## 2 Materials and Methods  
### Electromagnetic Harvester Device  
A photograph of the proposed two-degrees-of-freedom (2 DOF) harvester is shown in Figure 1a. In this harvester, resonance frequency and magnetic forces can be adjusted by grade, diameter, and shape of the permanent magnets and the distance (stroke) between the fixed magnets. The device consists of two neodymium magnets, \(A_{1}\) and \(A_{2}\), which move due to magnetic repulsion forces of the fixed (end) magnets, \(B_{1}\) and \(B_{2}\). Each of the moving magnets had a diameter of 20 mm and a length of 30 mm, while the end magnets had a diameter of 20 mm and a height of 5 mm. The properties of the harvester's components are listed in Table 1. The magnets were made of materials such as NdFeB N38. The tube had an internal diameter of 21 mm. A small clearance between the tube and the moving magnets allowed the magnet to move freely. The clearance needed to be as small as possible to reduce the leakage rate of the magnetic field. A copper wire was wrapped around the portion of the tube and had 12,740 turns of coil. The coil resistance was estimated to be 1148 \(\Omega\), which implied an average of 0.09 \(\Omega\) per turn. The coil wire had a diameter of 0.14 mm.  
Geometric and physical parameters of the magnetic and electrical harvester components are shown in Table 1.  
All magnets were mounted in a non-magnetic PVC hollow cylinder equipped with a special air canal to eliminate air compression. The large height and small air gap of the floating magnets did not allow for rotation in the tube. The magnetic forces acting on the moving magnets were exerted by the lower and upper fixed magnets (end magnets). The tube was equipped with two bumpers to reduce the magnets' collisions. These movable magnets could move inside the tube, and the end magnet forces acted as a magnetic spring. The opposite orientation of the magnets (poles) caused them to stabilize in an equilibrium position. The magnetic repulsive forces, which are described in Section 2.2 of this paper, were considered as linear damper and nonlinear spring forces induced by the movement of the magnets in the coil. The relative motion of the magnets inside the tube with respect to the fixed coil created a time-varying magnetic flux; therefore, an electromo  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline magnet moving diameter & 20 (mm) \\ magnet moving height & 30 (mm) \\ magnet fixed diameter & 20 (mm) \\ magnet fixed height & 5 (mm) \\ coil length & 50 (mm) \\ coil inner diameter & 22 (mm) \\ wire diameter & 0.14 (mm) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometric parameters of the harvester device.  
Figure 1: Images of a 2 DOF magnetic levitation energy harvester (**a**) and scheme of the experimental setup with the 2 DOF harvester (**b**).  
The harvester was connected to the harvester's module and a computer with own software prepared in the C++ programming language to measure voltage induced from the harvester and magnet displacements as well as to provide load resistance (Figure 1b). The harvester module consists of a MicroDAQ module with OMAP L137 Texas Instruments processor and a conditioning device. The key role of the module is to measure the recovered voltage and control the load resistance. The analog outputs in the module made it possible to connect the device to the LMS Scadas data acquisition system. The harvester was mounted on the Tira shaker operated by the LMS system with Test.Lab. A special wireless sensor was attached to one of the magnets to measure magnet displacement. The sensor is based on a commercial ADXL354 accelerometer with added memory and a battery.