STUDY OF FREE UNDAMPED AND DAMPED VIBRATIONS OF A CRACKED CANTILEVER BEAM

Abstract

This paper deals with the analytical study on the free un-damped and damped vibration of Euler–Bernoulli beam containing edge cracks. In this study, the effects of the different crack parameters such as crack depth, crack location and crack angle on the dynamic responses of the beam are discussed. Research studies presented the effect of transverse cracks on the natural frequency. Earlier studies have not considered the effect of oblique cracks on the cantilever beam. Presence of cracks in various parts of machine changes its vibration parameters to a considerable degree i.e. natural frequency and damping factor. In this paper, the transverse cracks and oblique cracks are considered on a cantilever beam at different locations and depths to study its effects on the various vibration parameters. The information of the dynamic response i.e. changes in the natural frequency, is much needed in the health monitoring of the beam to determine the location and depth of the crack in the beam. The response of a cracked cantilever beam for a damping factor has been studied by the combination of finite element analysis and theoretical method. Tests were conducted on the cantilever beam for both an intact and cracked cases by using FFT Analyzer. ANSYS software is used to validate the experimental results. The results of this study suggest that the natural frequency of the beam decreases significantly, when crack depth increases to 80% of the depth of the beam and it is least affected, when depth of the crack is either 20% or less than 20% of the depth the beam. Further it is also observed that the value of damping factor is least affected when crack remains present in the beam more towards the free end, when compared to damping factor of an intact beam.

Keywords

• Cracked beams
• Natural frequency
• Crack Angle
• ANSYS
• Damping factor