Abstract
In this paper we investigate the dynamic stability and response of stepped tubes subjected to a stream of moving objects. The equations of motion for the transverse vibrations of the tube are developed using a Hamilton's principle that accounts for the out-release energy of the moving objects. The Hsu theory is used to predict the stability of the tube when subjected to periodic parametric excitations. The accuracy of the result is verified by obtaining the stability boundaries of simply supported tubes and comparing the results with the results reported in the literature. Stability maps are then obtained for clamped-free uniform tubes as well as clamped-free stepped tubes. The stability maps demonstrate that increasing the number of moving objects can deteriorate the stability characteristics of the tube. It is found that the stability of certain tube modes can be improved by providing the tube with appropriately spaced steps. It is shown that better stability characteristics can be achieved by using piezoelectric actuators. To give clear insight into the tube behavior, the dynamic response is presented for clamped-free tubes. The dynamic analyses of tubes with periodic piezoelectric and viscoelastic steps are the natural extension of the present work.
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