Skip to main content
SpringerLink
Log in

An efficient wavelet finite element method in fault prognosis of incipient crack

  • Published:
Science in China Series E Aims and scope Submit manuscript

Abstract

The method of constructing any scale wavelet finite element (WFE) based on the one-dimensional or two-dimensional Daubechies scaling functions was presented, and the corresponding WFE adaptive lifting algorithm was given. In order to obtain the nested increasing approximate subspaces of multiscale finite element, the Daubechies scaling functions with the properties of multi-resolution analysis were employed as the finite element interpolating functions. Thus, the WFE could adaptively mesh the singularity domain caused by local cracks, which resulted in better approximate solutions than the traditional finite element methods. The calculations of natural frequencies of cracked beam were used to check the accuracy of given methods. In addition, the results of cracked cantilever beam and engineering application were satisfied. So, the current methods can provide effective tools in the numerical modeling of the fault prognosis of incipient crack.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Zhang Jingfen, Zhao Deyou, Summary review of vibration-based crack diagnosis technique for engineering structures, Journal of Vibration and Shock, 2002, 21(4): 21, 22–25

    Google Scholar 

  2. He Yongyong, Chu Fulei, Guo Dan et al., Study on genetic algorithms based rotor crack detection for rotating machine, Chinese Journal of Mechanical Engineering, 2001, 37(10): 69–74.

    Google Scholar 

  3. Sekhar, A. S., Crack identification in a rotor system: a model-based approach, Journal of Sound and Vibration, 2004, 270: 887–902.

    Article  Google Scholar 

  4. Lele, S. P., Maiti, S. K., Modelling of transverse vibration of short beams for crack detection and measurement of crack extension, Journal of Sound and Vibration, 2002, 257(3): 559–583.

    Article  Google Scholar 

  5. Kardestuncer, H., A Handbook of Finite Element Methods (translated by Zhu Dechao), Beijing: Science Press, 1996.

    Google Scholar 

  6. Lou Luliang, Zeng Pan, Nie Lei, Meshless method for numerical simulation of crack propagation. Journal of Aeronautical Materlals, 2001, 21(3): 51–55.

    Google Scholar 

  7. Belytschko, T., Organ, D., Gerlach, C., Element-free Galerkin methods for dynamic fracture in concrete, Comput. Methods Appl. Mech. Engrg., 2000, 187: 385–399.

    Article  Google Scholar 

  8. Fan, S., Sheng, N., Meshless formulation using NURBS basis functions for eigenfrequency changes of beam having multiple open-cracks Journal of Sound and Vibration, 2004, 269: 781–793.

    Article  Google Scholar 

  9. Dahmen, W., Wavelet methods for PDEs — some recent developments, Journal of Computational and Applied Mathematics, 2001, 128: 133–185.

    Article  MATH  MathSciNet  Google Scholar 

  10. Bertoluzza, S., Verani, M., Convergence of a nonlinear wavelet algorithm for the solution of PDEs, Applied Mathematics Letters, 2003, 16(1): 113–118.

    Article  MathSciNet  Google Scholar 

  11. Sudarshan, R., Heedene, S., Amaratunga, K., A multiresolution finite element method using second generation Hermite multiwavelets, Second MIT Conference on Computational Fluid and Solid Mechanics, 2003, 1-6.

  12. Ho, S. L., Yang, S. Y., Wavelet-Galerkin method for solving parabolic equations in finite domains, Finite Elements in Analysis and Design, 2001, 37: 1023–1037.

    Article  MathSciNet  Google Scholar 

  13. Mei Shuli, Zhang Senwen, Lei Tingwu, Wavelet numerical method for nonlinear FPK stationary equations with random vibration, Journal of Jinan University (Natural Science), 2002, 23(1): 29–33.

    Google Scholar 

  14. Ma Junxing, Xue Jijun, He Zhengjia et al., A study of the construction and application of a Daubechies wave-let-based beam element, Finite Elements in Analysis and Design, 2003, 39(10): 965–975.

    Article  Google Scholar 

  15. Chen Xuefeng, Yang Shengjun, He Zhengjia, et al., The construction of wavelet finite element and its application, Finite Elements in Analysis and Design, 2004, 40: 541–554.

    Google Scholar 

  16. Chen Xuefeng, Li Bing, He Zhengjia et al., Crack fault diagnosis based on wavelet finite elements, Journal of Xi’an Jiaotong University, 2004, 38(3): 295–298.

    Google Scholar 

  17. Daubechies, I., Orthonormal basis of compactly supported wavelets, Comm. Pure and Appl. Math., 1988, 41: 909–996.

    MATH  MathSciNet  Google Scholar 

  18. Silva, J. M., Gomes, A., Experimental dynamic analysis of cracked free-free beams, Experimental Mechanics, 1990, 30 (1): 20–25.

    Google Scholar 

  19. Kim, J. T., Stubbs, N., Crack detection in beam-type structures using frequency data, Journal of Sound and Vibration, 2003, 259 (1): 145–160.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Chen Xuefeng, He Zhengjia, Li Bing & Xiang Jiawei

Authors
  1. Chen Xuefeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. He Zhengjia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li Bing
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiang Jiawei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chen Xuefeng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, X., He, Z., Li, B. et al. An efficient wavelet finite element method in fault prognosis of incipient crack. SCI CHINA SER E 49, 89–101 (2006). https://doi.org/10.1007/s11431-004-5276-5

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-004-5276-5

Keywords

Search

Navigation