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ABSTRACT
Due to the limitations of the manufacturing processes, defect like crack is produced in the structures. Crack gives the catastrophic failure of the structures or beams; hence, the detection and classification of the cracks are important issues in the scientific research. For a long time, the free vibration-based crack detection methods have been used for the possible crack detection in the structures. On the other hand, the effect of arbitrary and random defect geometry, i.e. V-shaped, U-shaped open edge cracks on the applicability of these methods has been overlooked. In order to investigate this issue, three crack parameters, i.e. crack geometry, crack depth and crack locations, were considered on the cantilever beam to study its effect on the mode shapes of cracked beams. The stiffness of cracked cantilever beams was evaluated by the deflection method using ANSYS. Theoretical method, Numerical method and Experimental method have been used to compute the mode shapes of cracked beams. Through free vibration study, it is found that spring steel structures are somewhat sensitive to the change in crack geometries as far as the mode shapes are concerned. So, it is obvious that the mode shape based free vibration method can satisfactorily predict the crack depth and location in spring steel structures irrespective of the crack geometries.
Nomenclature
| L | = | Length of the beam, m |
| L1 | = | Distance of the crack from cantilevered end, m |
| B | = | Width of the beam, m |
| H | = | Depth of crack, m |
| D | = | Depth of beam, m |
| KO | = | Open-edged crack beam stiffness, N/m |
| ωO | = | Angular velocity of cracked beam, rad/sec |
| fn | = | Natural frequency of cracked beam, Hertz |
| µ | = | Poisson’s ratio |
| E | = | Young’s modulus, N/m2 |
| ρ | = | Mass density of the beam, kg/m3 |
| m | = | Mass of the cantilever beam, kg |
| meff | = | Effective mass of the beam, kg |
| M1 | = | Lumped mass at the crack, kg |
| M2 | = | Lumped mass at the crack, kg |
Abbreviation
| FFT | = | Fast Fourier Transform |
| EN | = | Euro Norm |
| FEA | = | Finite Element Analysis |
| pm | = | pico meter |
| nn | = | nano meter |
| SHM | = | Simple Harmonic Motion |
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Notes on contributors
V. Khalkar
V. Khalkar received his PhD degree from Sathyabama Institute of Science and Technology. Presently he is working as an Associate Professor in the department of mechanical engineering of Gharda Institute of Technology, Mumbai University, India
K. Logesh
K. Logesh received his PhD degree from Sathyabama Institute of Science and Technology. Presently he is working as an Assistant Professor in the department of mechanical engineering of Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Chennai, Tamil Nadu, India.