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The interaction of ultrasound with an interface between two rough surfaces in contact has become a quite popular topic in many areas related to non-destructive evaluation (NDE). We proposed a theory of ultrasonic nonlinear interaction between some random rough elastic interfaces. The model of random elastic-contact interface is first described, and then the nonlinear ultrasonic interaction of interfaces with stress-strain relationship is studied, by using different models including linear simplified model, exponential model, and Gaussian model. Results of numerical simulations and experiments demonstrate that the Gaussian model is more suitable for describing the solid rough interfaces. This study provides an explanation of the ultrasonic interaction on mesoscopic level, which is a theoretical basis for practical application to detect cracks, defects and injuries in industrial ultrasonic NDE.
[1] Baltazar A, Rokhlin S I, Pecorari C 2002 J. Mech. Phys. Solids 50 1397
[2] Wang J S, Xu X D, Liu X J, Xu G C 2008 Acta Phys. Sin. 12 7765 (in Chinese) [王敬时, 徐晓东, 刘晓峻, 许钢灿 2008 物理学报 12 7765]
[3] Pecorari C 2003 J. Acoust. Soc. Am. 113 3065
[4] Hertz H 1896 Miscellaneous papers (London: Macmillan) p146
[5] Greenwood J A, Williamson J B P 1966 Proc. R. Soc. London A 295 300
[6] Brown S R, Scholz C H 1985 J. Geophys. Res. 90 5531
[7] Richardson J M 1979 Int. J. Eng. Sci. 17 73
[8] Swan G 1983 Rock Mechanics and Rock Engineering 16 19
[9] Adler R J, Firman D 1981 Philos. Trans. R. Soc. London A 303 433
[10] Shampine L F 2008 Journal of Computational and Applied Mathematics 211 131
[11] Dormand J R, Prince P J 1980 J. Comp. Appl. Math. 6 19
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[1] Baltazar A, Rokhlin S I, Pecorari C 2002 J. Mech. Phys. Solids 50 1397
[2] Wang J S, Xu X D, Liu X J, Xu G C 2008 Acta Phys. Sin. 12 7765 (in Chinese) [王敬时, 徐晓东, 刘晓峻, 许钢灿 2008 物理学报 12 7765]
[3] Pecorari C 2003 J. Acoust. Soc. Am. 113 3065
[4] Hertz H 1896 Miscellaneous papers (London: Macmillan) p146
[5] Greenwood J A, Williamson J B P 1966 Proc. R. Soc. London A 295 300
[6] Brown S R, Scholz C H 1985 J. Geophys. Res. 90 5531
[7] Richardson J M 1979 Int. J. Eng. Sci. 17 73
[8] Swan G 1983 Rock Mechanics and Rock Engineering 16 19
[9] Adler R J, Firman D 1981 Philos. Trans. R. Soc. London A 303 433
[10] Shampine L F 2008 Journal of Computational and Applied Mathematics 211 131
[11] Dormand J R, Prince P J 1980 J. Comp. Appl. Math. 6 19
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