Nonlinear Dynamics

, Volume 92, Issue 2, pp 429–441 | Cite as

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

  • Jianjun Ma
  • Fengjun Liu
  • Mengqiang Nie
  • Junbo Wang
Original Paper


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.


Beam Winkler foundation Soil mass Natural frequency Nonlinear normal modes Method of multiple scales 



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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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Civil EngineeringHenan University of Science and TechnologyLuoyangPeople’s Republic of China
  2. 2.School of Civil EngineeringXi’an University of Architecture and TechnologyXi’anPeople’s Republic of China

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