Numerical and fem investigation on dynamic response of damaged cantilever structures carrying transit load

In the present investigation, the effects of crack related features such as crack position, crack height, as well as the mass and the velocity of the moving load on the vertical deflection of the damaged beams under the effect of moving load are analyzed. The governing equations of motion for cracked beams subjected to moving load have been obtained and they have been solved by applying the Duhamel integral technique. The responses of the structures due to the consequences of crack depth, crack location, moving speed, and moving mass are also determined. At first, the results between undamaged and damaged beams have been compared. Then, a comparative study between double and triple cracked beams has been conducted in order to understand the consequence of third crack on the dynamic characteristics of the beam. The mass-beam structural system has been modelled mathematically with the presence of open and transverse cracks with different crack configuration (crack depth and locations). Several numerical examples have been executed. In order to confirm the validity of the formulation, finite elements analysis has been carried out. The results gathered from the numerical analysis along with finite element analysis for undamaged, double, and triple cracked beams have been plotted for comparative results analysis. It has been concluded that the aforementioned parameters (crack depth, crack location, moving mass and moving speed) play an important role on the dynamic behaviour of the damaged structures.