单转向轮摆振非线性动力学研究

摘要

The caster wheel of a wheelchair was simplified to a 2 —DOF dynamics model. Bifurcation characteristics of the self—excited shimmy and stability analysis were analyzed by Hopf bifurcation theory of nonlinear dynamics and by stability theory of ordinary differential equation. The amplitude of limit cycle was calculated. The computation results indicate that the self—excited shimmy is a stable limit cycle occurring after Hopf bifurcation and it can occur on the steering wheel with a certain set of parameters.%建立了单转向轮系统的非线性动力学微分方程;以常微分方程稳定性理论为基础,研究了系统参数对稳定性的影响;运用非线性动力学稳定性理论,阐明了单转向轮的等幅摆振是一种Hopf分岔后出现的稳定的极限环振动现象;计算了临界分岔参数和极限环半径,即摆振振幅;通过数值仿真,证明了自激振动的存在,当系统参数达到临界值时,发生Hopf分岔现象.