Vibration analysis of cracked beam based on Reddy beam theory by finite element method

The lateral vibration of cracked isotropic thick beams is investigated. Generally, the analysis of thick beam based on line elements can be undertaken using either Timoshenko beam theory or a third order beam theory (TSDT) such as Reddy beam theory. TSDT is superior to Timoshenko beam theory, as it eliminates the need for a shear correction coefficient. However, there is no available solution for a cracked beam based on Reddy beam theory which is the main focus of this paper. The investigated beam is divided into several elements where their stiffness and mass matrices are derived using Reddy beam theory. Each element has two nodes with 3 degrees of freedom (1 lateral and 2 rotational) at each node. The crack was modeled using two rotating springs with stiffnesses that varied with crack depth. These elements are used to connect the adjacent beam elements. The impact of boundary conditions, slenderness ratio, crack location, and crack depth are investigated. In addition, experimental and finite element analyses of cracked steel beams is undertaken to validate the results of the present model. The results show that the maximum deviation between the analytical and the experimental results is less than 3% up to the third mode shape.