刚性杆-弹簧摆模型复杂动力学特性的数值仿真  

Numerical Simulation of Complex Dynamics in the Rigid Rod-Spring Pendulum Model

作　　者：赵聪[1] 于洪洁[1] 

机构地区：[1]上海交通大学工程力学系,上海200240

出　　处：《力学季刊》2015年第1期62-69,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11132007)

摘　　要：建立一种刚性杆-弹簧摆刚柔耦合强非线性动力学系统模型,给出了无量纲的动力学微分方程.该模型同时存在小幅度快速振荡和大范围慢速摆动的快、慢双时间尺度变量.针对工程中此类系统数值求解容易产生的刚性问题,采用一种三次Hermite插值精细积分法进行数值计算.将频率比、摆长比和初始摆角作为控制参数,研究刚性杆-弹簧摆刚柔耦合系统快、慢变量的复杂动力学行为.通过数值仿真分析,发现系统在不同的控制参数组合下呈现出混沌运动状态,并给出了与系统运动状态相关的控制参数范围,为复杂的刚柔耦合多体系统的设计与数值分析提供了参考.A rigid rod-spring pendulum model, which was a rigid-flexible coupling and strongly nonlinear dynamical system, was established and dimensionless dynamic equations were given. There exist two-time-scale variables in this system, including the fast variable of slight oscillation and the slow variables of swing in wide range. A cubic interpolation precise integration method was applied to solve stiff problems that commonly appear in numerical solving process. The dynamical behavior of the rigid rod-spring pendulum system was analyzed as applied the frequency ratio, the length ratio and large initial swing angle as control parameters. It is found that the system presents a chaotic motion under different control parameters. The range of control parameters related to the state of motion was given, which is expected to provide a reference for design and numerical analysis of complex rigid-flexible coupling multi-body systems.

关 键 词：刚柔耦合系统 双时间尺度 弹簧摆 插值精细积分法 混沌 

分 类 号：O313[理学—一般力学与力学基础] O322[理学—力学]