Free-vibration analysis of cracked beam with constant width and linearly varying thickness

This study carries out free-vibration analysis of a cracked tapered beam with a constant width and a linearly varying thickness. The finite-element and component mode synthesis methods are used to determine the dynamic behavior of the tapered cracked beam. In accordance with the Bernoulli–Euler beam theory, the stiffness and mass matrices are obtained to find the natural frequencies and mode shapes of the tapered beam. The beam containing a crack is divided into subcomponents from the crack section. A massless spring model is used to define the local flexibility caused by the crack in the beam. The spring stiffness is calculated by taking the inverse of the compliance matrix found by using proper stress intensity factors and strain energy release rates calculated from linear elastic fracture mechanics. Different boundary conditions are considered such as fixed–free and pinned–pinned ends. Variations of natural frequencies and mode shapes depending on the crack location, crack depth and taper ratio of the beam are found, presented in graphs and examined. The applicability, accuracy and validity of the present method are found to be compatible with the literature.