 6344]
[7] Hurley D H, Spicer J B 2004 J. Acoust. Soc. Am. 116 2914
[8] Cai C, Liu G R, Lam K Y 2001 Journal of Sound and Vibration 248 71
[9] Kim Y, Hunt W D 1990 IEEE Ultrasonics Symposium 90 179
[10] Lefebvre J E, Zhang V, Gazalet J 1999 J. Appl. Phys. 85 3419
[11] Datta S, Hunsinger B J 1978 J. Appl. Phys. 49 475
[12] Lefebvre J E, Zhang V, Gazalet J 2001 IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 48 1332
[13] Elmaimouni L, Lefebvre J E, Zhang V 2005 NDT & E International 38 344
[14] Liu G R, Han X, Xu Y G, Lam K Y 2001 Composites Science and Technology 61 1401
[15] Yang J, Cheng J C, Berthelot Y H 2002 J. Acoust. Soc. Am. 111 1245
[16] Yu J G, Wu B 2009 NDT & E International 42 452
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[1] Han Q B, Qian M L, Zhu C P 2007 Acta Phys. Sin. 56 313 (in Chinese) [韩庆邦、钱梦禄、朱昌平 2007 物理学报 56 313]
[2] Chona R, Suh C S, Rabroker G A 2003 Optics and Lasers in Engineering 40 371
[3] Dewhurst R J, Edwards C, McKie A D W, Palmer S B 1987 Appl. Phys. Lett. 51 1066
[4] Xu B Q, Shen Z H, Ni X W 2004 Appl. Phys. Lett. 85 6161
[5] Yuan L, Shen Z H, Ni X W 2007 Acta Phys. Sin. 56 7058 (in Chinese) [袁 玲、沈中华、倪晓武 2007 物理学报 56 7058]
[6] Sun H X, Xu B Q, Wang J J, Xu G D, Xu C G, Wang F 2009 Acta Phys. Sin. 58 6344 (in Chinese) [孙宏祥、许伯强、王纪俊、徐晨光、王 峰 2009 物理学报 58 6344]
[7] Hurley D H, Spicer J B 2004 J. Acoust. Soc. Am. 116 2914
[8] Cai C, Liu G R, Lam K Y 2001 Journal of Sound and Vibration 248 71
[9] Kim Y, Hunt W D 1990 IEEE Ultrasonics Symposium 90 179
[10] Lefebvre J E, Zhang V, Gazalet J 1999 J. Appl. Phys. 85 3419
[11] Datta S, Hunsinger B J 1978 J. Appl. Phys. 49 475
[12] Lefebvre J E, Zhang V, Gazalet J 2001 IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 48 1332
[13] Elmaimouni L, Lefebvre J E, Zhang V 2005 NDT & E International 38 344
[14] Liu G R, Han X, Xu Y G, Lam K Y 2001 Composites Science and Technology 61 1401
[15] Yang J, Cheng J C, Berthelot Y H 2002 J. Acoust. Soc. Am. 111 1245
[16] Yu J G, Wu B 2009 NDT & E International 42 452
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