Dynamic and steady analysis of a 2-DOF vehicle system by modified incremental harmonic balance method

  • Shihua ZhouEmail author
  • Guiqiu Song
  • Yiming Li
  • Zhilong Huang
  • Zhaohui Ren
Original paper


In this study, the dynamic response and stability of two-degree-of-freedom vehicle system subjected to an external excitation force with quadratic and cubic nonlinearities simultaneous are researched, and the differential equations of motion are deduced by utilizing the mechanical constitutive relationship. The accuracy of the model and the efficiency of modified incremental harmonic balance method are compared and verified with literature and numerical simulation results. Then the parameter researches of the system are carried out to investigate the influences of the mass ratio, excitation amplitude and nonlinear stiffness ratio of tire on the nonlinear characteristics and steady-state responses by amplitude–frequency curves, which have different level of influences on the dynamic responses of the vehicle system. Depending on the different control parameters, the system displays rich and varied behaviors including the jump discontinuity, multiple solution properties, super-harmonic resonance and softening/hardening-type nonlinearity, which are attributed to the strong nonlinearity and dynamical coupling characteristics of the vehicle system. Besides, the two remarkable resonance peaks and different branching paths between steady-state solution and unsteady-state solution are observed. The contributions of this study can provide valuable information to optimize and control the vehicle system, and be helpful for knowing more about nonlinear dynamic behaviors and stability of the system.


Vehicle system Modified IHBM Nonlinear dynamics Hardening nonlinearity Amplitude–frequency curves 



The project is supported by Natural Science Foundation of China (No. 51805075), Natural Science Foundation of Liaoning Province (No. 20180551094) and the Fundamental Research Funds for the Central Universities (No. N180304018).


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Shihua Zhou
    • 1
    Email author
  • Guiqiu Song
    • 1
  • Yiming Li
    • 1
  • Zhilong Huang
    • 1
  • Zhaohui Ren
    • 1
  1. 1.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangChina

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