Abstract
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 solved by the unconstrained modal analysis. In modal analysis, the exact normal mode solutions corresponding to the eigenfrequencies for each position of 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 responses of the system in tracking pre-designed paths of the moving mass. The simulation results show that the model predicts the dynamic behavior of the beam–mass–cart system well. Experiments are carried out to show the validity of the proposed analytical method.
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