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Symplectic Approach on the Wave Propagation Problem for Periodic Structures with Uncertainty

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Abstract

An effective method is proposed in this paper for the symplectic eigenvalue problem of a periodic structure with uniform stochastic properties. Since structural parameters are uncertain, the symplectic transfer matrix of a typical substructure, which is described in the state space, also has stochastic properties. An effective spectral stochastic finite element method is adopted to ensure the symplectic orthogonality of the random symplectic matrix on the premise of certain precision. By means of the Rayleigh quotient method, the symplectic eigenvalue problem of random symplectic matrix is investigated. On the basis of this, the mean value and the standard deviation of the random eigenvalues are fully discussed. The comparison between the numerical results derived from the proposed method and the Monte-Carlo simulation indicates that the proposed method has high precision. This research provides a useful guidance for the dynamic analysis of periodic structures with stochastic properties.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11402043, 11772084).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Center for Computational Mechanics, Dalian University of Technology, Dalian, 116023, China

    Yan Zhao, Hui Liang, Youwei Zhang & Jiahao Lin

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  1. Yan Zhao
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  2. Hui Liang
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  3. Youwei Zhang
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  4. Jiahao Lin
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Correspondence to Youwei Zhang.

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Zhao, Y., Liang, H., Zhang, Y. et al. Symplectic Approach on the Wave Propagation Problem for Periodic Structures with Uncertainty. Acta Mech. Solida Sin. 32, 287–297 (2019). https://doi.org/10.1007/s10338-019-00084-9

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  • DOI: https://doi.org/10.1007/s10338-019-00084-9

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