## 3 Results and Discussion
### Tuning Resolution  
The frequency tuning resolution that can be achieved is also important, as most low-frequency MEMS energy-harvesting devices have narrow bandwidths of approximately 1-3 Hz (approximately 1% of the resonant frequency) [5; 6]. Therefore, the ability to tune the frequency to sub-Hz resolution is desired to maximize power output. Individual cavities were filled with various powders to demonstrate the potential frequency tuning resolution that could be achieved. Figure 4 illustrates the frequency values for filling the middle column cavities in the 7 \(\times\) 9 array. The results illustrate that filling the free end Row 1 (H15) middle cavity had the largest change in frequency of 1 Hz, 2.9 Hz, and 3.5 Hz for Silica, Mo, and W, respectively. However, filling the last row closer to the tethered end (H75) had the least change, resulting in change of frequency of 0.1 Hz, 0.5 Hz, and 0.7 Hz for Silica, Mo, and W, respectively. The results were expected, as Equation (2) illustrates that as the center of gravity moves closer to the free end, the frequency will decrease compared to a central center of gravity. The frequency was dependent on the density of the filler, as W powder caused a larger change in frequency than Silica or Mo, given the same filled cavity. Figure 4b demonstrates that the FEM model had similar results compared to the experimental data, thus validating the model. Figure 3: Experimental results illustrating power as a function of frequency for the 1 st resonant frequency mode in (**a**) a low-frequency cantilever (V25W) with various filled proof masses and (**b**) a high-frequency cantilever (S233-H5 FR-1107 XB) with empty and Tungsten-filled proof mass. The effect on tuning resolution by filling a row instead of a column is illustrated in Figure 5, where the middle row cavities were filled (H4n, where n is the various columns in the array). Filling cavities along the row had little impact on the resonant frequency as it was mostly influenced by the overall change in mass and not the location of the cavity. The frequency difference between filling the middle cavity (H45) versus filling the most lateral cavity (H41) was 0.5 Hz, 1 Hz, and 0.5 Hz for Silica, Mo, and W, respectively. However, there was a frequency reduction from the original frequency of 49.1 Hz for all proof masses, where W had the largest reduction, which was expected. This illustrates that additional mass added to lateral cavities reduces the frequency due to the mass change but not due to the lateral location, so filling these cavities could be used to tune the frequency with sub-Hz resolution. The lateral filled cavities could help to reduce the 2 nd frequency mode which has a twisting motion, but this mode would have higher frequency and lower displacement, resulting in low power density, so we primarily investigated the 1 st mode. Figure 5b illustrates similar results between the FEM and the experimental versions. The dimensions of the proof mass cavities have a significant influence on the range and resolution of the tuning capabilities. Figure 6 illustrates the impact of using a 7 \(\times\) 9 array with smaller width and length of cavities compared to a 5 \(\times\) 7 array with larger cavities. The overall dimensions of the proof mass remained the same except for the cavity and gap dimensions. The results illustrate that the larger cavities from the 5 \(\times\) 7 array caused a decrease in frequency for any given filled column. Since filling the columns resulted in a symmetric frequency change as shown in Figure 5, the filling order does not have an influence on the resonant frequency. Figure 4: (**a**) Experimental results illustrating 1 st mode resonant frequency as a function of filling individual cavities along the middle column with W, Mo, and Silica powders, (**b**) results of simulated FEM versus experimental results of W-filled cavities, and (**c**) image of filled column.