## 1 Introduction
from 2017 [41] gives an overview of VEHs using different magnetostrictive materials in both rod and beam configurations. [PERSON] et al. [42] published a review in 2018, including other transduction types, providing an interesting comparison. [PERSON] et al. have in their research [43; 44] evaluated and compared energy harvesting using various magnetostrictive materials. Their conclusion is that, given sufficient magnetic biasing, Terfenol D and galfenol provide the best performance. From 2019 to 2022, [PERSON] et al. published several papers dealing with the modeling of galfenol rods [45; 46; 47; 48; 49] and galfenol cantilever beam energy harvesting [50]. Thermodynamic constitutive laws and an equivalent stress model are implemented within the finite element modeling (FEM) simulation tool COMSOL, and a linearized small signal model is developed and evaluated. The simulation results are shown to correspond well with measurements. Similarly, [PERSON] et al. published several papers describing and modeling magnetostrictive energy harvesters. [PERSON] et al. primarily took an equivalent circuit approach to develop a (non-linear) model for the VEH voltage and power output. In [51], such a model is implemented in COMSOL. Following the equivalent circuit approach, [PERSON] et al. explored circuit designs with active control to maximize the converted voltage and power (i.e., the rectified and voltage converted signal) [52; 53; 54]. [PERSON] also provides an example of utilizing magnetostriction for energy harvesting in a vehicle suspension system [55]. In this work, we build upon the concept of a variable reluctance EH, as described in [25]. The EH comprises a magnetic circuit, including a variable air gap. The components making up the path to one side of the gap are essentially rigid, while the components for the \"return\" path have significant elasticity. Both paths are connected at one end and separated at the other by an air gap. In this way, the gap size is coupled to external vibrations. Given the harmonic vibrations of the EH, the dynamic oscillation of the elastic components, relative to the static parts, will depend on material properties (elasticity and mechanical damping), mass and magnetic forces acting to close the air gap. It is vital that the reluctance of the air gap is significant compared to the reluctance of the total magnetic circuit; any additional static reluctance will decrease performance. An important benefit to using this method is that the induced voltage is not only a function of the vibration rate, but also of the area of the air gap. In this work, we will explore the effect of adding additional magneto-mechanical coupling through magnetostriction. We provide a proof of concept for a novel energy harvesting mechanism, synergistically combining magnetostriction with variable reluctance in an electromagnetic energy harvester to increase power output without significantly increasing the size of the energy harvester. The aim of this paper consists of two parts. First, to provide experimental data and equivalent simulated data (based on FEM, with a model equivalent to the VEH under measurement). Second, to use the FEM to find a solution closer to optimum. The scope consists of describing the experimental setup, procedure and results; describing the simulation model and results; discussing the results based on comparisons and drawing conclusions from the results and discussions. Deriving an analytical solution, which would be less accurate than FEM simulations yet less computationally heavy, may provide additional insights but is outside the scope of this paper. In this paper, we will give a detailed description of the proposed energy harvester design (Section 2.1) and its working principles (Section 2.2). We describe the tools used to evaluate these principles, in the form of a simulation model (Section 2.3) and a corresponding prototype (Section 2.4). The results gained from these tools are discussed (Section 3.1) and compared with state-of-the-art energy harvesters (Section 3.2).