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Bifurcation and chaos of the traveling membrane on oblique supports subjected to external excitation

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Abstract

This paper analyzes bifurcation and chaos of the traveling membrane on oblique supports subjected to external excitation. Through coordinate transformation, the Von Karman nonlinear plate theory was employed to derive the non-linear governing equations of membrane on oblique supports in terms of axial movement in the oblique coordinate system. The boundary conditions were also given in the oblique coordinate system. The approximate solution for the governing equations was found via the Galerkin method as well as the fourth-order Runge-Kutta numerical computing method. The nonlinear dynamic techniques including Lyapunov exponents diagrams, bifurcation plots, Poincare maps, phase trajectories, and time histories were introduced to analyze the impacts of the angles of oblique supports, aspect ratios and traveling velocities on dynamics responses and the various forms of vibration regarding the membrane system.

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Acknowledgements

The author gratefully acknowledges the support of the National Natural Science Foundation of China (No. 11272253, 52075435) and Xi’an Science and Technology Project 2018 (No. 201805037YD15CG21(26)).

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Authors and Affiliations

  1. Faculty of Printing, Packing and Digital Media Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Mingyue Shao, Jiajuan Qing & Jimei Wu

Authors
  1. Mingyue Shao
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  2. Jiajuan Qing
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  3. Jimei Wu
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Corresponding author

Correspondence to Jimei Wu.

Additional information

Mingyue Shao, born in 1989, is currently a Ph.D. in Xi’an University of Technology, China. Her research interests are the vibration characteristics and stability of the membrane. ]E-mail: shaomingyue_xaut@163.com

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Shao, M., Qing, J. & Wu, J. Bifurcation and chaos of the traveling membrane on oblique supports subjected to external excitation. J Mech Sci Technol 34, 4513–4523 (2020). https://doi.org/10.1007/s12206-020-1011-9

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  • DOI: https://doi.org/10.1007/s12206-020-1011-9

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