Archive of Applied Mechanics

, Volume 87, Issue 4, pp 737–750

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

Original

## 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.

## Keywords

An elastic layer Symmetric and skew-symmetric waves The Green’s matrix Boundary integral equations Eigen frequencies

## Notes

### 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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