Forced Vibration Analysis of a Cracked Frame

Abstract

In this study, undamped and damped forced vibration responses of a single span frame with cracks are investigated. The vibration analysis of the cracked frame is examined by using the Euler-Bernoulli beam theory. The local flexibility resulting from the crack effect is modeled with a massless and dimensionless finite element beam in the crack section. The local flexibility is obtained by using the stress intensity factor and strain energy release rates according to the opening mode (Mode 1) and the in-plane shear mode (Mode 2) based on the linear elastic fracture mechanics theory. The crack stiffness is obtained by taking the inverse of the flexibility of the crack. Assembly of global finite element matrices are obtained by adding the crack stiffness to the finite element model. In solution of the forced vibration problem, the central difference method is used in the time history. In the numerical results, the effects of the crack depth, the crack location and dimension of the frame on the undamped and damped forced vibration responses of the cracked frame are investigated. Also, the validation studies are performed in order to accuracy of the presented method.