## 1 Introduction  
Energy harvesters provide a useful alternative to traditional sources of energy for low-power electronics. The purpose of an energy harvester is to generate electrical power by energy conversion from the local environment. While the source of energy is available, the energy harvester generates power, excluding the need for bulky power wiring or battery replacement. This can enable increased cost effectiveness and/or energy efficiency for current applications. Truly self-sufficient electronics can also rewrite certain design requirements and make completely new applications possible, e.g., in the wearable electronics [1, 2], IoT [3], automotive [4], medical implants [5] and railway [6] fields. Renewable energies based on energy harvesting are key solutions for 'green' energy sources and for sustainable IoT and WSN devices. This is seen in the roadmap and forecast [7] as well as in the European Union R&D programs [8, 9]. This article will focus on addressing certain challenges for energy harvesters which make use of the kinetic energy provided by vibrations. This type of energy harvester is called a vibrational energy harvester (VEH). A number of different physical effects have to date been utilized to convert movement to energy. These typically include piezoelectricity, electrostatics, electromagnetic induction and triboelectricity [10; 11; 12]. In this article, we focus on conversion by magnetic induction [13]. Such an energy harvester is often called an electromagnetic energy harvester (EMEH). Most VEHs consist of a mass-spring-damper system utilizing the resonance effect to increase the amount of power which can be extracted, within a certain range of vibration frequency. As it is increasingly difficult to achieve a low resonance frequency as the system size decreases, these systems are typically challenged in achieving high performance under the condition of small size and low vibration frequency. High performance in this regard refers to high output voltage, high output power and large bandwidth in the frequency response. A high output voltage mitigates losses in the signal processing circuitry. A high output power and wide bandwidth will improve the VEH's capability of enabling applications in general. There are a number of methods, used in research, to overcome these challenges. Multi-modal VEHs make use of multiple bending modes, each with an increasingly larger resonance frequency, to increase the system bandwidth [14; 15; 16; 17; 18; 19]. In non-resonant VEHs, the moving mass is not connected to any type of spring. There is, in this case, no performance peak at a certain frequency. However, this facilitates achieving greater performance at very low frequencies, below 10 Hz, as well as a relatively large bandwidth in this region [20; 21]. Nonlinear techniques can be used to modify the frequency range. Some examples of these are based on implementing bi-stability, stoppers, spring non-linearity or non-linear damping [22; 23; 24; 25; 26]. As described in [27], an EH operating at anti-resonance can benefit from increased output voltage and input-to-output efficiency. Another approach to increasing bandwidth is to implement resonance frequency tuning. A number of techniques are described in the review by [28], which include sliding mass, sliding fixed point, stiffness control (via, e.g., PZT patch), magnetic force modulation (via, e.g., variable reluctance), etc. Other examples are using electrostatic force [29; 30] or pre-buckling [31; 32]. Research on vibrational energy harvesting using magnetostrictive components stems from the discovery of room-temperature giant magnetostrictive materials (such as Terfenol-D [33] and later galfenol). The work by [PERSON] et al. [34] (with ship hull vibrations in mind) provides an early example of galfenol use in vibrational energy harvesting. Since then, there have been several publications on both magnetostrictive cantilever beam VEHs [35; 36; 37; 38] and magnetostrictive rod type VEHs [39; 40]. The review by [PERSON] et al.