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The boundary integral equations method for analysis of high-frequency vibrations of an elastic layer

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Abstract

The boundary integral equations are derived in the framework of the analytical five-mode models for propagation of symmetric and skew-symmetric waves in a straight elastic layer of the constant thickness. The forcing problems for fundamental loading cases are solved with the bi-orthogonality conditions employed. By these means, the Green’s matrices are constructed. The derivation of the Somigliana’s identities for the five-mode models is presented. To exemplify application of the method of boundary integral equations, eigenfrequencies of a layer of the finite length are found for two sets of boundary conditions. In the course of analysis, the essential features and advantages of the method are highlighted. The isogeometric analysis at several approximation levels and the standard finite element software are also used to calculate the eigenfrequencies. The results obtained by alternative methods are shown to be in an excellent agreement with each other.

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Acknowledgements

The work of R. Kolman was supported by the Centre of Excellence for nonlinear dynamic behaviour of advanced materials in engineering CZ.02.1.01/0.0/0.0/15_003/0000493 (Excellent Research Teams) in the framework of Operational Programme Research, Development and Education. The work of J. Kopacka was supported by the grant project of the Czech Science Foundation, 16-03823S, within institutional support RVO:61388998.

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Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, Aalborg University, Fibigerstræde 16, 9220, Ålborg, Denmark

    Sergey Sorokin

  2. Institute of Thermomechanics, The Czech Academy of Sciences, Dolejskova 5, 182 00, Prague, Czech Republic

    Radek Kolman & Jan Kopacka

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  1. Sergey Sorokin
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  2. Radek Kolman
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  3. Jan Kopacka
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Correspondence to Sergey Sorokin.

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Sorokin, S., Kolman, R. & Kopacka, J. The boundary integral equations method for analysis of high-frequency vibrations of an elastic layer. Arch Appl Mech 87, 737–750 (2017). https://doi.org/10.1007/s00419-016-1220-y

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  • DOI: https://doi.org/10.1007/s00419-016-1220-y

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