对称双弹簧振子横向振动的复杂性研究

Study on Complexity of the Transverse Vibration of Symmetric Double-Spring Oscillator

利用MATLAB数值求解对称双弹簧振子横向振动的微分方程,程序设计为对任意选取的系统参数和初始条件,均可绘制出振动曲线和相图.数值实验表明:对称双弹簧振子的横向运动是周期振动,振动特性随初始条件发生改变;当振幅远大于弹簧原长时,横向振动趋于简谐振动,并与纵向振动有相同的周期;当振幅远小于弹簧原长时,横向振动趋于立方非线性振动,其振动周期与振幅成反比.

The numerical solution of differential equation of transverse vibration of symmetric double-spring oscillator has been gotten with MATLAB.The vibration curves and phase diagrams could be drawn for arbitrarily selected system parameters and initial conditions with program.It is found that the transverse vibration of symmetric double-spring oscillator is always periodic,and the nature of vibration varies with the initial conditions.If the amplitude is larger than the length of the original spring,the transverse vibration is trending to harmonic oscillation.If the amplitude is smaller than the length of the original spring,the transverse vibration is trending to cubic nonlinear oscillation.