超低频标准振动台非线性运动方程共振/非共振解比较

Comparative Study on Resonance and Non-resonance Solution of Non-linear Dynamic Equation Based on Standard Ultra-low Frequency Vibrator

给出了一类超低频标准振动台非线性运动方程的两种近似解析解——非共振解法和共振解法。通过对其解的组成及方程中系数改变的分析计算 ,可知 ,采用非共振解法 ,在强阻尼的情况下 ,可较好地表达了振幅、相位与频率间的关系 ,且能容易求出解中各次谐波分量值 ,在弱阻尼下 ,则不能全面地反映非线性方程同频多值现象。而共振解法则不管阻尼大小 ,均能较好地反映振幅、相位与频率间的关系 ,缺点是较难求解出各次谐波分量值。通过对两种解析解的比较分析研究 ,为今后设计波形失真度最小的超低频标准振动台结构参数提供了理论依据。

This paper presents two kinds of approximate analytical solution, non-resonance solution and resonance solution, of non-linear dynamic equation based on a type of ultra-low frequency vibrator. Then the paper gives a conclusion through analysis of the format of the result and changing the coefficient of the equation. Study shows that non-resonance solution can describe the relationship among amplitude, phase and frequency very well and can easily obtain all the harmonic's amplitudes on the strong damping condition. But this solution cannot reveal the phenomenon that a non-linear equation may have several results corresponding to the same frequency on the weak damping circumstance. At the same time, resonance solution can account for the relationship among amplitude, phase and frequency very well no matter for strong damping condition or weak damping condition, but it is very difficult to obtain all the harmonic's amplitudes.