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《Mechanical Science and Technology》 2005-06
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An Improved IHB Method and Its Application to Non-Linear Vibration

GAO Yang, WANG San-ming, LIU Xiao-ning (Northwestern Polytechnical University, Xi′an 710072)  
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.
【Fund】: 航空科学基金项目(02C53019);; 汕头大学重点实验室开放基金项目资助
【CateGory Index】: TB535
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