Free vibration of the double tapered cracked beam

This study presents the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods. To determine the natural frequency and mode shape of the double tapered cracked beam, the stiffness and mass matrices of the beam have been obtained. The crack in the beam is modeled as a massless spring, and the beam is divided into two subcomponents from the crack section. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expressions. It has been observed that natural frequencies and mode shapes vary depending on the location of the crack, the depth of the crack and the aspect ratios of the beam. The results of the present study and those in the literature are compared and a great deal of consistency has been found.