An Analysis of the Lateral Dynamic Response of an Axially Moving Cantilever Beam under a Moving Mass
From the view of flexible multibody dynamics, this paper considers not only Euler-Bernoulli beam assumption but also the effects of rotary inertia and beam’s inner tension, the equation of motion and associated boundary conditions of the dynamic model are derived by using the extended Hamilton’s principle. Converting the varying-time equation into a varying-coefficient differential equation in fixed region by substituting argument. And truncating the equation to a set of varying-time ordinary equations expressed by modal coordinates based on Assumption Modal Method and Galerkin Discrete Method. Then the equations were solved by using Newmark time integration method. The results show that moving mass excites mainly the first order mode vibration of beam. Before the moving mass disengages the beam, the dynamic effect of mass is so small that cantilever beam is lacked of obvious vibration. Its transverse displacement was mainly driven by static load. After the moving mass disengages the beam, the shorten length and shrinking movement of beam make the instantaneous vibration frequency continuously reduce and the vibration displacement gradually decrease too. While, at the same time, its total mechanical energy is increasing, so the beam is in unsteady vibration state.
Quan Yang, Xiaozhong Du, Xingzhong Zhang, Xiaochen Wang and Fei He
Z. X. Zhang and Z. D. Hu, "An Analysis of the Lateral Dynamic Response of an Axially Moving Cantilever Beam under a Moving Mass", Applied Mechanics and Materials, Vols. 215-216, pp. 934-940, 2012