Application of the pseudo-spectral method to 2D eigenvalue problems in elasticity

A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considered using differentiation matrices. The governing partial differential equations and associated boundary conditions on regular domains can be translated into matrix eigenvalue problems. Accurate results are obtained to the precision expected in spectral-type methods. However, we show that it is necessary to apply an additional "pole" condition to deal with the r = 0 coordinate singularity arising in the case of a 2D disc.