The Method of Fundamental Solutions Applied to the Calculation of Eigensolutions for Simply Connected Plates

In this work we study the application of the Method of Fundamental Solutions (MFS) to the numerical calculation of the eigenvalues and eigenfunctions for the 2D Bilaplacian in simply connected plates. This problem was considered in [20] using wave-type functions and in [14] using radial basis function for a circular and rectangular domain. The MFS is a meshfree method that was already applied to the calculation of the eigenvalues and eigenfunctions associated to the Laplace operator (cf. [21], [10] and [2]). The application of this method to the Bilaplacian was already considered in [13], but only for simple shapes. Here we apply an algorithm for the choice of point-sources, as in [2], that leads to very good results for a fairly general class of domains.