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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 907627, 17 pages
Research Article

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

1College of Information Engineering, Qingdao University, Qingdao 266071, China
2Shandong Jiaotong University, Jinan 250023, China

Received 20 May 2014; Revised 4 August 2014; Accepted 3 September 2014; Published 9 October 2014

Academic Editor: Francesco Pellicano

Copyright © 2014 Jieyu Ding and Qingquan Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonlinear equilibrium curvatures and free vibration characteristics of a two-pulley belt-driven system with belt bending stiffness and a one-way clutch are investigated. With nonlinear dynamical tension, the transverse vibrations of the translating belt spans and the rotation motions of the pulleys and the accessory shaft are coupled. Therefore, nonlinear piecewise discrete-continuous governing equations are established. Considering the bending stiffness of the translating belt spans, the belt spans are modeled as axially moving beams. The pattern of equilibria is a nontrivial solution. Furthermore, the nontrivial equilibriums of the dynamical system are numerically determined by using two different approaches. The governing equations of the vibration near the equilibrium solutions are derived by introducing a coordinate transform. The natural frequencies of the dynamical systems are studied by using the Galerkin method with various truncations and the differential and integral quadrature methods. Moreover, the convergence of the Galerkin truncation is investigated. Numerical results reveal that the study needs 16 terms after truncation in order to determine the free vibration characteristics of the pulley-belt system with the belt bending stiffness. Furthermore, the first five natural frequencies are very sensitive to the bending stiffness of the translating belt.