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Analytical and experimental studies on nonlinear characteristics of an L-shape beam structure

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Abstract

This paper focuses on theoretical and experimental investigations of planar nonlinear vibrations and chaotic dynamics of an L-shape beam structure subjected to fundamental harmonic excitation, which is composed of two beams with right-angled L-shape. The ordinary differential governing equation of motion for the L-shape beam structure with two-degree-of-freedom is firstly derived by applying the substructure synthesis method and the Lagrangian equation. Then, the method of multiple scales is utilized to obtain a four-dimensional averaged equation of the L-shape beam structure. Numerical simulations, based on the mathematical model, are presented to analyze the nonlinear responses and chaotic dynamics of the L-shape beam structure. The bifurcation diagram, phase portrait, amplitude spectrum and Poincare map are plotted to illustrate the periodic and chaotic motions of the L-shape beam structure. The existence of the Shilnikov type multi-pulse chaotic motion is also observed from the numerical results. Furthermore, experimental investigations of the L-shape beam structure are performed, and there is a qualitative agreement between the numerical and experimental results. It is also shown that out-of-plane motion may appear intuitively.

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Authors and Affiliations

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

    Dong-Xing Cao, Wei Zhang & Ming-Hui Yao

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  1. Dong-Xing Cao
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  2. Wei Zhang
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  3. Ming-Hui Yao
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Correspondence to Wei Zhang.

Additional information

The project was supported by the National Science Foundation for Distinguished Young Scholars of China (10425209), the National Natural Science Foundation of China (10732020, 10802001, 11072008 and 10872010), the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality and the Ph.D. Programs Foundation of Beijing University of Technology (X0001015200801).

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Cao, DX., Zhang, W. & Yao, MH. Analytical and experimental studies on nonlinear characteristics of an L-shape beam structure. Acta Mech Sin 26, 967–976 (2010). https://doi.org/10.1007/s10409-010-0385-9

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  • DOI: https://doi.org/10.1007/s10409-010-0385-9

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