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The self-excited vibrations of an axially retracting cantilever beam using the Galerkin method with fitted polynomial basis functions

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Abstract

In the present study, the self-excited vibrations of an axially retracting beam under gravity is investigated. A GFB method is presented to discretize the system energy functions, in which the orthogonality relationships between the basis functions are needless. In this way, the motion equations can be derived in a much simpler way of matrix. The presented method and the derived motion equations are validated by comparing the computed results with which from previous literature. Based on the computed dynamic responses, the effect of gravity on beam dynamic behavior is investigated. An interesting phenomenon of self-excited vibration is observed as the beam retracts with a certain axial speed. Finally, the effects of retracting speed, structural damping and static tip deflection on self-excited vibration are investigated.

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Authors and Affiliations

  1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Hongliang Hua, Zhenqiang Liao & Xiangyan Zhang

Authors
  1. Hongliang Hua
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  2. Zhenqiang Liao
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  3. Xiangyan Zhang
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Corresponding author

Correspondence to Hongliang Hua.

Additional information

Recommended by Associate Editor Eung-Soo Shin

Hongliang Hua is a doctoral student at Nanjing University of Science and Technology in Nanjing, China. His current research interests include nonlinear dynamics, structural optimization, time-varying Finite element method and rigid-flexible coupled dynamics.

Zhenqiang Liao received his Ph.D. degree in Engineering from Nanjing University of Science and Technology in Nanjing, China. He is a Professor at Department of Mechanical Design, School of Mechanical Engineering, Nanjing University of Science and Technology. His main subjects are multi-body dynamics, vibration reduction for machine gun system and weapon structural optimization.

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Hua, H., Liao, Z. & Zhang, X. The self-excited vibrations of an axially retracting cantilever beam using the Galerkin method with fitted polynomial basis functions. J Mech Sci Technol 32, 29–36 (2018). https://doi.org/10.1007/s12206-017-1204-z

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  • DOI: https://doi.org/10.1007/s12206-017-1204-z

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