ON THE DYNAMIC BEHAVIOR OF A FLEXIBLE BEAM CARRYING A MOVING MASS

The behaviour of a system containing a mass traveling on a cantilever beam is considered. The mass is induced to move by an applied force as opposed to the case which has been considered in most literature wher e the position of the moving mass is assumed to be known and independe nt of the motion of the beam. Furthermore, the system to be discussed has the unique characteristic that the motions of the mass and the bea m are coupled. The mathematical model of the system includes two coupl ed nonlinear integral/partial differential equations which are impossi ble to solve analytically and are difficult to solve numerically in th eir original form. As a remedy, the solution is discretized into space and time functions and the equations of motion are reduced to a set o f ordinary differential equations. The shape function is chosen so tha t it satisfies the boundary conditions of the beam as well as the tran sient conditions imposed by the traveling mass. This choice of the sha pe function, which considers the mass-beam interaction, provides an im provement over the conventional method of using a simple cantilever be am mode shapes. The ordinary differential equations of motion using th e 'improved' shaped functions, are solved numerically to obtain the dy namic behaviour of the system. The results illustrate the validity of the model, and demonstrate the advantages of the 'improved' model to t he 'un-improved' equations.