Identification of two cracks with different severity in beams and rods from minimal frequency data Articles uri icon

publication date

  • July 2016

start page

  • 3102

end page

  • 3117


  • 13


  • 22

International Standard Serial Number (ISSN)

  • 1077-5463

Electronic International Standard Serial Number (EISSN)

  • 1741-2986


  • It has been known for a long time that the problem of identifying two small cracks in a simply supported beam from the first three natural frequencies can be analytically formulated and solved if the two cracks have equal severity. In this paper we extend this result to the case of cracks with different severity. Each crack is simulated by a rotational elastic spring and the inverse problem is solved in terms of the damage-induced changes in the first four natural frequencies. Closed-form expressions of the damage parameters in terms of the measured frequencies are obtained. The results can be extended to the identification of two cracks in a longitudinally vibrating beam based on a suitable set of natural frequency and antiresonant frequency data. Numerical simulations support the theory, and show that if accurate input data are available and the cracks are not too close, then damage identification leads to satisfactory results.


  • multiple cracks; damage identification; natural frequencies; antiresonant frequencies; beams; rods; damage detection; modal-analysis