Nonlinear Dynamics

, Volume 88, Issue 4, pp 2947–2956 | Cite as

Internal resonance vibration induced by nonlinearity of primary suspension system in high-speed vehicle system

  • Yu Biao Liu
  • Yun Lin Xing
  • S. S. Law
  • Ying Ying Zhang
Original Paper


This paper studies the phenomenon of internal resonance in high-speed vehicle system under high frequency periodic excitations. A numerical model of the vehicle system, taking into consideration the dynamic effects of the primary suspension system and the flexibility of the car-body, is established for the study. An approximate approach incorporating the incremental harmonic balance method with frequency response function is adopted to solve the dynamic responses of the vehicle system in frequency domain. Numerical results show that internal resonance vibration in the vehicle system may occur with certain combinations of design parameters of the vehicle system. The vibration of the car-body and the primary suspension system are significantly amplified with energy transmitted between the natural modes of the car-body and the primary suspension system. Parametric studies on the internal resonance are further explored. Results show that the nonlinearity of the primary suspension spring and the modal damping ratio of the vehicle system play very important roles to the occurrence of internal resonance.


High-speed vehicle Incremental harmonic balance method Nonlinear steady-state solution Internal resonance 



This work was supported by a grant from the Major State Basic Research Development Program of China (973 Program, No. 2011CB711100) and a grant from the National Key Research and Development Plan of China (No. 2016YFC0701302).


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Yu Biao Liu
    • 1
  • Yun Lin Xing
    • 2
  • S. S. Law
    • 3
  • Ying Ying Zhang
    • 1
  1. 1.Key Laboratory for mechanics in Fluid Solid Coupling Systems, Institute of MechanicsChinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.Beijing Engineering Technology Research Center for Micro-Vibration Environmental ControlChina Electronics Engineering Design InstituteBeijingPeople’s Republic of China
  3. 3.Department of Civil and Environmental EngineeringThe Hong Kong Polytechnic UniversityHunghom, KowloonPeople’s Republic of China

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