摘要
针对二维弹簧摆中弹簧型和摆型的振动两种模态,建立了系统的动力学方程。运用Matlab对该方程进行了数值求解,绘制了弹簧摆的演化曲线、相图以及运动轨迹,并对系统进行了动力学行为分析。结果发现:弹簧摆动与弹簧振子的固有频率之比f为1/2且初始摆角极小时,弹簧摆有内共振现象且作准周期运动;在初始摆角不变时,通过改变参数f,弹簧摆的运动特点不同;在参数f不变时,通过改变初始摆角,弹簧摆呈现出复杂的混沌运动特性。
Aiming at the two modes of spring vibration and pendulum vibration in two-dimensional spring pendulum,the dynamic equations of the system are established.The equations are solved numerically with Matlab,and the evolution curve,phase diagram and movement trajectory of spring pendulum are drawn,and the dynamic behavior of the system is analyzed.The results indicate that the spring pendulum has an internal resonance phenomenon and performs a quasi-periodic motion when the ratio of the natural frequency of the spring swing to the natural frequency of the spring oscillator,f,is 1/2 and the initial pendulum angle is very small.When the initial pendulum angle is constant,the motion characteristics of the spring pendulum are different by changing the parameter f.The spring pendulum presents a complex chaotic motion behavior by changing the initial pendulum angle under the condition that the parameter f is constant.
作者
张义灵
蓝冬云
张振美
凌晓菲
罗志荣
ZHANG Yiling;LAN Dongyun;ZHANG Zhenmei;LING Xiaofei;LUO Zhirong(School of Physics and Telecommunication Engineering,Yulin Normal University,Yulin 537000,China;College of Physics and Electronic Information Engineering,Zhejiang Normal University,Jinhua 321004,China)
出处
《大学物理实验》
2020年第4期84-89,共6页
Physical Experiment of College
基金
广西高等教育本科教学改革工程项目(2019JGB313)
玉林师范学院高等教育本科教学改革工程重点项目(2020XJJGZD19)
大学生创新训练计划项目(201910606130,201910606115)。
关键词
弹簧摆
内共振
混沌运动
MATLAB
spring pendulum
internal resonance
chaotic motion
Matlab
