Some Studies on Verifying the Applicability of Free Vibration-based Modes Shapes Method to Rectangular Shaped Cracks in a Cantilever Beam

Abstract

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.