Complex Dynamical Behavior of Rigid-flexible Coupling Spring Pendulum

  • YU Hongjie;ZHANG Jingshu;HONG Jiazhen
  • Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, China

Received date: 2012-12-04

  Revised date: 2013-04-03

  Online published: 2013-06-28


Aiming at the time-varying, strong nonlinear rigid-flexible coupling multi-body systems with both variables of fast and slow speeds, qualitative analysis is carried out and complex dynamical behaviors are numerically simulated by using a spring pendulum model. A dimensionless dynamical equation of the two-time scale variable rigid-flexible coupling spring pendulum system is established. A more appropriate numerical method for solving stiff problems is compared and selected from the perspective of energy conservation. The frequency ratio between different time scale variables and the initial value of swing angle are taking as the control parameters; on the condition of greater frequency ratio and the large range of initial swing angle, the complex dynamical behavior of wide range swing coupling with small amplitude oscillation is analyzed by means of the numerical simulation of spring pendulum system. The parameter domain for the different dynamical behavior corresponding to different time scale variables is given within a certain range. Results indicate that two-time scale variable system has a complex dynamical behavior including chaos with the change of the frequency ratio between the different time scale variables and the change of initial conditions. Especially, the initial value of large swing angle is easier to cause the chaotic behavior of different time scale variables. A foundation for further qualitative analysis and numerical simulation studies on the dynamical behavior of rigid-flexible coupling multi-body systems is laid down and references and evidence are provided.

Cite this article

YU Hongjie;ZHANG Jingshu;HONG Jiazhen . Complex Dynamical Behavior of Rigid-flexible Coupling Spring Pendulum[J]. Science & Technology Review, 2013 , 31(18) : 32 -38 . DOI: 10.3981/j.issn.1000-7857.2013.18.004