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Research Papers

Constrained Optimization Shooting Method for Predicting the Periodic Solutions of Nonlinear System

[+] Author and Article Information
Haitao Liao

Chinese Aeronautical Establishment,
Beijing 100012, China
e-mail: ht0819@163.com

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received November 7, 2012; final manuscript received February 23, 2013; published online March 26, 2013. Assoc. Editor: D. Dane Quinn.

J. Comput. Nonlinear Dynam 8(4), 041006 (Mar 26, 2013) (8 pages) Paper No: CND-12-1194; doi: 10.1115/1.4023916 History: Received November 07, 2012; Revised February 23, 2013

An original method for calculating the maximum vibration amplitude of the periodic solution of a nonlinear system is presented. The problem of determining the worst maximum vibration is transformed into a nonlinear optimization problem. The shooting method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the effectiveness and ability of the proposed approach are illustrated through two numerical examples. Numerical examples show that the proposed method can give results with higher accuracy as compared with numerical results obtained by a parameter continuation method and the ability of the present method is also demonstrated.

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References

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Figures

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Fig. 1

A flow chart of the OQNLP MultiStart algorithm

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Fig. 3

The time responses of the Duffing oscillator

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Fig. 4

The time errors between the proposed method and the HBM-ANM-HILL method

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Fig. 2

Frequence-response curves of the Duffing system

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Fig. 5

The worst time histories of the nonlinear bladed assembly for different engine orders

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