Detection of Cracks in a Cantilever Metal Plate Using Vibrational Techniques

Abstract

The main objective of this research is to detect crack at different positions of the thin metal cantilever plate based on the natural frequency. Most of the researchers have investigated on beam. Few researchers have investigated on thin plate. The crack depth and crack thickness in standard convention of beam are considered as crack length and depth of crack respectively in this research for the thin metal plate. Some theoretical approach considering bilinear stiffness have been found in some literatures. Numerical and experimental analysis due to crack in cantilever beam or plate have been investigated by different researchers. In this research work, a thin plate is considered made of aluminum alloy and structure steel. A slit crack is considered for different cases of investigations. The crack length, width, depth, location, etc. are taken as parameters. These are investigated on the change of natural frequencies through modal analysis due to the mentioned parameters change. The study confirms that when the crack length affects the most in frequency drop than that of crack width and crack depth. The drop of frequency is massive when the crack length increases. However, when the crack width increases the drop of frequency remains constant. Moreover, thorough crack on a plate shows more drop of frequency than that of a plate with crack, which is not thorough. Therefore, thorough cracks on plates are more detectable Along the longitudinal direction (Z-axis), the effect of transverse edge crack is more significant and visible (with large frequency drop) than that of longitudinal crack (surface defect). The maximum drop in frequency in both the bending and torsional modes is shifted to free end along the relative distance on the plate. While along transverse direction (X-axis) of free end of the thin plate, the effect of longitudinal edge cracks are visible in torsional modes with massive frequency drop. In this case, the frequency of transverse cracks (surface defects) found in bending modes is greater than healthy plate and longitudinal curve. Surface defects, i.e., the vi longitudinal crack along the longitudinal direction and the transverse crack along the transverse direction, along the edge of the plate remain undetectable. Although, the longitudinal embedded crack remain undetectable, the transverse embedded crack is traceable by the aid of bending modes only. Angle between 75o to 105o of the inclined cracks are more prone to detection. The effect of stiffness on the crack position on the plate near a bend or a twist (found in mode shape) is greater than any other region. Crack located in this region is more likely to be detected. In static structural analysis along the longitudinal direction, stress concentration and total deformation is maximum while the first natural frequency is the minimum at fixed end. While at free end stress and deformation becomes minimum but first natural frequency becomes maximum. It is also found that, for healthy plate and plate with crack near free ends (with relative distance > 70%), the maximum von-Mises stress is located near fixed region of the plate. While for crack positions near fixed end and at mid-region (0% ≤ relative distance ≤ 70%), the maximum von-Mises stress is located at the tip of the crack. It is also observed that the pattern of normalized frequency curve in metal (structural steel) and metal alloy (aluminum alloy) are same. An analytical FEM approach has been performed for without crack condition and numerical validation with published paper has been done and found in good agreement.