In our experiment we studied the vibration of four different kinds of metal plates; circular, thick square, thin square and rectangular. Instead of vibrating just a fixed, circular plate with a violin bow in the style of Chladni, we used a mechanical driver controlled by an electical oscillator so that the whole system functioned something like a stereo speaker. The edges of the plates were unbound and the plates were vibrated from their center. Using an instrument that allowed us to delicately vary the frequency and amplitude of the driver we were able to locate the different modal frequencies of each plate.
At each modal frequency we sprinkeled a glass beads across the plate which would settle along the various nodal lines. (We've also heard of experimenters using fine sand, salt, or even Cream of Wheat.) Intricate patterns popped out before us. Then by counting the number of diametric and radial nodes (lines and circles) we could record the "m" and "n" values for each modal frequency. Finally, using the "m", "n" and frequency values for each mode we graphed the results of our experiment for each plate and compared them to either Chladni's Law or the general wave equation.
A good set of earplugs is a must.