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IMA Journal of Applied Mathematics Advance Access published online on March 18, 2008
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxn005
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Trapped modes in 3D topographically varying plates

J. Postnova and R. V. Craster{dagger}

Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

{dagger} Email: r.craster{at}imperial.ac.uk

Received on August 3, 2007; Accepted on January 30, 2008

Trapped modes in 3D elastic plates are considered as a model of waves that are guided along, and localized to the vicinity of, welds. These waves propagate unattenuated along the weld and exponentially decay with distance transverse to it. In the direction of propagation (y), there is no change in geometry and we assume that waves have the form exp(iβy). An asymptotic long-wave theory provides numerical values of the trapped mode frequencies and gives conditions at which trapping can occur; these depend on the components of the wave number in different directions and variations of the plate thickness. The results of this long-wave theory are compared with a numerical solution of the full governing equations.

Keywords: trapped modes; asymptotic expansion; group velocity; resonance frequency.


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