Vibration Analysis of Cracked Beam

Abstract

Cracks in vibrating component can initiate catastrophic failures. The presences of cracks change the physical characteristics of a structure which in turn alter its dynamic response characteristics. Therefore there is need to understand dynamics of cracked structures. Crack depth and location are the main parameters for the vibration analysis. So it becomes very important to monitor the changes in the response parameters of the structure to access structural integrity, performance and safety. To examine the effect of the crack to the natural frequency of beams. In the present study, vibration analysis is carried out on a cantilever beam with two open transverse cracks, to study the response characteristics. In first phase local compliance matrices of different degree of freedom have been used model transverse cracks in beam on available expression of stress intensity factors and the associated expressions for strain
energy release rates. Suitable boundary condition are used to find out natural frequency and mode shapes. The results obtained numerically are validated with the results obtained from the simulation. The simulations have done with the help of ANSYS software. A neural network for the cracked structure is trained to approximate the response of the
structure by the data set prepared for various crack sizes and locations. Feed-forward multilayer neural networks trained by back-propagation are used to learn the input (the location and depth of a crack)-output (the structural eigenfrequencies) relation of the structural system. With this trained neural network minimizing the difference from the measured frequencies. It is verified from both computational and simulation analysis that the presence of crack decreases the natural frequency of vibration. The mode shapes also changes considerably due to the presence of crack.