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Dynamical stability of the cantilever beam with oscillating length

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Abstract

The dynamical stability and transverse vibration of the cantilever beam with oscillating length are analyzed in this study. The differential equation of motion with time-dependent coefficients is discretized by the Galerkin method, and then the method of multiple scales for multi-degree of freedom is applied to investigate the parametric resonances of the cantilever beam with oscillating length. The effects of the oscillation amplitude and frequency on the parametric resonance regions and the tip responses are discussed. Tip responses simulation by Runge–Kutta method confirms the parametric resonance regions obtained by multiple scales method. In addition, the ‘jump’ phenomenon on the tip response of the axially oscillating deploying cantilever beam is also discussed.

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Acknowledgements

The authors are grateful to the supports of the National Natural Science Foundation of China (Nos. 11472211 and 11272254), and the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2015JM1029).

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Authors and Affiliations

  1. School of Mechanical and Precision Instrument Engineering, Xi’ an University of Technology, No. 5 South Jinhua Road, Xi’an, 710048, China

    Yin-lei Huo

  2. Department of Packaging Engineering, Henan University of Science and Technology, No. 263 Kaiyuan Road, Luoyang, 471023, China

    Yin-lei Huo

  3. School of Civil Engineering and Architecture, Xi’ an University of Technology, No. 5 South Jinhua Road, Xi’an, 710048, China

    Zhong-min Wang

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  1. Yin-lei Huo
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Correspondence to Zhong-min Wang.

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Huo, Yl., Wang, Zm. Dynamical stability of the cantilever beam with oscillating length. Arch Appl Mech 87, 1281–1293 (2017). https://doi.org/10.1007/s00419-017-1249-6

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  • DOI: https://doi.org/10.1007/s00419-017-1249-6

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