Modelling wave propagation in two-dimensional structures using a wave/finite element technique

Abstract

The purpose of this work is to present a general method for the numerical analysis of wave
propagation in 2-dimensional structures by the use of a finite element method (FEM). The
method involves typically just one finite element to which periodicity conditions are applied
instead of modelling the whole structure, thus reducing drastically the cost of calculations. The
mass and stiffness matrices are found using conventional FE software. The low order dynamic
stiffness matrix so obtained is post-processed and the wavenumbers and the frequencies then
follow from various resulting eigenproblems.
The method is described and numerical examples given. These include isotropic and orthotropic
plates, isotropic cylindrical shells and the more complex case of sandwich cylindrical shells for
which analytical solutions are not available. The last two cases are studied by postprocessing
an ANSYS FE model.
The main advantage of the technique is its flexibility since standard FE routines can be used
and therefore a wide range of structural configurations can be easily analysed. Moreover the
propagation constants for plane harmonic waves can be easily predicted for different propagation
directions along the structure. The method is seen to give accurate predictions at negligible
computational cost

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Identifiers

ORCID for B.R. Mace: orcid.org/0000-0003-3312-4918

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