一种改进的增量谐波平衡法及其在非线性振动中的应用

An Improved IHB Method and Its Application to Non-Linear Vibration

对于一般的增量谐波平衡法而言,在求解分段线性系统周期响应时存在收敛速度慢的缺点。针对这一缺点,本文根据最小二乘法原理和增量过程提出了一种改进的增量谐波平衡算法,通过和原有算法进行对比发现二者之间存在着统一的算法形式,因此只要对原有算法作简单的改进即可方便地使用此方法。利用此方法成功计算了齿轮传动分段线性系统的周期解,通过对计算结果比较,发现迭代次数要比一般的增量谐波平衡法少30%左右。从而可以看出这种算法具有收敛速度快的优点。

The general incremental harmonic balance(IHB) method has an inextricable shortcoming——the convergence rate is slow, or even the result is not convergent when it was used to deal with the periodic solution in piecewise linear vibration. In this paper, an improved incremental harmonic balance method was put forward to deal with this shortcoming. This improved method was based on least-square method and incremental disposal. The least-square method was used for obtaining the least values of harmonic coefficient and the incremental disposal was used to obtain the increment of every iterative step. Compared with the general incremental harmonic balance method, a united computing form is obtained. So long as a simple replacement was concerned, this improved method can be used directly in former formulas. When this method is used to deal with the periodic solution in piecewise linear system, the results by the improved method and the general method were compared, and we found that they were the same in phase plane. So this method is valid and the result is credible. It is noted that the iterative number of improved method was decreased by 30% as compared with the general incremental harmonic balance method. So this improved method has the advantage of quicker convergence.