## 3 Results and Discussion
### Comparing Measurements with Simulations
For the modified design, the tuning sensitivity is on average 140 Hz/mm in the range of \(\beta\) from 4.75 mm to 4.95 mm. For the initial design, it is 160 Hz/mm in the range of \(\beta\) from 4.0 mm to 4.15 mm. As for the initial design, the results using \(\lambda_{\mathrm{S}}\) = 0 show less tunability. As there is no magnetostriction, the voltage amplitude is expected to be low. From Figure 9, the non-linear behavior of the output voltage can be seen. For \(\beta\) > 4.7 mm, the non-linearity decreases, and the curve gradually becomes more sinusoidal. The curves closely resemble those shown by [PERSON] et al. [35] for cantilever magnetostrictive beams of varying composition and damping. An optimal magnetostrictive effect is generally achieved for a certain magnetization bias and pre-stress [39; 62; 63]. For the energy harvester designs described in this work, magnetization bias and pre-stress are coupled by the air gap distance, reluctance and force. Thus, optimization with regard to the magnetostrictive effect is a complex process which is not attempted here. As described, measures were taken to reduce magnetic bias. From  
Figure 8: RMS of the simulated open-circuit coil voltage for the modified design. Curves from right to left result from increasing values of \(\beta\). Circles, dots and crosses are data points. Lines are added as visual aid. Solid lines correspond to using \(\lambda_{\mathrm{S}}\) = 200 and dashed lines for \(\lambda_{\mathrm{S}}\) = 0. Figure 9: Simulated O/C RMS coil voltage at resonance and at the end of the time series. (**a**) \(\beta\) from 4.5 mm to 4.7 mm. (**b**) \(\beta\) from 4.8 mm to 4.95 mm. the simulations, it was determined that only removing either magnet was insufficient in reducing the magnetic field bias in the magnetostrictive component to reasonable levels. Removing one magnet and using a shorter segment of galfenol (less than half the original length) also did not solve the issue. To find the optimal design, a number of geometry and material properties must be considered, such as magnet energy grade, thickness, length and material type of the beam components and the dimension of the core components. As an example, an increase of 0.8 V in output voltage (RMS) was noted when decreasing the length magnetostrictive component by 1 mm (\(\beta\) = 4.8 mm). An intrinsic flaw in the design of this energy harvester is the magnets themselves, as they introduce a large reluctance. A large total system reluctance will result in a small relative change in reluctance due to the air gap variations, and thus small variations in flux and induced voltage amplitude. We determine the composite beam's mechanical properties by running a simulation with an initial transient and free oscillations thereafter. Magnetic fields and magnetostriction are in this case deactivated. Applying the logarithmic decrement method, we find the damping ratios to be 0.0081 and 0.0088 for the two designs described above. From the same simulations, the natural frequency is found to be 227 Hz for the design in Figure 1 and 273 Hz for the design in Figure 7.  
The effects of hysteresis are inherently included in the measurement data. The similarity between simulated and measured curves in Figure 4 indicates that magnetic hysteresis has a minor effect in our case.