Nonlinear Dynamics

, Volume 78, Issue 2, pp 1553–1575 | Cite as

Static and dynamic behaviors of belt-drive dynamic systems with a one-way clutch

  • Hu Ding
  • Da-Peng Li
Original Paper


This paper focuses on the nontrivial equilibrium and the steady-state periodic response of belt-drive system with a one-way clutch and belt flexural rigidity. A nonlinear piecewise discrete–continuous dynamic model is established by modeling the motions of the translating belt spans as transverse vibrations of axially moving viscoelastic beams. The rotations of the pulleys and the accessory are also considered. Furthermore, the transverse vibrations and the rotation motions are coupled by nonlinear dynamic tension. The nontrivial equilibriums of the belt-drive system are obtained by an iterative scheme via the differential and integral quadrature methods (DQM and IQM). Moreover, the periodic fluctuation of the driving pulley is modeled as the excitation of the belt-drive system. The steady-state periodic responses of the dynamic system are, respectively, studied via the high-order Galerkin truncation as well as the DQM and IQM. The time histories of the system are numerically calculated based on the 4th Runge–Kutta time discretization method. Furthermore, the frequency–response curves are presented from the numerical solutions. Based on the steady-state periodic response, the resonance areas of the dynamic system are obtained by using the frequency sweep. Moreover, the influences of the truncation terms of the Galerkin method, such as 6-term, 8-term, 10-term, 12-term, and 16-term, are investigated by comparing with the DQM and IQM. Numerical results demonstrate that the one-way clutch reduces the resonance responses of the belt-drive system via the torque-transmitting directional function. Furthermore, the comparisons in numerical examples show that the investigation on steady-state responses of the belt-drive system with a one-way clutch and belt flexural rigidity needs 16-term truncation


Nonlinear vibration One-way clutch Dynamic system Galerkin method Differential quadrature Integral quadrature 



The authors gratefully acknowledge the support of the State Key Program of National Natural Science Foundation of China (No. 11232009), the National Natural Science Foundation of China (No. 11372171), and Innovation Program of Shanghai Municipal Education Commission (No. 12YZ028).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina

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