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A new method for predicting the maximum vibration amplitude of periodic solution of non-linear system

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Abstract

An original method based on the proposed framework for calculating the maximum vibration amplitude of periodic solution of non-linear system is presented. The problem of determining the worst maximum vibration is transformed into a non-linear optimization problem. The harmonic balance method and the Hill method are selected to construct the general non-linear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the effectiveness of the proposed approach is illustrated through two numerical examples. Numerical examples show that the proposed method can, at much lower cost, give results with higher accuracy as compared with numerical results obtained by a parameter continuation method.

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Acknowledgements

The author is grateful to the anonymous referees for their valuable comments. This study has been financially supported by Natural Science Foundation of China (Project No. 10904178).

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  1. Chinese Aeronautical Establishment, Beijing, 100012, China

    Haitao Liao & Wei Sun

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  1. Haitao Liao
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  2. Wei Sun
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Correspondence to Haitao Liao.

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Liao, H., Sun, W. A new method for predicting the maximum vibration amplitude of periodic solution of non-linear system. Nonlinear Dyn 71, 569–582 (2013). https://doi.org/10.1007/s11071-012-0682-x

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