Estimation of Reduced Stiffness under the Influence of Crack in a Beam

Abstract

Machine components with cantilever boundary conditions are most prominently used in mechanical engineering applications. When such components are subjected to fatigue loading, crack may get initiated and failure may occur. In order to prevent catastrophic failure and safe guard these components one has to condition monitor the dynamic behavior under fatigue loading condition. Vibration based condition monitoring is one of the most effective method to assess the fatigue failure of the component. In this paper, a cantilever beam is analyzed for its dynamic behaviour under the influence of crack. The cantilever beam considered for the analysis is of rectangular cross section and is uniform throughout its length. The characteristic equation was derived for the Euler-Bernoulli cantilever beam to obtain the relationship between the location of the crack and stiffness of the beam because the stiffness of the beam influences the natural frequency. It is found that the stiffness of the cantilever beam is varying for varying locations of the crack in different modes of vibration. It is clearly understood from the analysis that the vibration response of the cracked cantilever beam in its modes of vibration is affected by the corresponding stiffness reduction based upon the location of the crack. So, it can be inferred that the natural frequency of the cracked cantilever beam may have different values for different locations of the crack.