A novel damage index extracted from frequency response of cracked Timoshenko beam subjected to moving harmonic load

Nguyen Tien Khiem, Phi Thi Hang
Author affiliations


  • Nguyen Tien Khiem Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam https://orcid.org/0000-0001-5195-2704
  • Phi Thi Hang Electric Power University, Hanoi, Vietnam




cracked beams, moving load, frequency response, damage index


In this paper, there is proposed a novel damage index extracted from frequency response of cracked Timoshenko beam under moving harmonic load using the so-called Modal Assurance Criterion (MAC) concept. First, frequency response of a cracked Timoshenko beam subjected to harmonic force moving on the beam with constant speed is obtained in an analytical expression. Then, a scalar characteristic like the coherence between the frequency responses of intact and cracked beams is determined and called herein Spectral Assurance Criterion (SAC). Such designed criterion is dependent upon crack parameters (location and depth), the load frequency and speed as well as position on beam where the responses have been measured. Numerical analysis shows that SAC is much more sensitive to crack than natural frequencies and can be used as a novel damage index for crack detection in beam using moving load. The effect of moving load frequency and speed has been also examined with the aim to have got an indicator most adequate for the crack detection problem.


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