Dynamic behavior of cracked frame structures

Cracks in engineering structures due to manufacturing errors and destructive effects during the service period are one of the most important problems in engineering. Cracks change the strength, stability and dynamic behavior of the structures and considerably and the lifetime and strength of the structures are reduced significantly. In order to more safe desing of structures, the crack effects should be considered in the structural analysis. In this study, free vibration, 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 energy based finite element method within Euler -Bernoulli beam theory. The Kelvin-Voigt viscoelastic model is used for the damping effect. 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 the solution of the problem and obtaining of the results, algorithms and codes are written in Matlab program. The vibration frequencies are obtained by applying the eigenvalue-eigenvector procedure in the free vibration solution of the problem. 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, number of crack 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.