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In this paper, PM (Preisach-Mayergoyz) model in one dimension is extended to two dimensions. Hysteretic stress-strain relation could be obtained when hysteretic mesoscopic elastic unit (HMEU) is considered.The sound field is calculated using a first-order finite difference equation, and the high-odd-order harmonic waves can be found apparently in the sound field. Then, the received full waves are filtered,amplified, time-reversed, and re-emitted through corresponding receiving transducers. The high-order harmonic waves focus on the micro-damage zone. So this method can be used to detect the micro-damages by nonlinear high-order harmony waves. Furthermore, it also provides a method of the early detection of fatigue damages.
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Keywords:
- nonlinear acoustics /
- high-order harmonic wave /
- hysteretic stress-strain relationship /
- time reversal
[1] Suresh S 1998 Fatigue of Materials (Cambridge University Press) p11, 206
[2] Delsanto P P 2006 Universality of nonclassical nonlinearity: applications to non-destructive evaluations and ultrasonics (New York:Springer) p49
[3] Solodov I Y, Krohn N, Busse G 2002 Ultrasonics 40 621
[4] Zhang H Y, Sun X L, Cao Y P, Chen X H, Yu J B 2010 Acta Phys. Sin. 59 7111(in Chinese) [张海燕, 孙修立, 曹亚萍, 陈先华, 于建波 2010 59 7111]
[5] Park H W, Sohn H, Law K H, Farrar C R 2007 J. Sound & Vib 302 50
[6] Zhang B X, Lu M H 2002 ACTA Acustica 27 541(in Chinese) [张碧星, 陆铭慧 2002 声学学报 27 541]
[7] Ulrich T J, JohnsonP A, Guyer R A 2007 Phys. Rev. Lett. 98 104301
[8] Ulrich T J, SutinA M, GuyerR A 2008 Inter. J. Non-linear Mech. 43 209
[9] Goursolle T, Santos S D, MatarO B, Calle S 2008 Inter. J. Non-linear Mech. 43 170
[10] Dhital D, LeeJ R 2012 Exp. Mech. 52 1111
[11] Gao G L, Li D Y, Dong J W, Shi D Q, Teng F 2010 J. Harbin Engineering University 31 395(in Chinese) [高桂丽, 李大勇, 董静薇, 石德全, 滕飞 2010 哈尔滨工程大学学报 31 395]
[12] Kim C S, Jhang K Y 2012 Chin. Phys. Lett. 29 060702
[13] McCall K R, GuyerR A 1994 J. Geophys. Res. 99 23887
[14] GuyerR A, McCallK R, Boitnott G N 1995 Phys. Rev. Lett. 74 3491
[15] Aleshin V, Gusev V, Zaitsev V 2004 Ultrasonics 42 1053
[16] Gusev V 2000 J. Acoust Soc. Am. 107 3047
[17] Guo X S, Zhang D, Zhang J 2012 Ultrasonics 52 912
[18] Liu Y, Guo X S, Zhang D, Gong X F 2011 Acta Acustica 36 179(in Chinese) [刘洋, 郭霞生, 章东, 龚秀芬 2011 声学学报 36 179]
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[1] Suresh S 1998 Fatigue of Materials (Cambridge University Press) p11, 206
[2] Delsanto P P 2006 Universality of nonclassical nonlinearity: applications to non-destructive evaluations and ultrasonics (New York:Springer) p49
[3] Solodov I Y, Krohn N, Busse G 2002 Ultrasonics 40 621
[4] Zhang H Y, Sun X L, Cao Y P, Chen X H, Yu J B 2010 Acta Phys. Sin. 59 7111(in Chinese) [张海燕, 孙修立, 曹亚萍, 陈先华, 于建波 2010 59 7111]
[5] Park H W, Sohn H, Law K H, Farrar C R 2007 J. Sound & Vib 302 50
[6] Zhang B X, Lu M H 2002 ACTA Acustica 27 541(in Chinese) [张碧星, 陆铭慧 2002 声学学报 27 541]
[7] Ulrich T J, JohnsonP A, Guyer R A 2007 Phys. Rev. Lett. 98 104301
[8] Ulrich T J, SutinA M, GuyerR A 2008 Inter. J. Non-linear Mech. 43 209
[9] Goursolle T, Santos S D, MatarO B, Calle S 2008 Inter. J. Non-linear Mech. 43 170
[10] Dhital D, LeeJ R 2012 Exp. Mech. 52 1111
[11] Gao G L, Li D Y, Dong J W, Shi D Q, Teng F 2010 J. Harbin Engineering University 31 395(in Chinese) [高桂丽, 李大勇, 董静薇, 石德全, 滕飞 2010 哈尔滨工程大学学报 31 395]
[12] Kim C S, Jhang K Y 2012 Chin. Phys. Lett. 29 060702
[13] McCall K R, GuyerR A 1994 J. Geophys. Res. 99 23887
[14] GuyerR A, McCallK R, Boitnott G N 1995 Phys. Rev. Lett. 74 3491
[15] Aleshin V, Gusev V, Zaitsev V 2004 Ultrasonics 42 1053
[16] Gusev V 2000 J. Acoust Soc. Am. 107 3047
[17] Guo X S, Zhang D, Zhang J 2012 Ultrasonics 52 912
[18] Liu Y, Guo X S, Zhang D, Gong X F 2011 Acta Acustica 36 179(in Chinese) [刘洋, 郭霞生, 章东, 龚秀芬 2011 声学学报 36 179]
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