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Nonlinear dynamics of axially moving beam with coupled longitudinal–transversal vibrations

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Abstract

In this study, the nonlinear vibrations of an axially moving beam are investigated by considering the coupling of the longitudinal and transversal motion. The Galerkin method is used to truncate the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. By detuning the axially velocity, the exact parameters with which the system may turn to internal resonance are detected. The method of multiple scales is applied to the governing equations to study the nonlinear dynamics of the steady-state response caused by the internal–external resonance. The saturation and jump phenomena of such system have been reported by investigating the nonlinear amplitude–response curves with respect to external excitation, internal, and external detuning parameters. The longitudinal external excitation may trigger only longitudinal response when excitation amplitude is weak. However, beyond the critical excitation amplitude, the response energy will be transferred from the longitudinal motion to the transversal motion even the excitation is employed on the longitudinal direction. Such energy transfer due to saturation has the potential to be used in the vibration suppression.

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Acknowledgments

This investigation is supported by the National Natural Science Foundation of China (Project Nos. 11322214, 11172010, and 11290152) and by the State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) under Grant No. MCMS-0112G01.

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Authors and Affiliations

  1. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Xiao-Dong Yang & Wei Zhang

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  1. Xiao-Dong Yang
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  2. Wei Zhang
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Correspondence to Xiao-Dong Yang.

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Yang, XD., Zhang, W. Nonlinear dynamics of axially moving beam with coupled longitudinal–transversal vibrations. Nonlinear Dyn 78, 2547–2556 (2014). https://doi.org/10.1007/s11071-014-1609-5

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  • DOI: https://doi.org/10.1007/s11071-014-1609-5

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