A New Continuous Model for Transverse Vibration Analysis of a Cracked Beam by Using Hu-Washizu Variational Principle

In this research, a new continuous model for vibration analysis of a simply support cracked Euler Bernouli beam is proposed. The effect of the crack on the stress, strain and displacement field is modeled as a continuous disturbance function. The equation of motion and the corresponding boundary conditions for bending vibration of a cracked beam with an open edge crack, are derived by using Hu-Washizu variational principle. By employing the Galerkin method, the natural frequencies and mode shapes are obtained, and the influence of the crack parameters (crack depth and location) on the vibration behavior of the cracked beam is studied. The results have been validated by the experimental and theoretical dada reported in the literature. There is a good agreement between the results obtained through the proposed method and those obtained from the reported experimental data.