Vibration of a cracked cantilever beam under moving mass load

Abstract

This study is devoted to the investigation of the vibration of a cracked cantilever beam under moving mass load. The present formulation contains inertial, centripetal and Coriolis forces that depend on mass and the velocity of the moving load. The existence of crack induces a local flexibility which is a function of the crack depth, thereby changing its vibration behavior and the eigen-values of the system. The response of the system is obtained in terms of Duhamel integral. The differential equation which involves complicated terms on the right side is solved via an iterative procedure. It has been shown that the centripetal and Coriolis forces make an effect to decrease the deformations on the beam since the deformed beam remains concave during the passage of the moving load. It has also been detected that the previous solutions for the case of moving constant force had several mistakes. The results are exemplified for various values of the variables.