Interesting effects in harmonic generation by plane elastic waves 
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期刊名称Acta Mechanica Sinica
作者Yanzheng Wang; Jan D. Achenbach
栏目THEMED ARTICLES FOR CCTAM 2017 SPECIAL ISSUE-SOLID MECHANICS
摘要The harmonics of plane longitudinal and transverse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic. This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a primary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.
英文栏目名称THEMED ARTICLES FOR CCTAM 2017 SPECIAL ISSUE-SOLID MECHANICS
关键词Cubic nonlinearity; Third harmonic; Quadratically cumulative behavior; Interface; Compensatory wave
参考文献1. Hikata, A., Chick, B. B., Elbaum, C.:Dislocation contribution to the second harmonic generation of ultrasonic waves. J. Appl. Phys. 36, 229-236 (1965)  
2. Hikata, A., Sewell Jr, F. A., Elbaum, C.:Generation of ultrasonic second and third harmonics due to dislocations. b. Phys. Rev. 151, 442-449 (1966)  
3. Hikata, A., Elbaum, C.:Generation of ultrasonic second and third harmonics due to dislocations. I. Phys. Rev. 144, 469-477 (1966)  
4. Pruell, C., Kim, J. Y., Qu, J., et al.:Evaluation of plasticity driven material damage using Lamb waves. Appl. Phys. Lett. 91, 231911 (2007)  
5. Cantrell, J. H., Yost, W. T.:Nonlinear ultrasonic characterization of fatigue microstructures. Int. J. Fatigue 23, 487-490 (2001)  
6. Kim, J. Y., Jacobs, L. J., Qu, J., et al.:Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves. J. Acoust. Soc. Am. 120, 1266-1273 (2006)  
7. Frouin, J., Matikas, T. E., Na, J. K., et al.:In-situ monitoring of acoustic linear and nonlinear behavior of titanium alloys during cycling loading. In:Nondestructive Evaluation of Aging Materials and Composites c, Newport Beach, February 8 (1999)
8. Korneev, V. A., Demčenko, A.:Possible second-order nonlinear interactions of plane waves in an elastic solid. J. Acoust. Soc. Am. 135, 591-598 (2014)  
9. Chen, Z., Tang, G., Zhao, Y., et al.:Mixing of collinear plane wave pulses in elastic solids with quadratic nonlinearity. J. Acoust. Soc. Am. 136, 2389-2404 (2014)
10. Tang, G., Jacobs, L. J., Qu, J.:Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity. J. Acoust. Soc. Am. 131, 2570-2578 (2012)  
11. Wang, Y., Achenbach, J. D.:The effect of cubic material nonlinearity on the propagation of torsional wave modes in a pipe. J. Acoust. Soc. Am. 140, 3874-3883 (2016)  
12. Liu, Y., Chillara, V. K., Lissenden, C. J., et al.:Third harmonic shear horizontal and Rayleigh Lamb waves in weakly nonlinear plates. J. Appl. Phys. 114, 114908 (2013)  
13. Lissenden, C. J., Liu, Y., Choi, G. W., et al.:Effect of localized microstructure evolution on higher harmonic generation of guided waves. J. Nondestruct. Eval. 33, 178-186 (2014)  
14. Rénier, M., Gennisson, J. L., Barrière, C., et al.:Fourth-order shear elastic constant assessment in quasi-incompressible soft solids. Appl. Phys. Lett. 93, 101912 (2008)  
15. Chillara, V. K., Lissenden, C. J.:Constitutive model for third harmonic generation in elastic solids. Int. J. Non Linear Mech. 82, 69-74 (2016)  
16. Hamilton, M. F., Ilinskii, Y. A., Zabolotskaya, E. A.:Separation of compressibility and shear deformation in the elastic energy density (L). J. Acoust. Soc. Am. 116, 41-44 (2004)  
17. Zhou, S., Shui, Y.:Nonlinear reflection of bulk acoustic waves at an interface. J. Appl. Phys. 72, 5070-5080 (1992)  
18. Deng, M.:Cumulative second-harmonic generation of Lamb-mode propagation in a solid plate. J. Appl. Phys. 85, 3051-3058 (1999)  
19. Bender, F. A., Kim, J. Y., Jacobs, L. J., et al.:The generation of second harmonic waves in an isotropic solid with quadratic nonlinearity under the presence of a stress-free boundary. Wave Motion 50, 146-161 (2003)
20. Nagy, P. B.:Fatigue damage assessment by nonlinear ultrasonic materials characterization. Ultrasonics 36, 375-381 (1998)  
21. Zhang, Z., Nagy, P. B., Hassan, W.:Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface. Ultrasonics 65, 165-176 (2016)  
2017
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开始页码754
结束页码762
DOI10.1007/s10409-017-0676-5
基金项目The work was supported by the National Natural Science Foundation of China (Grants 11621062 and 11532001) and the China Scholarship Council (CSC).
点击率38
作者地址1 Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China;
2 Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA

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