A hybrid analytical/graphical method is presented to calculate the fundamental natural frequency of rectangular mirrors mounted at 3 points. A NASTRAN assisted parametric approach was used to calculate the characteristic roots of the plate vibration equation for mirrors with aspect ratios ranging from 1.0 x 1.0 to 10.0 x 1.0. Also considered were simply supported boundary conditions at three mirror corner points or at two corner points on one edge and one point along the opposite edge. Experimental varification within 6.0% was achieved for the extreme case tested with approximately a +2.0% average experimental error overall.
William J Nowak,
"A Parametric Approach To Mirror Natural Frequency Calculations", Proc. SPIE 0450, Structural Mechanics of Optical Systems I, (5 January 1984); doi: 10.1117/12.939280; https://doi.org/10.1117/12.939280