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The mathematical expressions both of displacement and stress fields of circumferential wave propagation in circular tube structure with a weak interface are derived on condition that the interfacial properties between the two circular tubes are characterized by the interfacial spring model. Based on the said displacement and stress expressions derived, the dispersion equation of ultrasonic guided circumferential wave (UGCW) modes is formally presented by using the corresponding mechanical boundary conditions. According to the technique of modal expansion analysis for waveguide excitation, for a given excitation source used to generate circumferential wave in circular tube structure, the corresponding field of circumferential wave propagation can be decomposed into a series of UGCW modes. Using the reciprocity relations and mode orthogonality, the analytical expression of UGCW mode expansion coefficient is derived, which is closely related to the given excitation source for UGCW generation and the interfacial properties between the two tubes. The influences of change in the interfacial property on dispersion and acoustic field of the UGCW propagation are numerically analyzed. In the cases of perfect and sliding interfaces, for a given UGCW mode, the relative change rate of phase velocity is defined, and then its curve versus frequency is calculated, through which the specific frequency can be determined where the UGCW phase velocity appears to be most sensitive to the change in the interfacial property. For a given UGCW mode and driving frequency, it is numerically found that the displacement field on the outside surface of the circular tube structure changes sensitively and monotonically with change in interfacial property between the tubes. Clearly, through choosing the appropriate driving frequency and the mode of UGCW propagation, both the UGCW phase velocity and the displacement field on the outside surface of the circular tube structure will be monotonic and sensitive to change in interfacial property. It is expected that the results obtained in this paper will be of significance for accurately characterizing the interfacial properties of composite circular tube structures by using the UGCW technique.
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Keywords:
- ultrasonic guided circumferential wave /
- interfacial properties between two tubes /
- modal expansion analysis /
- dispersion
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[2] Peng F, Hu S Y 2009 Chin. J. Appl. Mech. 26 55 (in Chinese) [彭飞, 胡时岳 2009 应用力学学报 26 55]
[3] Du G S, Wang Y J, Yuan Y F, Zhao Q C 1998 Acta Phys. Sin. 47 27 (in Chinese) [杜光升, 王耀俊, 袁忆丰, 赵庆昌 1998 47 27]
[4] Deng M X 2005 Acta Acust. 30 542 (in Chinese) [邓明晰 2005 声学学报 30 542]
[5] Wu C P, Syu Y S, Lo J Y 2007 Int. J. Mech. Sci. 49 669
[6] Valle C, Qu J M, Jacobs L J 1999 Int. J. Eng. Sci. 37 1369
[7] Zhang H L, Yin X C 2010 J. Ship Mech. 14 930 (in Chinese) [张慧玲, 尹晓春 2010 船舶力学 14 930]
[8] He C F, Li L T, Wu B 2004 Chin. J. Mech. Eng. 40 7 (in Chinese) [何存富, 李隆涛, 吴斌 2004 机械工程学报 40 7]
[9] Huang P P, Yao Y W, Wu F G, Zhang X, Li J, Hu A Z 2015 Chin. Phys. B 24 054301
[10] Yang W, Fung T C, Chian K S 2007 J. Biomech. 40 481
[11] Zhang R, Wan M X 2000 Acta Phys. Sin. 49 1297 (in Chinese) [张锐, 万明习 2000 49 1297]
[12] Liu G, Qu J M 1998 ASME J. Appl. Mech. 65 424
[13] Liu Y, Li Z, Gong K Z 2012 Mech. Syst. Signal Process. 30 157
[14] Lu P, Wang Y J 2001 Acta Phys. Sin. 50 697 (in Chinese) [陆鹏, 王耀俊 2001 50 697]
[15] Wang Y J 2004 Acta Acust. 29 97 (in Chinese) [王耀俊 2004 声学学报 29 97]
[16] Auld B A 1973 Acoustics Fields and Wave in Solids (Vol. 2) (New York: John Willey Sons, Inc.) pp151-162
[17] Deng M X, Xiang Y X 2010 Chin. Phys. B 19 114302
[18] Deng M X 2006 Nonlinear Lamb Waves Propagate in the Solid Plates (Beijing: Science Press) pp12-40 (in Chinese) [邓明晰 2006 固体板中的非线性兰姆波 (北京: 科学出版社) 第1240页]
[19] Walsley R J 1973 Stress Wave Propagation in Solids (New York: Marcel Dekker, Inc.) pp128-159
[20] Rose J L 1999 Ultrasonic Waves in Solid Media (Cambridge: Cambridge University Press) pp35-41
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[1] Packer J A, Henderson J E (translated by Cao J J) 1997 Hollow Structural Section Connections and Trusses: A Design Guide (Beijing: Science Press) pp1-4 (in Chinese) [帕克J A, 亨德森J E 著 (曹俊杰 译) 1997 空心管结构连接设计指南 (北京: 科学出版社) 第14页]
[2] Peng F, Hu S Y 2009 Chin. J. Appl. Mech. 26 55 (in Chinese) [彭飞, 胡时岳 2009 应用力学学报 26 55]
[3] Du G S, Wang Y J, Yuan Y F, Zhao Q C 1998 Acta Phys. Sin. 47 27 (in Chinese) [杜光升, 王耀俊, 袁忆丰, 赵庆昌 1998 47 27]
[4] Deng M X 2005 Acta Acust. 30 542 (in Chinese) [邓明晰 2005 声学学报 30 542]
[5] Wu C P, Syu Y S, Lo J Y 2007 Int. J. Mech. Sci. 49 669
[6] Valle C, Qu J M, Jacobs L J 1999 Int. J. Eng. Sci. 37 1369
[7] Zhang H L, Yin X C 2010 J. Ship Mech. 14 930 (in Chinese) [张慧玲, 尹晓春 2010 船舶力学 14 930]
[8] He C F, Li L T, Wu B 2004 Chin. J. Mech. Eng. 40 7 (in Chinese) [何存富, 李隆涛, 吴斌 2004 机械工程学报 40 7]
[9] Huang P P, Yao Y W, Wu F G, Zhang X, Li J, Hu A Z 2015 Chin. Phys. B 24 054301
[10] Yang W, Fung T C, Chian K S 2007 J. Biomech. 40 481
[11] Zhang R, Wan M X 2000 Acta Phys. Sin. 49 1297 (in Chinese) [张锐, 万明习 2000 49 1297]
[12] Liu G, Qu J M 1998 ASME J. Appl. Mech. 65 424
[13] Liu Y, Li Z, Gong K Z 2012 Mech. Syst. Signal Process. 30 157
[14] Lu P, Wang Y J 2001 Acta Phys. Sin. 50 697 (in Chinese) [陆鹏, 王耀俊 2001 50 697]
[15] Wang Y J 2004 Acta Acust. 29 97 (in Chinese) [王耀俊 2004 声学学报 29 97]
[16] Auld B A 1973 Acoustics Fields and Wave in Solids (Vol. 2) (New York: John Willey Sons, Inc.) pp151-162
[17] Deng M X, Xiang Y X 2010 Chin. Phys. B 19 114302
[18] Deng M X 2006 Nonlinear Lamb Waves Propagate in the Solid Plates (Beijing: Science Press) pp12-40 (in Chinese) [邓明晰 2006 固体板中的非线性兰姆波 (北京: 科学出版社) 第1240页]
[19] Walsley R J 1973 Stress Wave Propagation in Solids (New York: Marcel Dekker, Inc.) pp128-159
[20] Rose J L 1999 Ultrasonic Waves in Solid Media (Cambridge: Cambridge University Press) pp35-41
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