测定欠阻尼系统阻尼比的一种方法

A Method for Estimating Damp Ratio of a Underdamped System

提出了一种适用于实验测量欠阻尼系统阻尼比的方法 ,即通过计算相邻两个周期波形的面积之比来测定系统的阻尼比。文中就典型的二阶欠阻尼系统给出了算法的数学推导 ,并从数学上证明了该方法比目前常用的用相邻波峰值之比估计阻尼比的方法具有更好的抗干扰能力 ,同时该方法简单 ,实时性强。此外 ,在实际应用中该方法可适用于所有可近似为二阶欠阻尼系统的高阶系统之阻尼测定。文中对一柔性悬垂梁的自由衰减运动进行了实验测定 ,结果表明用本文提出的方法测定系统的阻尼比比用波峰值之比进行阻尼比估算 。

A new method of estimating damp ratio of a underdamped system is presented by calculating area ratio of two contiguous periods, which is applicable to experimentation. Mathematical development of the algorithm is also presented on typical second order underdamped system. It is proved that the method is more excellent in anti jamming than the usual method presently by calculating ratio of two contiguous wave crest. The method is simple and real time at the same times. It is applicable to high order system that approximate second order underdamped system. A experiment on the free vibration of the cantilever is carried out. Experimental result indicates that the standard deviation is 1/10 compared with the method for calculating the ratio of the contiguous wave crest.