Modal analysis of cracked cantilever beam by finite element simulation

Abstract

Any structure in presence of crack is susceptible to failure depending on the mode of vibration. Failure is due to the resonance formed by the superposition of frequency of periodic force acting on structure and the natural frequency of the structure. To be alert about resonance due to periodic load, it is important to determine natural frequency. In this study of modal analysis, natural frequency and mode shapes of transverse vibration for both un-cracked and cracked cantilever beam has been extracted for first three modes. The analysis has been extended to investigate the effect of crack opening size and mesh refinement. For cracked beam, analysis is performed for various crack depth and crack location. As structural discontinuity problems are difficult to solve analytically, leading commercial Finite Element Analysis software - "Abaqus" is used to perform all the analysis computationally. For modeling un-cracked beam, hexahedral element is used whereas for cracked beam modeling, both hexahedral and wedge elements are selected for better result. In our study we observed that natural frequency reduces with the presence of crack. The amount of reduction varies depending on crack location, depth and crack opening size. Non-dimensional representation highlights that failure criteria largely depend on mode of vibration. The findings of this study can be applied to predict the structural sustainability under varying loads.