## 2 Experimental Methods
### Prototype and Measurement Setup  
The design of the prototype is based on the same components and geometry as shown in Figure 1. The core components are made of soft magnetic steel (cold drawn s235 jr), the beam substrate is aluminum, the magnets are made of neodymium (energy grade N36) and the magnetostrictive material is galfenol (Fe\({}_{1.6}\)Ga\({}_{18.4}\)). Additionally, a shaker fixture, coil bobbins and a fixture to hold the bobbins are 3D-printed in polyamide (PA2200). The coil bobbins are wound with 0.1 mm copper wire, with 3200 turns. The dimensions of the magnets are 10 mm \(\times\) 10 mm \(\times\) 10 mm. The core components all have the same cross-sectional dimensions of 10 mm \(\times\) 10 mm. To simplify the explanation, we have numbered each of the separate core components in Figure 1. Parts 3-5 are identical, with a height of 2.5 mm, and are glued to the magnets. Parts 2 and 6 are exchangeable and have been fabricated with various heights, from 1.5 mm to 4 mm. The length of part 1 is 53 mm. The lengths of the substrate and magnetostrictive beam are also 53 mm. Each layer of the beam is 1 mm thick, i.e., the beam's total thickness is 2 mm. The beam components are glued together (with a very thin layer of liquid metal). Threaded, and non-threaded, holes allow for all parts to be screwed together. The screws used are magnetic, yet their permeability is unknown. The coil bobbins are glued to a fixture which fits tightly around core part 1. Figure 3 shows the manner in which the components are assembled (Figure 3a) and the assembled prototype (Figure 3b). An overview of the VEH properties is given in Table 2.  
Two M5 screws are used to fix the energy harvester to the shaker fixture and a single M5 fixes the shaker fixture to the shaker. The fixture-to-shaker mounting hole is extended in one direction to allow for balancing of the system. The hardware for the measurement setup consists of a shaker (2007E, Modal Shop, Cincinnati, OH, USA), Laser Doppler Vibrometer (LDV, OFV 056, Polytec, Waldbronn, Germany), controllable current source, digital oscilloscope, waveform generator (Analog Discovery 3, AD3, Digilent, Pullman, WA, USA) and laptop. The current source, which drives the shaker, is controlled by a waveform from the AD3. The LDV measures the velocity at a position on the energy harvester. The measured velocity is output as a voltage signal from the LDV, which is measured by the AD3. The output from the induction coil is also measured by the AD3 on a high impedance (1 M\(\Omega\)) input, thus resulting in the open-circuit voltage of the energy harvester. The measurement procedure consists of driving the shaker over a range of frequencies while measuring the LDV output. A script is implemented with the software (WaveForms 3.21.3) running the AD3, which converts the LDV signal to an equivalent acceleration value and modulates the amplitude of the driving signal (to current source), ensuring that the measured acceleration is constant over the frequency range. The base acceleration amplitude is ensured to be 0.5 g (\(\pm\)1%) for all frequencies. If the system is unbalanced on the shaker, it will lead to unpredictable behavior of the measured frequency response and control signal; in part due to this, the LDV measures only at a single point. To determine if this is the case or not, an additional component was added which allowed for the velocity of the shaker fixture to be measured along its longest dimension. If the measured velocity is essentially the same for all measurement points along this dimension (for a set of frequencies in the relevant range), then it is assumed to be balanced. A series of frequency sweeps were performed, each with a different configuration of the energy harvester. For each sweep, the thickness of core part 6 (see Figure 1) was increased (replacing the part with a corresponding yet thicker piece). The thickness of the core parts is in increments of 0.5 mm. To allow for smaller increments, steel shims of 0.1 mm thickness were used. The thickness of part 2 was kept at 3.5 mm.