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Frequency error based identification of cracks in beam-like structures

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Abstract

A crack identification method of a single edge cracked beam-like structure by the use of a frequency error function is presented in this paper. First, the dynamic theory of Euler-Bernoulli beams was employed to derive the equation of the natural frequency for a single edge cracked cantilever beam-like structure. Subsequently, the cracked section of the beam was simulated by a torsional spring. The flexibility model of the torsional spring due to the crack was estimated by fracture mechanics and energy theory. Thereafter, a function model was proposed for crack identification by using the error between the measured natural frequencies and the predicted natural frequencies. In this manner, the crack depth and crack position can be determined when the total error reaches a minimum value. Finally, the accuracy of the natural frequency equation and the viabilty of the crack identification method were verified in the case studies by the measured natural frequencies from the literature. Results indicate that the first two predicted natural frequencies are in good agreement with the measured ones. However, the third predicted natural frequency is smaller than the measured natural frequency. In the case of small measured frequency errors, the predicted crack parameters are in good agreement with the measured crack parameters. However, in the case of large measured frequency errors, the predicted crack parameters only give roughly estimated results.

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Authors and Affiliations

  1. School of Aeronautic Manufacturing Engineering, Nanchang Hangkong University, Nanchang, JX, 330063, China

    Wenguang Liu

  2. Department of Aerospace Engineering and Mechanics, The University of Alabama, Tuscaloosa, AL, 35487, USA

    Mark E. Barkey

Authors
  1. Wenguang Liu
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  2. Mark E. Barkey
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Correspondence to Wenguang Liu.

Additional information

Recommended by Associate Editor Daeil Kwon

Wenguang Liu received his Ph.D. from Nanjing University of Aeronautics and Astronautics, China. He is currently an Associate Professor in Nanchang Hangkong University, China.

Mark E. Barkey received his Ph.D. from the University of Illinois at Urbana-Champaign, USA. He is currently a Professor at the University of Alabama, USA.

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Liu, W., Barkey, M.E. Frequency error based identification of cracks in beam-like structures. J Mech Sci Technol 31, 4657–4667 (2017). https://doi.org/10.1007/s12206-017-0912-8

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  • DOI: https://doi.org/10.1007/s12206-017-0912-8

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