trend of the hybrid energy harvester as a function of the distance between the magnets, the base excitation level, the excitation frequency and the load. The Virtual Sine Sweep (VSS) feature of Siglab has been used to collect the data presented in this section. The VSS software only records the ratio between input to its 2nd-4th channel and the voltage reading at its first channel. We therefore have measured the transfer function corresponding to tip velocity, piezoelectric voltage and the electromagnetic voltage divided by the base accelerations. As the first step we only implement the piezoelectric harvesting and do not install the electromagnetic coils. Magnet spacing The distance between the magnets changes the magnetic force and thus changes both the natural frequency and the nonlinearities. The smaller the distance between the magnets, the smaller the natural frequency and the more significant the nonlinear effect. It can be seen from Fig. 4 that smaller magnet gap also corresponds to larger damping . Clearly the peaks of tip velocity FRF at small magnet gaps are shorter and wider compared to the corresponding peaks when the magnets are far from each other. One reason for this phenomenon is the eddy currents generated in the steel block, which hold the base magnet in place. When the tip and base magnets are close to each other the magnetic field fluctuations due to the motion of the tip magnet are significant. This field fluctuation induces eddy currents in the structure and dissipates some energy. The nonlinearity is hardening nonlinearity and becomes more visible when the amplitude of the tip deflection is large. For large tip deflections the peaks of FRF curve bends to the right, but at the same time shortens. This increases the bandwidth of the harvester but reduces the power generation. (a) (b) Fig. 4: Relation between the magnet spacing and a) Tip velocity/base acceleration frequency response function and b) harvested power/ base acceleration2 frequency response function. The colors represent different base acceleration: blue: 0.15, green 0.3, red 0.74, cyan 1.5, magenta 3 m.s-2. 4 6 8 10 12 14 50 100 0 0.2 0.4 0.6 0.8 (mm) Frequency (Hz) Tip velocity FRF, R 1 =100k 1/S 2 4 6 8 10 12 14 50 100 0 0.2 0.4 0.6 0.8 1 1.2 1.4 (mm) Frequency (Hz) Power FRF R 1 =100k Watt / g 2 468
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