I did some FEA simulation of fused silica disks, to identify the lowest usable eigenmode. By usable I mean a mode that has zero elastic energy stored in the center. 

In the attached figures, the dfisk deformation is shown exaggerated, and the color map shows the elastic energy density. All results are obtained with COMSOL/MATLAB, the disk are constrained at a point corresponding to the center of the lower surface. No gravity.