Dynamic analysis of a simply supported beam with crack

Abstract

The crack present in the structure changes the physical nature of it as well as changes the dynamic response towards the vibration. For the analysis the depth and location of the crack are important parameters which change the response. So it is important to study these changes for the structural integrity, performance and safety. In the current project titled “Dynamic Analysis of A Simply Supported Beam with Crack” the response nature of both cracked and uncracked beam is predicted. Also the responses for different crack depths are studied. In the present study, vibration analysis is done on a simply supported beam with and without crack. The beam is considered to be an Euler-Bernoulli beam which is the most ideal case for simple calculation. The methods used here are both non-dimensional and parametric. At first the problem was solved using the boundary conditions and the normal equations to find out the natural frequency of the beam. Then the cracked beam was studied taking all the effects of the crack into consideration and the physical property of the material. Here the cracked beam is considered to be two beams connected by a mass less spring at the crack point. The proposed method had been compared with the analytical calculation and then with the help of MATLAB the frequency response had been plotted to see the deviation from the natural response.