基于谐波平衡法的Broyden网格分区迭代算法

Research of a novel Broyden grid iteration algorithm based on harmonic balance method

在融合Broyden算法与网格分区思想的基础上,提出一种基于谐波平衡法且适用于对间隙型非线性动力系统进行频响特性分析的新型Broyden网格迭代算法.阐述了Broyden网格迭代算法的基本思想与计算流程.对决定该算法有效性的Broyden算法发散特性及不完整变量循环迭代过程等关键特性进行了分析与讨论.通过与相关文献采用的二分法所得的同等条件下的计算结果进行对比,证明该算法比二分法具有更好引导性与更全面的求解能力.通过网格分区的引导,该方法避免了数值迭代方法中普遍面临的迭代初值的盲目选择问题,为基于谐波平衡法全面考察间隙型非线性动力系统的频响特性提供了新途径.

Based on the convergence of Broyden algorithm and grid partition idea, a novel type of Broy- den Grid Iterative Algorithm （BGIA） for analysing the frequency response characteristic of gap-type nonlinear dynamic system with the Harmonic Balance Method （HBM） has been proposed in this pa- per. The main idea and computational procedure of BGIA has been introduced. The divergent charac- teristic of Broyden algorithm and the iteration process with the incomplete variables, which determine the effectiveness of the proposed algorithm, have been deeply analyzed and discussed. Finally, by com- paring with the results of the related literature in the same condition, it could be concluded that the novel algorithm is a more instructive and comprehensive algorithm than the traditional method. This algorithm could avoid the blindness of iterative initial value selection, and provide a new route for solv- ing the frequency response characteristic of gap-type dynamic system with HBM.