非线性振子的改进Mickens迭代法

IF 4.3 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration Pub Date : 2008-07-22 DOI:10.1016/j.jsv.2008.03.007

Y.M. Chen, J.K. Liu

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引用次数: 29

摘要

基于Mickens过程，提出了一种新的非线性振子迭代格式。与现有的Mickens方法不同，该方法在每个迭代阶段推导出的控制振荡频率的代数方程始终是线性的。以Duffing方程为例，可以很容易地得到很好的近似。进一步，将所提出的方法推广到求得van der Pol方程的极限环。此外，消除了Mickens过程的计算缺点。

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A modified Mickens iteration procedure for nonlinear oscillators

Based on the Mickens procedure, a new iteration scheme is proposed for nonlinear oscillators. Different from the existing Mickens procedures, in the proposed procedure, the algebraic equation governing the frequency of oscillation deduced at each iteration stage is always linear. Taking the Duffing equation as an illustrative example, excellent approximations can be easily obtained. Furthermore, the proposed procedure is extended to obtain the limit cycle of the van der Pol equation. Additionally, a computational disadvantage of the Mickens procedure is eliminated.

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来源期刊

Journal of Sound and Vibration 工程技术-工程：机械

CiteScore

9.10

自引率

10.60%

发文量

551

审稿时长

69 days

期刊介绍： The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application. JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.