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Nonlinear free vibration of a beam on Winkler foundation with consideration of soil mass motion of finite depth

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Abstract

Nonlinear free vibration characteristics of a beam on elastic foundation are investigated. Considering the effect of soil–structure interaction on the nonlinear dynamic response of the beam and using the expression of subgrade reaction obtained from the equation of motion of Winkler foundation, the nonlinear equation of motion of the beam on Winkler foundation with the soil mass motion of finite depth is derived. Then, using the eigenvalue analysis method and the method of multiple scales, the linear and nonlinear natural frequencies and mode shapes of the beam are obtained. Finally, by means of numerical calculation and parameter analysis, the effects of Winkler foundation mass, stiffness and damping on the dynamic characteristics of the beam are explored.

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Acknowledgements

The study was supported by the National Natural Science Foundation of China (11502072, 51474095 and 11602089), and the Key Program of Scientific Research of Education Department Henan Province (14A410003).

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Authors and Affiliations

  1. School of Civil Engineering, Henan University of Science and Technology, Luoyang, Henan, 471023, People’s Republic of China

    Jianjun Ma, Fengjun Liu & Mengqiang Nie

  2. School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, Shanxi, 710055, People’s Republic of China

    Junbo Wang

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  1. Jianjun Ma
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  2. Fengjun Liu
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Correspondence to Jianjun Ma.

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Ma, J., Liu, F., Nie, M. et al. Nonlinear free vibration of a beam on Winkler foundation with consideration of soil mass motion of finite depth. Nonlinear Dyn 92, 429–441 (2018). https://doi.org/10.1007/s11071-018-4066-8

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  • DOI: https://doi.org/10.1007/s11071-018-4066-8

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