20170809

From the data I have gathered from a variety of MATLAB sweeps, I think that the optimal geometry I can produce has the parameters in the attached image. Neither the original or optimized drawing is to scale. The gap between the arms of the electrodes should be 1.25 mm, the arm width 0.55 mm, the arm length 16 mm, and the offset of the arms 3.5 mm.

It is also optimal to place the ESD as close to the sample disk as can reasonably be achieved, at around 0.5 mm away. Since the force on the disk scales exponentially with the distance from the ESD, decreasing that gap is the most substantial way to impact the excitation. Decreasing the gap from 1 mm to .5 mm increases the excitation of the modes by approximately a factor of 8.

From my simulations, the shift in geometry alone still has a useful impact on the excitation. Modes 1 and 3 are the only two modes that are less excited by the new geometry, mode 1 is 10% weaker and mode 5 is 5% weaker. Modes 5 and 6 are nearly unaffected by the shift, mode 5 is 2% stronger and mode 6 is 5% stronger. Modes 7, 18 and 19 are outliers, 7 is excited by a factor of 7, 18 by a factor of 4 and 19 by a factor of 17. The rest of the modes are improved by between a factor of 1.5 and 3. For mode numbers, shapes, and frequencies a plot is included.
