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The influences of the interfacial properties on second-harmonic generation by primary circumferential ultrasonic guided wave (CUGW) propagation in a composite tube are investigated in this paper.Within a second-order perturbation approximation,the nonlinear effect of primary CUGW propagation may be treated as a second-order perturbation to its linear response.Due to the interfacial spring model,the properties of interface between the inner and outer circular tubes constituting the composite tube are characterized by the normal and tangential interfacial stiffness values.According to the technique of modal expansion analysis for waveguide excitation,the second-harmonic field of primary CUGW propagation can be decomposed into a series of double frequency CUGW modes.It is found that changes of the interfacial properties of composite tube will obviously influence the efficiency of second-harmonic generation by primary CUGW propagation.Specifically,for a given composite tube with a perfect interface,an appropriate fundamental and double frequency CUGW mode pair that satisfies the phase velocity matching condition can be chosen to enable the double frequency CUGW mode generated by the primary CUGW propagation to accumulate along the circumferential direction,and an obvious second-harmonic signal of primary CUGW propagation to be observed.When the changes of the interfacial properties of composite tube (versus the perfect interface with infinite interfacial stiffnesses) take place,the effect of second-harmonic generation by primary CUGW propagation will be influenced in the following aspects.Firstly, the changes of the interfacial properties in the case of perfect interface may provide different acoustic fields for the primary CUGW.This will influence the magnitude of the modal expansion coefficient of double frequency CUGW mode generated,because both the second-order bulk forcing source (due to the double frequency bulk driving force) and the second-order surface/interface forcing source (due to the quadratic term of expression of the first Piola-Kirchhoff stress tensor) in the governing equation of the double frequency CUGW are both proportional to the squared amplitude of the primary CUGW.Secondly,the second-order surface/interface forcing source in the said governing equation is directly associated with the interfacial stiffnesses.This will also lead to the change of the magnitude of the modal expansion coefficient of double frequency CUGW mode when the change of interfacial stiffnesses takes place.Thirdly,the change of the interfacial stiffnesses will influence the dispersion relation of CUGW propagation.The phase velocity matching conditions for the fundamental and double frequency CUGW mode pair,which are satisfied originally in the case of perfect interface,may not now be satisfied.This will remarkably influence the efficiency of second-harmonic generation by the primary CUGW propagation.It is found that when there is a clear difference between the phase velocities of the fundamental and double frequency CUGW mode pair (caused by the changes in the interfacial stiffnesses),the double frequency CUGW mode generated may not have a cumulative effect along the circumferential direction.In this case,the efficiency of second-harmonic generation by primary CUGW propagation will become more and more weak.Theoretical analyses and numerical simulations performed both demonstrate that the effect of second-harmonic generation by primary CUGW propagation is very sensitive to changes in the interfacial properties of composite tube, and that it can be used to accurately characterize the interfacial properties in composite tube structures.
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Keywords:
- interfacial properties between two tubes /
- circumferential ultrasonic guided wave /
- second-harmonic generation /
- modal expansion analysis
[1] Gu J Z 2000 Shanghai Metals 22 16 (in Chinese) [顾建忠2000上海金属22 16]
[2] Rokhlin S I, Wang Y J 1991 J. Acoust. Soc. Am. 89 2758
[3] Zhang R, Wang M X 2000 Acta Phys. Sin. 49 7
[4] Lu P, Wang Y J 2001 Acta Phys. Sin. 50 697 (in Chinese) [陆鹏, 王耀俊2001物理学报50 697]
[5] Wang Y J 2004 Acta Acust. 29 97 (in Chinese) [王耀俊2004声学学报29 97]
[6] Heller K, Jacobs L J, Qu J M 2000 NDT&E Int. 33 8
[7] Rose J L 2002 J. Press Vessel Tech. 124 273
[8] Zhang H L, Yin X C 2007 Chin. J. Solid Mech. 28 109 (in Chinese) [张慧玲, 尹晓春2007固体力学学报28 109]
[9] Zhang H L, Yin X C 2007 Acta Mech. Solida Sinica 20 110
[10] Zhang H L, Yin X C 2008 J. Vib. Eng. 21 471 (in Chinese) [张慧玲, 尹晓春2008振动工程学报21 471]
[11] Gao G J, Deng M X, Li M L 2015 Acta Phys. Sin. 64 224301 (in Chinese) [高广健, 邓明晰, 李明亮2015物理学报64 224301]
[12] Deng M X 2007 Acta Acust. 32 205 (in Chinese) [邓明晰2007声学学报32 205]
[13] Deng M X, Wang P, Lú X F 2006 J. Phys. D: Appl. Phys. 39 3018
[14] Gao G J, Deng M X, Li M L 2015 Acta Phys. Sin. 64 184303 (in Chinese) [高广健, 邓明晰, 李明亮2015物理学报64 184303]
[15] Deng M X, Gao G J, Li M L 2015 Chin. Phys. Lett. 32 124305
[16] Deng M X 1996 Acta Acust. 21 429 (in Chinese) [邓明晰1996声学学报21 429]
[17] Xiang Y X, Deng M X 2008 Chin. Phys. B 17 4232
[18] Hamilton M F, Blackstock D T 1998 Nonlinear Acoustics (New York: Academic Press) Chapter 9 and 10
[19] Deng M X 2006 Nonlinear Lamb Waves in 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12–40页]
[20] Auld B A 1973 Acoustic Fields and Waves in Solids Vol. Ⅱ (New York: John Wiley) pp151-162
[21] Jia X 1997 J. Acoust. Soc. Am. 101 834
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[1] Gu J Z 2000 Shanghai Metals 22 16 (in Chinese) [顾建忠2000上海金属22 16]
[2] Rokhlin S I, Wang Y J 1991 J. Acoust. Soc. Am. 89 2758
[3] Zhang R, Wang M X 2000 Acta Phys. Sin. 49 7
[4] Lu P, Wang Y J 2001 Acta Phys. Sin. 50 697 (in Chinese) [陆鹏, 王耀俊2001物理学报50 697]
[5] Wang Y J 2004 Acta Acust. 29 97 (in Chinese) [王耀俊2004声学学报29 97]
[6] Heller K, Jacobs L J, Qu J M 2000 NDT&E Int. 33 8
[7] Rose J L 2002 J. Press Vessel Tech. 124 273
[8] Zhang H L, Yin X C 2007 Chin. J. Solid Mech. 28 109 (in Chinese) [张慧玲, 尹晓春2007固体力学学报28 109]
[9] Zhang H L, Yin X C 2007 Acta Mech. Solida Sinica 20 110
[10] Zhang H L, Yin X C 2008 J. Vib. Eng. 21 471 (in Chinese) [张慧玲, 尹晓春2008振动工程学报21 471]
[11] Gao G J, Deng M X, Li M L 2015 Acta Phys. Sin. 64 224301 (in Chinese) [高广健, 邓明晰, 李明亮2015物理学报64 224301]
[12] Deng M X 2007 Acta Acust. 32 205 (in Chinese) [邓明晰2007声学学报32 205]
[13] Deng M X, Wang P, Lú X F 2006 J. Phys. D: Appl. Phys. 39 3018
[14] Gao G J, Deng M X, Li M L 2015 Acta Phys. Sin. 64 184303 (in Chinese) [高广健, 邓明晰, 李明亮2015物理学报64 184303]
[15] Deng M X, Gao G J, Li M L 2015 Chin. Phys. Lett. 32 124305
[16] Deng M X 1996 Acta Acust. 21 429 (in Chinese) [邓明晰1996声学学报21 429]
[17] Xiang Y X, Deng M X 2008 Chin. Phys. B 17 4232
[18] Hamilton M F, Blackstock D T 1998 Nonlinear Acoustics (New York: Academic Press) Chapter 9 and 10
[19] Deng M X 2006 Nonlinear Lamb Waves in 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12–40页]
[20] Auld B A 1973 Acoustic Fields and Waves in Solids Vol. Ⅱ (New York: John Wiley) pp151-162
[21] Jia X 1997 J. Acoust. Soc. Am. 101 834
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