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An experimental study on second harmonic generation of guided wave in fatigued spring rod

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Abstract

Conventional ultrasonic inspection techniques especially ultrasonic guided wave and wave testing methods show excellent capability for evaluating the material integrity of the structures. The dominate characteristics of nonlinear guided wave testing are long-range testing and higher sensitivity through various modes selection, which are favorable for diagnosing micro-defects or micro-structural changes at early stage. In this study, nonlinear studies on the valve spring coil using nonlinear induced ultrasound conducted. The nonlinear guided ultrasonic test performed on four specimens subjected to the Nakamura fatigue test. Experimental results show that nonlinear parameters increase with increasing distance. In addition, the nonlinear parameters increased with increasing fatigue degree. This study suggests a method to diagnose early damage of machine structure in an appropriate way and it expected to prevent accidents of structures.

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Abbreviations

β l :

Longitudinal second harmonic nonlinear parameter

ρ :

Density

c l :

Velocity of the longitudinal wave

A l :

Amplitude of the primary harmonic

A 2 :

Amplitude of the second harmonic

k :

Wave number

x :

Propagating distance

References

  1. Reseach Committee on Standardization for Nakamura, Standardization for large deflection rotating-bending fatigue testing method, J-STAGE Transactions of Japan Society of Spring Engineers, 1996 (41) (1996) 65–110.

    Article  Google Scholar 

  2. C. Bermes, J. Y. Kim, J. Qu and L. J. Jacobs, Experimental characterization of material nonlinearity using lamb waves, Applied Physics Letters, 90 (2007) 0219011.

  3. P. B. Nagy, Fatigue damage assessment by nonlinear ultrasonic material characterization, Ultrasonics, 36 (1998) 275- 381.

  4. O. Buck, Harmonic generation for measurement of internal stress as produced by dislocation, IEE Transaction on Sonics and Ultrasonics, 23 (5) (1976) 346–350.

    Article  Google Scholar 

  5. J. Y. Kim, J. Qu and L. J. Jacobs, Acoustic nonlinearity parameter due to micro-plasticity, Journal of Nondestructive Evaluation, 25 (1) (2006) 29–37.

    Article  Google Scholar 

  6. W. Li, Y. Cho and J. D. Achenbach, Detection of thermal fatigue in composites by second harmonic lamb waves, Smart Materials and Structures, 21 (2012) 085019 (8pp).

    Article  Google Scholar 

  7. W. Li, J. Choi and Y. Cho, Second harmonic generation of shear horizontal guided wave propagation in plate-like structures, Physics Procedia, 70 (2015) 451–454.

    Article  Google Scholar 

  8. M. Deng, Cumulative second-harmonic generation accompanying nonlinear shear horizontal mode propagation in a solid plate, Journal of Applied Physics, 84 (7) (1998) 3500–3505.

    Article  Google Scholar 

  9. M. Deng and Z. Liu, Modal analysis of second-harmonic generation of shear horizontal modes in an elastic plate, Applied Physics Letter, 81 (10) (2002) 1916–1918.

    Article  Google Scholar 

  10. M. Deng, Analysis of second-harmonic generation of Lamb modes using a modal analysis approach, Journal of Applied Physics, 94 (2003) 4152.

    Article  Google Scholar 

  11. W. J. N. de Lima and M. F. Hamilton, Finite-amplitude waves in isotropic elastic plates, Journal of Sound and Vibration, 265 (2003) 819–839.

    Article  Google Scholar 

  12. W. J. N. de Lima and M. F. Hamilton, Finite-amplitude waves in isotropic elastic waveguides with arbitrary constant cross-sectional area, Wave Motion, 41 (2006) 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. C. Gazis, Three dimensional investigation of the propagation of waves in hollow circular cylinders, 1. Analytical foundation, The Journal of the Acoustical Society of America, 31 (5) (1959) 568–573.

    Article  MathSciNet  Google Scholar 

  14. J. L. Rose, A baseline and vision of ultrasonic guided wave inspection potential, J. Pressure Vessel Technol., 124 (3) (2002) 273–282.

    Article  Google Scholar 

  15. M. J. S. Lowe, D. N. Alleyne and P. Cawley, Defect detection in pipes using guided waves, Ultrasonics, 36 (1998) 147–154.

    Article  Google Scholar 

  16. W. J. N. de Lima and M. F. Hamilton, Finite amplitude waves in isotropic elastic waveguides with arbitrary constant cross-sectional area, Wave Motion, 41 (1) (2005) 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  17. W.-B. Li, M. Deng and Y.-X. Xiang, Review on secondharmonic generation of ultrasonic guided waves in solid media (I): Theoretical analyses, Chinese Physical B, 26 (11) (2017) 114302.

    Article  Google Scholar 

  18. B. A. Auld, Acoustic Fields and Waves in Solids, Wiley, 1 & 2 (1990).

  19. O. Buck, Harmonic generation for measurement of internal stress as produced by dis-location, IEE Transaction on Sonics and Ultrasonics, 23(5) (1976) 346–350.

    Article  Google Scholar 

  20. K. H. Matlack, J. Y. Kim, L. J. Jacobs and J. Qu, Experimental characterization of efficient second harmonic generation of lamb wave modes in a nonlinear elastic isotropic plate, Journal of Applied Physics, 109 (1) (2011) 014905.

    Article  Google Scholar 

  21. W. Li, M. Deng and Y. Cho, Cumulative second harmonic generation of ultrasonic guided waves propagation in tubelike structiur, Journal of Computational Acoustics, 24 (3) (2016) 1650011.

    Article  MathSciNet  MATH  Google Scholar 

  22. Y. Yamada, Materials for Springs, Springer (2007) ISBN 9783-540738114.

    Google Scholar 

  23. J. L. Rose, Ultrasonic Waves in Solid Media, Cambridge University Press (1999).

    Google Scholar 

  24. R. Bussoloti, L. L. M. Albano and L. de C. F. Canale, Delta ferrite in heat treated bolts - Characterization and consequences, Heat Treat 2013 American Society for Metals (2013).

    Google Scholar 

Download references

Acknowledgments

This work was supported by Daewon Kang Up Co., Ltd. and National Research Foundation of Korea (NRF) grant funded by Korea government (MSIT) (No.2016M2A2 A9A03913295).

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Correspondence to Younho Cho.

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Recommended by Associate Editor Daeil Kwon

Younho Cho is a Professor of the School of Mechanical Engineering, Pusan National University, Pusan, Korea. He received his master degree in Pennsylvania State University. And he is the leader of the Wave & SHM Lab.

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Kim, J., Zhu, B. & Cho, Y. An experimental study on second harmonic generation of guided wave in fatigued spring rod. J Mech Sci Technol 33, 4105–4109 (2019). https://doi.org/10.1007/s12206-019-0805-0

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  • DOI: https://doi.org/10.1007/s12206-019-0805-0

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