Cracks weaken structures. When the crack size increases in service, the structure becomes weaker than its earlier condition. Lastly, the structure may break down due to a small crack. Therefore, crack detection and classification is a fundamental issue. Many aspects of defects have already been addressed, but the application of non-destructive testing methods to structural materials has become more widespread. For a long time, vibration methods based on Natural Frequency and Mode Shapes have been used for possible cracks detection in the beams. The impact of arbitrary and random defect geometry on applying these methods has been overlooked. This study focuses on a mode shapes-based vibration analysis of a cracked cantilever beam to investigate this issue. The effects of crack geometries on mode shapes are examined theoretically and numerically using a new crack model (Rectangular shaped crack), which differs from the well-known V-shaped crack. A MATLAB code is written to obtain the natural frequencies and mode shapes for all cracked instances of beams. The mode shapes result of both the new (Rectangular), and V-shaped models are compared, and it is found that the results are less sensitive to the geometry change.

The cracks alter the physical and modal properties of the beam, i.e., stiffness, damping, natural frequency, and mode shapes, and, in turn, the dynamic response of the beam changes to a considerable extent. The condition monitoring of the beams is essential to avoid its catastrophic failure in applications. A basic criterion has been followed for modal parameters like natural frequencies, mode shapes, and stiffness for the possible crack detection. In contrast, damping as a dynamic property to represent structural damage has been limited due to the difficulties in measuring damping and analysis. Therefore, in this study, the effect of various possible crack profiles, i.e., V-shaped and U-shaped, on the applicability of using the damping criterion for determining the presence of damage in the cantilever structure was investigated. The damping loss factor for all the cracked cases of a cantilever beam was computed using ANSYS and experimental analysis. The numerical results of the damping loss factor were compared with experimental results. It was understood that the results were susceptible to the crack geometries changes.