## 3 Results and Discussion
### Comparing Measurements with Simulations
The equilibrium state of the energy harvester should therefore correspond to a magnetic field bias, of the magnetostrictive part, that is far from saturation but still provides sufficient bias. To achieve this, an alternative design (Figure 6) is evaluated through numerical simulation. Figure 5: Simulation results, for the original design, in the vicinity of the magnetostrictive component. (**a**) von Mises stress distributions. (**b**) Magnetization, \(\lambda_{\text{S}}=200\). (**c**) Magnetization, \(\lambda_{\text{S}}=0\). Figure 6: Revised design. Compared to the original design, one magnet is removed, while the neodymium magnet (blue/red) acting as proof mass remains. The beam composition consists of cobalt steel Vacoflux 50 (light blue), galfenol (purple) and aluminum (green). The iron core components (gray) are identical to the original design. Maintaining the overall design, the magnetic bias is reduced by removing one magnet and replacing a portion of the magnetostrictive material with aluminum. A soft magnetic material (cobalt steel Vacoflux 50, from the COMSOL materials library, in the light blue region of Figure 6) is also used to further reduce the magnetic field within the magnetostrictive material. The thickness of the galfenol layer is here 1.2 mm. The total thickness of the beam is maintained at 2 mm. From Figure 7b, it can be seen that the simulation now gives a significantly lower magnetic bias in the magnetostrictive material. Comparing the distribution of magnetization (Figure 7b) and stress (Figure 7a), the magnetization is significantly higher in the region of larger stress. This indicates stronger dynamic coupling between stress and the magnetic field as compared to the previous design. Figure 7c shows the magnetization with saturation magnetostriction set to zero. For the new design, simulations showed the largest flux variations to be in the region of the magnetostrictive component. Figure 8 shows the open-circuit coil voltages derived from these flux variations. The variation in RMS voltage at resonance shows interesting behavior as the air gap distance is decreased (i.e., increasing \(\beta\)). The RMS voltage increases sharply between a \(\beta\) of 4.5 mm and 4.7 mm, from 1 V to 2.4 V (a factor of two of the RMS voltage from the original design), where after there is a sharp decrease in voltage. The reason for this behavior is not fully determined but it may be that the magnetic field bias and pre-stress resulting from using a spacer thickness, \(\beta\), of 4.7 mm is optimal for this specific design. Overall, the RMS voltage at resonance is 50% larger compared to the original design. The optimum load (regarding power output) is typically defined as that which matches the impedance of the VEH; this is not strictly correct [27] but is likely close to optimum. The impedance matched load equals \(\sqrt{\left(2\pi f_{exc}L\right)^{2}+\left(R_{W}\right)^{2}}\), where \(L\) and \(R_{W}\) are the inductance and resistance of the coil. \(\beta\) = 4.7 mm; the excitation frequency, \(f_{exc}\), was 216 Hz; the optimal load was 495 \(\Omega\), and the theoretically optimum RMS power was found to be 5.1 mW in simulation (assuming the load voltage is approx. half the open-circuit voltage and rectification loss is neglected). Figure 7: Simulation results, for the modified design, in the vicinity of magnetostrictive component. (**a**) von Mises stress distributions. (**b**) Magnetization, \(\lambda_{S}\) = 200. (**c**) Magnetization, \(\lambda_{S}\) = 0. The flux variations in the core were found to be smaller (e.g., generating 0.8 V peak at \(\beta\) = 4.8 mm) compared to the previous design. This is not unexpected as one magnet is used instead of two, and a large portion of the magnetic materials in the beam are replaced by aluminum in the new design, likely leading to less coupling between the beam displacement and flux in the core. The tuning sensitivity is comparable with the initial design.