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A projection-based model reduction strategy for the wave and vibration analysis of rotating periodic structures

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Abstract

The wave finite element method has proved to be an efficient and accurate numerical tool to perform the free and forced vibration analysis of linear reciprocal periodic structures, i.e. those conforming to symmetrical wave fields. In this paper, its use is extended to the analysis of rotating periodic structures, which, due to the gyroscopic effect, exhibit asymmetric wave propagation. A projection-based strategy which uses reduced symplectic wave basis is employed, which provides a well-conditioned eigenproblem for computing waves in rotating periodic structures. The proposed formulation is applied to the free and forced response analysis of homogeneous, multi-layered and phononic ring structures. In all test cases, the following features are highlighted: well-conditioned dispersion diagrams, good accuracy, and low computational time. The proposed strategy is particularly convenient in the simulation of rotating structures when parametric analysis for several rotational speeds is usually required, e.g. for calculating Campbell diagrams. This provides an efficient and flexible framework for the analysis of rotordynamic problems.

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Acknowledgements

The authors are grateful to the Brazilian agencies, São Paulo Research Foundation (FAPESP—São Paulo, Brazil ) for the financial support through Project Numbers 2010/17317-9, 2013/23542-3 and 2014/19054-6, to Coordination for the Improvement of Higher Education Personnel (CAPES—Brazil), and to the Program ’Cátedras Franco-Brasileiras’ at State University of Campinas (UNICAMP). The research of P. B. Silva has been performed within the framework of the 4TU. High-Tech Materials Research Programme ’New Horizons in designer materials’ (www.4tu.nl/htm).

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Authors and Affiliations

  1. Department of Computational Mechanics, School of Mechanical Engineering, State University of Campinas (UNICAMP), Rua Mendeleyev 200, Cidade Universitária Zeferino Vaz, Campinas, São Paulo, 13083-860, Brazil

    D. Beli & J. R. F. Arruda

  2. INSA Centre Val de Loire, Université d’Orléans, Université de Tours, Laboratoire de Mécanique Gabriel Lamé, 3 Rue de la Chocolaterie, 41034, Blois, France

    J.-M. Mencik

  3. Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands

    P. B. Silva

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  1. D. Beli
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  2. J.-M. Mencik
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  3. P. B. Silva
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  4. J. R. F. Arruda
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Correspondence to D. Beli.

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Flowchart of the proposed approach

Flowchart of the proposed approach

The flowchart of the procedure can be summarized as follows (Fig. 16):

Fig. 16
figure 16

Flowchart of the procedure used to perform free wave propagation (dispersion diagram) and forced response analysis of rotating structures. (Color figure online)

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Beli, D., Mencik, JM., Silva, P.B. et al. A projection-based model reduction strategy for the wave and vibration analysis of rotating periodic structures. Comput Mech 62, 1511–1528 (2018). https://doi.org/10.1007/s00466-018-1576-7

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  • DOI: https://doi.org/10.1007/s00466-018-1576-7

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