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Nonlinear dynamic analysis of a parametrically excited vehicle–bridge interaction system

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Abstract

In this paper, a nonlinear supported Euler–Bernoulli beam under harmonic excitation coupled to a 2 degree of freedom vehicle model with cubic nonlinear stiffness and damping is investigated. The equations of motion are derived by Newton’s law and discretized into a set of coupled second-order nonlinear differential equations via Galerkin’s method with cubic nonlinear terms. Based on the created model, numerical simulations have been conducted using the Runge–Kutta integration method to perform a parametric study on influences of the nonlinear support stiffness coefficient, mass ratio, excitation amplitude and position relation for the vehicle–bridge interaction (VBI) system by using bifurcation diagram and 3-D frequency spectrum. The results indicate that depending on different parameters, a diverse range of periodic motion, quasi-periodic response, chaotic behavior and jump discontinuous phenomenon are observed. And the chaotic regions are scattered between a number of periodic/quasi-periodic motions. The study may contribute to a further understanding of the dynamic characteristics and present useful information to dynamic design and vibration control for the VBI system.

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Acknowledgements

Collaborative Innovation Center of Major Machine Manufacturing in Liaoning; National Support Program, the key common technology research and demonstration of paving equipment for subgrade in alpine (No. 2015BAF07B07). The authors gratefully acknowledge the financial support provided by Natural Science Foundation of China (No. 51475084).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, 110819, Shenyang, China

    Shihua Zhou, Guiqiu Song, Zhaohui Ren & Bangchun Wen

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  1. Shihua Zhou
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  2. Guiqiu Song
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  3. Zhaohui Ren
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  4. Bangchun Wen
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Correspondence to Guiqiu Song.

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Zhou, S., Song, G., Ren, Z. et al. Nonlinear dynamic analysis of a parametrically excited vehicle–bridge interaction system. Nonlinear Dyn 88, 2139–2159 (2017). https://doi.org/10.1007/s11071-017-3368-6

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  • DOI: https://doi.org/10.1007/s11071-017-3368-6

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