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June 16th, 2019

In this chapter, an energy harvesting platform based on high-permeability material was theoretically studied and tested. Two generations of devices were designed. The first generation consisted of a high-p cantilever vibration energy harvester incorporated a vibrating high-permeability cantilever, a solenoid, and a bias magnet pair. Interaction between the high-permeability magnetic beam and the bias magnets leads to complete flux reversal of the high-permeability beam, which generates a maximum power of 74 mW and a high power density of 1.07 mW/cm3 at an ambient vibration frequency of 54 Hz and at an acceleration of 0.57 x g. The inhomogeneous magnetic field leads to a nonlinear magnetic force on the high-permeability beam, resulting in a nonlinear oscillator with a wide working bandwidth of 10 Hz or 18.5% of the operating frequency. A second generation high-permeability material-based vibration energy harvester was demonstrated, achieving a power density larger than 20 mW/cm3 when subjected to accelerations of 5 x g; this is over three times greater than the best power density data reported for vibration energy harvesters (Volture Piezo Energy Harvester-V25W). A wide working bandwidth of 14% (6 Hz halfpower bandwidth at a 42 Hz central working frequency) is still maintained due to the nonlinear effect.

The vibration energy harvesters based on high-permeability magnetic material exhibit high output power density, high output power, as well as wide working bandwidth, which provides great opportunities for practical compact vibration energy harvesters.

Acknowledgements Financial supports from NSF awards 0824008, 0746810 and ONR awards N00014710761, N00014080526 are gratefully acknowledged.

[1]A bimorph is a configuration that uses an elastic substructure sandwiched between two thickness – poled piezoelectric layers; a unimorph (not discussed here) is composed of a single thickness-poled piezoelectric layer attached to an elastic substructure.

[2]Electromechanical coupling of a piezoelectric energy harvester depends not only on the amount of the piezoelectric material used but also on the structural design of the harvester (such as the location of the piezoelectric material on the cantilever and the way it is bonded to its substrate).

[3]The properties of PZT can be tailored by adjusting the relative concentration of zirconium and titanium as well as by the addition of doping elements.

[4]The internal shim is optional but normally added to increase the mechanical robustness of the device. Typical materials are stainless steel or brass.

[5]The names series and parallel derive from the configuration of the electrical connections, for example, in a parallel bimorph, the two layers are electrically connected in parallel.

[6]It is assumed that the geometrical parameters of the bimorph permit the use the Euler-Bernoulli beam approximation.

[7]PZT ceramics are transversely isotropic as the poling direction is different from the other two directions.

[8]We are here adhering to the convention, common in piezoelectricity, of naming the stress T and the strain S.

[9]Soft PZT is characterised by larger piezoelectric coupling coefficients, which are useful for energy harvesting; hard PZT has lower piezoelectric activity but has also higher-quality factor, which reduces the energy dissipated and is essential in high-frequency resonators.

[10]The average power is given by Pav = E(t)/t (see Eq. (5.25)), where E(t) tends to an asymptotic value for t! 1.

[11]Point P2 identifies the expected location of a plectrum which, due to manufacturing imperfections, was actually too short to interact with the bimorph.

[12]This confirms that the resistive load RL = 14 kfi used in Sect. 6.4 is not the optimum one.

[13]The assumption of white noise is not as restrictive as it may appear. If the bandwidth of the excitation is sufficiently larger than that of the harvester’s, then a random excitation can be safely considered to be white.

[14] The reader can refer to Renno et al. [41] for more details on the optimization of energy harvesters under sinusoidal deterministic excitations.

[15] Cumulants are used to provide a measure of correlation strength among different random variables [42].

[16]Further experimental work is underway to determine whether the decrease in oscillation frequency is due to the motion of the cylinder or due to its finite length resulting in spiraling tip vortices emanating from both tips and directed towards the middle of the cylinder.

[17]Due to the construction and electrical connection of the harvester, the voltage outputs of the modes higher than the first bending mode were small and cannot be seen in Fig. 10.12. However, visual observation of the harvester and FFT analysis of the strain signal showed resonances in the first torsional mode and the second bending mode as detailed in [4].

[18]1 p,£ (called micro-strain) refers to a deformation of 10 6 m for the dimension of the structure

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