A single degree of freedom model for cracked beam

Tran Thanh Hai, Do Nam
Author affiliations


  • Tran Thanh Hai \(^1\) Institute of Mechanics, VAST, Hanoi, Vietnam
    \(^2\) VNU University of Engineering and Technology, Hanoi, Vietnam
  • Do Nam VNU University of Engineering and Technology, Hanoi, Vietnam




cracked beam, simplified model, frequency response function, frequency domain assurance criterion


This paper presents a simplified model of cracked beam by single-degree-of-freedom system. Equivalence between the beam and SDOF models means that they have the same fundamental natural frequency and similar frequency response functions (FRFs). Similarity of FRFs is checked by using the frequency-domain assurance criterion acknowledged herein as spectral similarity index (SSI). Finally, FRFs of both the cracked beam and its simplified SDOF model have been examined versus crack location and depth using the so-called spectral damage index (SDI). Numerical results show that SDI is significantly sensitive to crack and could be used as a novel indicator for crack detection in beam by measurements of frequency response functions.


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How to Cite

T. T. Hai and D. Nam, A single degree of freedom model for cracked beam, Vietnam J. Mech. 45 (2023) 183–196. DOI: https://doi.org/10.15625/0866-7136/18464.



Research Article