Numerical Study of Dry Friction Vibration System with Oblique Friction Force

  • Jiean Liao
  • Youqiang Zhang
  • Shuli Luo
  • Ling Zhou
Original Paper



This study investigates a vibration system considering friction force and external excitation. In particular, when the direction of the friction force is at an oblique angle along the horizontal and vertical directions, the influences of dry friction on the system dynamics are discussed.


The two-degree-of-freedom dynamical model with dry friction and external excitation is established. The piecewise analytical solution corresponding to different phases is deduced based on theoretical method, the complicated dynamic behaviors are investigated by numerical simulations.


The results indicate that there is no vibration of the system when external excitation does not act in either the horizontal or vertical direction, but system vibration remains when external excitation acts in both the vertical direction and horizontal direction. As parameters change largely, there exist rich symmetric and asymmetric motion, quasi-periodic motion, and chaos, and the system stability is discussed when the system parameters change within a certain range based on the Lyapunov exponent method.


Dry friction Dynamics Oblique friction force Numerical method 



This work is supported by the National Natural Science Foundation of PRC (Grant no. 11362020, Grant no. 51265048).


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© KrishteleMaging Solutions Private Limited 2019

Authors and Affiliations

  • Jiean Liao
    • 1
  • Youqiang Zhang
    • 1
  • Shuli Luo
    • 1
  • Ling Zhou
    • 1
  1. 1.School of Mechanical and Electrical Engineering, Key Laboratory of Modern Agricultural EngineeringTarim UniversityAlarPeople’s Republic of China

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