A novel criterion for crack detection in beam structures by frequency response functions

Author affiliations


  • Nguyen Tien Khiem Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam https://orcid.org/0000-0001-5195-2704
  • Tran Thanh Hai Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
  • Le Khanh Toan Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam https://orcid.org/0009-0002-9385-0890
  • Nguyen Thi Lan Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
  • Ho Quang Quyet Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam https://orcid.org/0009-0002-4071-1571




crack identification, frequency response function, frequency domain assurance criterion, contour method


The frequency response function (FRF) is a fruitful attribute that includes almost all dynamical characteristics of a structure such as natural frequencies and modes, damping coefficients, or resonance and antiresonance conceptions. However, the complex feature of FRF has not been thoroughly employed for structural damage detection. In the present study, a novel indicator extracted from FRFs of beam structures is developed for crack identification. The damage indicator originated from the well-known mode assurance criterion (MAC) and therefore it is termed spectral assurance criterion (SAC). First, a coherence coefficient calculated from FRFs of intact and damaged beams and called herein spectral damage index (SDI) is analyzed for examining sensitivity of FRFs to crack. Then, SAC calculated for different FRFs of the same damaged structure is employed for crack detection by the so-called contour method. Results obtained in numerical examples of the crack detection problem show that SAC is really a novel and efficient criterion for crack identification in beams from measured FRFs.


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