Abstract
Using an asymptotic method of nonlinear mechanics and concepts of linear fracture mechanics, we derive analytical expressions that relate the constant component and amplitudes of even harmonics, and the ratio of maximum deviations and half-periods of displacements of opposite signs in a vibration cycle of prismatic beams to the length of a closing transverse crack. The analytical solution is compared to the data of experimental determination of these parameters in bending vibrations of rectangular cantilever beams with an edge transverse crack. Analysis of the results of analytic and experimental investigations has shown that harmonic analysis of the strain waveform of beam-type elements in resonance vibrations can be used as an efficient diagnostic method for detecting fatigue damage such as closin cracks.
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Abbreviations
- Ω:
-
natural frequency of an intact beam
- Ω0 :
-
natural frequency of a beam with a closing crack
- Ω m :
-
natural frequency of a beam with an open crack
- β′:
-
relative change of the natural frequency of a beam with a closing crack
- L :
-
beam length
- h :
-
height of the cross section
- α:
-
coefficient of relative changes in the stiffness of a cracked beam
- l :
-
crack length
- γ:
-
relative crack length
- x c :
-
coordinate of the cracked section
References
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Additional information
Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 5–12, January–February, 2000.
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Matveev, V.V., Bovsunovskii, A.P. Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 4. Analysis of distortion of harmonicity of vibration cycle of beams with closing transverse cracks. Strength Mater 32, 1–6 (2000). https://doi.org/10.1007/BF02511502
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DOI: https://doi.org/10.1007/BF02511502