刚柔耦合弹簧摆的复杂动力学行为

Complex Dynamical Behavior of Rigid-flexible Coupling Spring Pendulum

针对同时具有快慢变量的时变、强非线性刚柔耦合的多体系统,利用弹簧摆模型定性分析和数值模拟系统复杂的动力学行为。建立双时间尺度变量刚柔耦合弹簧摆的无量纲动力学方程,从能量守恒角度出发,比较、选择更适用于容易产生刚性问题的数值求解方法。将不同时间尺度变量之间的频率比和初值摆角作为控制参数,数值模拟分析弹簧摆在较大频率比和大摆角初始条件下,大范围摆动和小幅度振荡相耦合的复杂动力学行为,给出了一定范围内系统快慢变量呈现不同动力学性态所对应的参数域。结果表明,双时间尺度变量系统随着不同尺度变量之间频率比和初始条件的变化呈现出包括混沌的复杂动力学行为,尤其大摆角初值更容易导致快慢变量产生混沌行为,这为进一步刚柔耦合多体系统动力学行为的定性分析、数值仿真研究打下一个基础并提出参考和依据。

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.