An analytical method for crack detection of Timoshenko beams with multiple open cracks using a test mass

Abstract

A crack identification approach in uniform simply supported beams with open cracks, using a test mass, is developed, based on changes in natural frequencies of cracked beams due to the test mass. Test mass is defined as a stationary mass, which is located in different places of the beam modelled by Timoshenko beam theory. The beam with an arbitrary number of cracks is modelled as segments connected by elastic springs illustrating open edge cracked cross-sectional flexibilities. The stiffness of the springs is determined using fracture mechanics theory. Solving the differential equations, the eigenfunctions of the problem are explicitly derived. Rayleigh’s quotient method is then used to consider the effect of the test mass. Consequently, natural frequencies of the cracked beam with a test mass are derived for each mode of transverse vibration. Knowing the natural frequencies of the beam carrying a test mass at some different locations, it is possible to identify cracks’ parameters (i.e. location and depth) by solving the system of equations. The proposed closed-form approach is also validated using numerical studies on multiple-cracked beam examples. There is quite encouraging agreement between the results of the present approach and those numerically computed using the finite element method.

Keywords:

• crack detection
• test mass
• Rayleigh’s quotient method
• Timoshenko beam
• finite element method
• natural frequencies

Acknowledgements

The authors wish to acknowledge and express their special gratitude to anonymous respectful reviewers for their constructive advice, which improved the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.