Free vibration analysis of a simply supported beam with a vertical embedded crack

Local stiffness and performances of a beam structure will be changed by a crack, which causes changes in mode parameters. Focused on this problem, a simply supported beam is studied based on finite element method. A finite element model of the beam with a vertical embedded crack is presented. Effects of crack length and location on natural frequencies and mode shapes are investigated. Relationships between curvatures of mode shapes and crack length are discussed, as well as those between curvature and crack location. Numerical results show that natural frequencies decrease with crack length, and differences of mode shapes between normal and abnormal beam increase with crack length. Local stiffness of the beam around crack location is changed by the presence of crack, whose area increases with crack length. Curvature of mode shape can be used to detect location of a vertical embedded crack in a simply supported beam.