A numerical study of co-linear mixing of two longitudinal waves

PDF(2982 KB)

Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (12) : 219-226.

SUN Zhenghao1,3, LI Hongguang2, LI Fucai2, MENG Guang2,3， SUN Hui1

Author information +

History +

Abstract

It is an urgent problem to identify and evaluate early weak fatigue damage of large complex equipment, and nonlinear ultrasonic nondestructive testing techniques based on the higher-order elastic modulus have aroused much attention in recent years because of their sensitivities to micro structural changes.Using a high-resolution semi-discrete central scheme, the ultrasonic wave mixing, a novel nonlinear ultrasonic nondestructive testing technique, was numerically investigated in the case of collinear wave mixing of two longitudinal waves in the same direction.The results of the generated components of resonant waves show that, both components of sum and different frequencies can be produced and propagate in two mutually perpendicular directions, and the component of different frequency brought about in the shear direction increases monotonically with material nonlinearity, which potentially offers an accurate measurement of material nonlinearity, and further provides effective methods and evidence for early weak damage of materials using the ultrasonic wave mixing technique.

Key words

nonlinear ultrasonic wave method / mixing technique / third-order elastic constants / detection of weak damage in fatigue

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

SUN Zhenghao1,3, LI Hongguang2, LI Fucai2, MENG Guang2,3， SUN Hui1. A numerical study of co-linear mixing of two longitudinal waves[J]. Journal of Vibration and Shock, 2021, 40(12): 219-226

References

［1］JONES G L, KOBETT D R.Interaction of elastic waves in an isotropic solid［J］.The Journal of the Acoustical Society of America, 1963, 35(1): 5-10.
［2］ZAREMBO L K, KRASIL′NIKOV V A.Nonlinear phenomena in the propagation of elastic waves in solids［J］.Soviet Physics Uspekhi, 1971, 13(6): 778.
［3］TAYLOR L H, ROLLINS F R Jr.Ultrasonic study of three-phonon interactions.I.Theory［J］.Physical Review, 1964, 136(3A): A591.
［4］ROLLINS F R Jr.TAYLOR L H, TODD JR P H.Ultrasonic study of three-phonon interactions.II.Experimental results［J］.Physical Review, 1964, 136(3A): A597.
［5］CHILDRESS J D, HAMBRICK C G.Interactions between elastic waves in an isotropic solid［J］.Physical Review, 1964, 136(2A): A411.
［6］KORNEEV V A, DEMCˇENKO A.Possible second-order nonlinear interactions of plane waves in an elastic solid［J］.The Journal of the Acoustical Society of America, 2014, 135(2): 591-598.
［7］SUN Z H, LI F C, LI H G.Two-way collinear interaction of longitudinal waves in an elastic medium with quadratic nonlinearity［J］.Journal of Vibroengineering, 2015, 17(7)：3988-3997.
［8］SUN Z H, LI F C, LI H G.A numerical study of non-collinear wave mixing and generated resonant components［J］.Ultrasonics, 2016, 71:245-255.
［9］SUN M, XIANG Y, DENG M, et al.Scanning non-collinear wave mixing for nonlinear ultrasonic detection and localization of plasticity［J］.NDT & E International, 2018, 93:1-6.
［10］CROXFORD A J, WILCOX P D, DRINKWATER B W, et al.The use of non-collinear mixing for nonlinear ultrasonic detection of plasticity and fatigue［J］.The Journal of the Acoustical Society of America,2009,126(5):EL117-EL122.
［11］LIN J, GUO P, WAN L, et al.Laboratory investigation of rejuvenator seal materials on performances of asphalt mixtures［J］.Construction and Building Materials, 2012, 37:41-45.
［12］TANG G, LIU M, JACOBS L J, et al.Detecting localized plastic strain by a scanning collinear wave mixing method［J］.Journal of Nondestructive Evaluation, 2014, 33(2): 196-204.
［13］DEMCˇENKO A, AKKERMAN R, NAGY P B, et al.Non-collinear wave mixing for non-linear ultrasonic detection of physical ageing in PVC［J］.NDT & E International, 2012, 49: 34-39.
［14］DEMCˇENKO A, MAININI L, KORNEEV V A.A study of the noncollinear ultrasonic-wave-mixing technique under imperfect resonance conditions［J］.Ultrasonics, 2015, 57: 179-189.
［15］KUVSHINOV B N, SMIT T J H,CAMPMAN X H.Non-linear interaction of elastic waves in rocks［J］.Geophysical Journal International, 2013,194(3): 1920-1940.
［16］WANG Yanzheng, JAN D.Achenbach.Interesting effects in harmonic generation by plane elastic waves［J］.Acta Mechanica Sinica,2017,33(3): 754-762.
［17］GUSEV V，TOURNAT V, CASTAGNEDE B.Nonlinear acoustic phenomena in micro-inhomogenous media［M］.in materials and Acoustics Handbook, M.Bruneau and C.Potel, Editors, 2009.
［18］SMITH R T, STERN R, STEPHENS R W B.Third-order elastic moduli of polycrystalline metals from ultrasonic velocity measurements［J］.The Journal of the Acoustical Society of America, 1966, 40(5): 1002-1008.
［19］KURGANOV A, TADMOR E, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations［J］ J.Comput.Phys., 2000,160:241-282.
［20］BALBS J, TADMOR E, CENTPACK, Available at <http://www.cscamm.umd.edu/centpack/software>