Abstract
Based on the Coriolis acceleration and the Lagrangian strain formula, a generalized equation for the transverse vibration system of convection belts is derived using Newton’s second law. The method of multiple scales is directly applied to the governing equations, and an approximate solution of the primary parameter resonance of the system is obtained. The detuning parameter, cross-section area, elastic and viscoelastic parameters, and axial moving speed have a significant influences on the amplitudes of steady-state response and their existence boundaries. Some new dynamical phenomena are revealed.
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Abrate, A. S. Vibration of belts and belt drives. Mechanism and Machine Theory 27(6), 645–659 (1992)
Moon, J. and Wickert, J. A. Nonlinear vibration of powertransmission belts. Journal of Sound and Vibration 200(4), 419–431 (1997)
Pellicano, F., Freglent, A., Bertuzzi, A., and Vestroni, F. Primary and parametric nonlinear resonances of power transmission belt: experimental and theoretical analysis. Journal of Sound and Vibration 244(4), 669–684 (2001)
Zhang, L. and Zu, J. W. Non-linear vibrations of viscoelastic moving belts, part I: free vibration analysis. Journal of Sound and Vibration 216(1), 75–91 (1998)
Zhang, L. and Zu, J.W. Non-linear vibrations of viscoelastic moving belts, part II: forced vibration analysis. Journal of Sound and Vibration 216(1), 93–105 (1998)
Zhang, L. and Zu, J. W. Non-linear vibrations of parametrically excited moving belts, part I: dynamic response. Journal of Applied Mechanics 66, 396–402 (1999)
Zhang, L. and Zu, J.W. Non-linear vibrations of parametrically excited viscoelastic moving belts, part II: stability analysis. Journal of Applied Mechanics 66, 403–409 (1999)
Nayfeh, A. H. and Mook, D. T. Nonlinear Oscillation, Wiley Inter Science, New York (1979)
Chen, L. Q. Analysis and control of transverse vibrations of axially moving strings. ASME Applied Mechanics Reviews 58(2), 91–116 (2005)
Chen, L. Q. Principal parametric resonance of axially accelerating viscoelastic strings with an integral constitutive law. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 461(2061), 2701–2720 (2005)
Chen, L. Q., Zu, Jean W., Wu, J., and Yang, Xiaodong. Transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity. Journal of Engineering Mathematics 48(2), 172–182 (2004)
Wu, J. and Chen, L. Q. Steady-state responses and their stability of nonlinear vibration of an axially accelerating strings. Applied Mathematics and Mechanics (English Edition) 25(9), 1001–1011 (2004) DOI: 10.1007/BF02438349
Wickert, J. A. and Mote, C. D., Jr. Classical vibration analysis of axially moving continua. Journal of Applied Mechanics 57, 1738–743 (1990)
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(Communicated by Li-qun CHEN)
Project supported by the Natural Science Foundation of Hebei Province (No. A200900997)
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Yang, Za., Li, Gf. Parametric resonances of convection belt system. Appl. Math. Mech.-Engl. Ed. 30, 753–764 (2009). https://doi.org/10.1007/s10483-009-0609-y
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DOI: https://doi.org/10.1007/s10483-009-0609-y