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IMA Journal of Applied Mathematics Advance Access originally published online on September 9, 2008
IMA Journal of Applied Mathematics 2009 74(4):548-558; doi:10.1093/imamat/hxn023
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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.

Integral equation methods for the Robin problem in stationary oscillations of elastic plates

G. R. Thomson and C. Constanda{dagger}

Department of Mathematical and Computer Sciences, The University of Tulsa, 800 South Tucker Drive, Tulsa, OK 74104, USA

{dagger} Email: christian-constanda{at}utulsa.edu

Received on May 14, 2008; Revision received May 14, 2008. Accepted on July 22, 2008

The interior and exterior Robin boundary-value problems for the model of flexural vibrations of plates with transverse shear deformation are solved by means of layer potentials. Existence theorems are proved when certain conditions are satisfied by the elastic constants, the frequency parameter and the matrix connecting the tractions and displacements on the boundary.

Keywords: elastic plate; harmonic oscillations; Robin boundary conditions; boundary integral methods.


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