Motion of a moving elastic beam carrying a moving mass - Analysis and experimental verification

In this paper, vibrational motion of an elastic beam fixed on a moving cart and carrying a moving mass is investigated. The equations of motion of the beam-mass-cart system are derived and the coupled dynamic equations are so lved by the unconstrained modal analysis. In modal analysis, the exact norm al mode solutions corresponding to the eigenfrequencies for each position o f the moving mass and the ratios of the weight of the beam-mass-cart system are used. Proper transformation of time solutions between the normal modes for a position and those for the next position of the moving mass is also considered. Numerical simulations are carried out to obtain open-loop respo nses of the system in tracking pre-designed paths of the moving mass. The s imulation results show that the model predicts the dynamic behavior of the beam-mass-cart system well. Experiments are carried out to show the validit y of the proposed analytical method. (C) 2001 Academic Press.