Free vibration analysis of cracked beams by a combination of finite elements and component mode synthesis methods

Previous work on the dynamics of defective structures, by the authors’ colleagues and other studies in the literature, has revealed substantial variability in predicted vibration behaviour depending on the interface conditions. In the current project the authors have set out to develop a strategy which retains the maximum amount of common information concerning the linear regions of the structure, whilst allowing the maximum scope to vary conditions at the (nonlinear) interface. In this paper, the vibrational characteristics of a cracked Timoshenko beam are analysed. The study integrates the finite element method and component mode synthesis. The beam divided into two components related by a flexibility matrix which incorporates the interaction forces. These forces can be derived from fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expressions. Each substructure is modelled by Timoshenko beam finite elements with two nodes and 3 degrees-of-freedom (axial, transverse and rotation) at each node.