**Damping**

An effective energy harvesting from vibrations results in an amplitude damping on the mechanical source, no matter what the harvesting method is. In other terms, though the principal aim of an harvesting device is to convert the available mechanical energy into electrical energy, at the same time a kind of *passive* mechanical damping occurs. The passive damping by smart materials has been generally addressed in [41]. Recent contributions deepen this damping effect for Piezo [28, 29] and Magnetostrictive materials [10, 13]. The latter presents a preliminary analysis showing the effects of the energy harvesting on mechanical damping which requires further effort. As already mentioned, the passive damping could be exploited in several application fields, for example, in automotive applications where the vibrations reduction is a concern and energy harvesting can help to improve the overall efficiency. Moreover, this concept is even more attractive if compared to the classical *active* mechanical damping, where an additional properly controlled actuator is needed with a consequent increase of cost, system complexity and use of energy.

**Figure 20.** Damping effect of the vibration harvesting. Two different resistors case are reported with a <sup>7</sup>*kA*/*<sup>m</sup>* magnetic bias. The power *<sup>p</sup>*(*t*) = *<sup>v</sup>*2(*t*)/*<sup>R</sup>* is represented with 10 log10( *<sup>p</sup>*(*t*) <sup>1</sup>*μ*<sup>W</sup> ).

dissipated power (down).

In Fig. 20 (a) the normalized displacement comparison between two different resistive loads is reported (2.3Ω- solid line, 1MΩ-dashed line). The Fig. 20 (b) shows the corresponding resistor voltage (up) and the instantaneous dissipated electric power (down). The mass is in mechanical contact with the active material and a controlled initial velocity is applied to them. The active material has suitable bias conditions (magnetic bias of 7*kA*/*m* and a mechanical prestress of 2.9MPa). The damping with the 1MΩ resistor is due only to mechanical friction, while with the 2.3Ω resistor there is a faster damping of the oscillation, both in amplitude and in time, because of the energy harvesting. Indeed, in this case a far larger power is extracted. Finally, the voltage is higher with the 1MΩ resistor as expected (a sort of open circuit condition).

#### **Power conversion circuits**

20 Will-be-set-by-IN-TECH

Another topic about materials synthesis concerns the *mechanical impedance* matching of the harvesters. Indeed, materials like terfenol or galfenol are quite *rigid* with a mechanical behavior near the one of bulk iron. In that case, the ideal vibrations have high stresses and low strains, in the 0 − 1000ppm range. If a softer magnetoelastic materials would exist, it would be possible to have vibrations harvesting with lower stresses and higher strains, in the 0.1 − 1%

Recently the use of another magnetoelastic material (Metglass) has been proposed for energy harvesting [45]. The main advantage respect to the others magnetostrictive material is that it can be laminated achieving a higher harvester compactness. The material is a Fe-based amorphous ribbons with excellent magnetic softness and elastic response and it is cheaper than Fe-Ga, Fe-Tb-Dy alloys. A recent new application design reached 20 *μ*W/cm<sup>3</sup> at

The further steps in the material modeling should aim to include the hysteresis in both characteristics in a thermodynamic compatible way. Indeed, up to now, this step is made only on one of the two characteristics when the other one is not relevant for the specific

Another topic in the analysis of a harvester, based on magnetoelastic materials, is the eddy currents effect due to the mechanical stress variations, that can have a detrimental effect on the harvester performances [51]. This phenomenon is present when the material has a finite electric resistivity, that is the case of magnetostrictive materials as Terfenol and Galfenol. The effect can be more harmful on the latter because of the high relative permeability. From the modeling point of view, the eddy currents problem can be formulated, as for standard magnetic materials, starting from Maxwell's equations in the magneto-quasistatic limit. The main difference is that the magnetic characteristics depends on the applied stress. Then, the

An effective energy harvesting from vibrations results in an amplitude damping on the mechanical source, no matter what the harvesting method is. In other terms, though the principal aim of an harvesting device is to convert the available mechanical energy into electrical energy, at the same time a kind of *passive* mechanical damping occurs. The passive damping by smart materials has been generally addressed in [41]. Recent contributions deepen this damping effect for Piezo [28, 29] and Magnetostrictive materials [10, 13]. The latter presents a preliminary analysis showing the effects of the energy harvesting on mechanical damping which requires further effort. As already mentioned, the passive damping could be exploited in several application fields, for example, in automotive applications where the vibrations reduction is a concern and energy harvesting can help to improve the overall efficiency. Moreover, this concept is even more attractive if compared to the classical *active* mechanical damping, where an additional properly controlled actuator is needed with a

applications. This is valid when the vibration source can be considered almost *ideal*.

stress acts as the *forcing term* in the magneto-mechanical problem [14, 15].

consequent increase of cost, system complexity and use of energy.

range, with a rubber-like behavior.

100 Hz [53].

**Models**

**Damping**

A magnetoelastic energy harvester is an unregulated AC power source. So it can not be directly interfaced to common electronic loads that need a regulated DC supply. Then, a power conversion stage must be a part of the harvester to overcome this issue. In particular, this stage should accomplish to two main functions:


These tasks can be afforded in different ways that strongly depend on the available AC power from the harvester and on the specific field of application. In fact, magnetoelastic energy harvesters output powers can range from milliwatt to watt levels depending on the mechanical source characteristics and its coupling with the active material. Moreover, also the dimensions of the magnetoelastic material influence the obtainable power, but in many applications they are limited by compactness requirements.

The choice of the topology and circuit implementation of the power conversion stage is based also on the following criteria, [42]:


The possible solutions to the above requirements and criteria can be identified in two different approaches, according to what has been done for piezoelectrics or other mature harvesting technologies, like electromagnetic and electrostatic generators:


Finally, another feature of a magnetoelastic harvester that challenges the definition and the modeling of the power conversion stage is its strong nonlinearities. For example, these can create on the AC side an additional harmonic content that is not present in the mechanical stimulus and it depends heavily on the harvester operating conditions (*e.g.* mechanical prestresses and magnetic biases). This pushes to the definition of new circuital multidomain modeling approaches for analyzing the coupling among the mechanical, magnetic and electronic worlds.
