对称四弹性振子的二维非线性振动

The non-linear vibration in two-dimension of three flexible symmetric simple harmonic oscillator

本文应用拉格朗日方程方法研究了理想对称四弹性振子做二维运动的变化规律,得到其微小振动的控制方程,用数值解法求解出了振动方程,得到了振子运动的时程响应和轨迹图样.结果表明:理想对称四弹性振子的振动为非简谐运动,它的运动周期在其x方向和y方向与振幅的大小成反比,但受振幅影响不大.波形与振幅无关,可看成是一个变形了的余弦波.

In this paper, we study two-dimension vibrations of four flexible symmetric simple harmonic oscillators. The non-linear vibration equations are obtained by using the Lagrange function method, then they are solve by using numerical method. Results show that the small vibration of this ideal model is non-simple harmonic, and the period of vibration in x direction and y direction are inverse ratio to the amplitude inverse ratio to the amplitude respectively, but influenced a little by them, and the waveform that could be seen as an asimilar cosine waveshap is independent with the amplitude.