Modeling and analysis of hybrid piezoelectric and electromagnetic energy harvesting from random vibrations

Abstract

We illustrate electroelastic modeling, analysis and simulation solutions, and experimental validation of hybrid piezoelectric (PE) and electromagnetic (EM) energy harvesting from broadband random vibration. For a more practically available ambient source, the more compact expressions of mean power and spectral density (SD) involving dimensionless parameters are derived when the harvester is subjected to random excitation. In the study, it is assumed that the base excitation is white noise. Then, the effect of acceleration SD, load resistance, coupling strength on harvester performances are analyzed by numerical calculation and simulation, and the results are validated by the experimental measurements. It is founded that, only if the load resistance of PE and EM element meet the impedance matching can the hybrid energy harvester output the maximal mean power and spectral density at the resonant frequency, which increases with PE load resistance increasing, but hardly affected by load resistance of EM element; the variation extent of mean power with SD of acceleration increasing varies with the load resistance, and it is up to the maximum under the condition of optimal load; moreover, the stronger the coupling strength is, the wider the frequency band becomes, and the greater the mean power and power spectral density are, while the increasing extent decreases with the coupling strength increasing. Besides, the coupling strength can affect the internal resistance of harvester. Furthermore, with coupling strength increasing, the decreasing degree of mean power falls when the load resistance is greater than the optimal load.

Appendix

By using the table in reference (Gradshtenyn and Ryzhik 1994), for the system if the complex frequency response function is of the form

$$H(\omega ) = \frac{{i\omega B_{1} + (i\omega )^{2} B_{2} }}{{A_{0} + i\omega A_{1} + (i\omega )^{2} A_{2} + (i\omega )^{3} A_{3} + (i\omega )^{4} A_{4} }}$$

(38)

Their integral of the square of the absolute value of complex frequency response can be computed as respectively

$$\int\limits_{ - \infty }^{\infty } {\left| {H(\omega )^{2} } \right|} d\omega = \pi \frac{{ - A_{1} B_{2}^{2} - A_{3} B_{1}^{2} }}{{A_{0} A_{3}^{2} + A_{1}^{2} A_{4} - A_{1} A_{2} A_{3} }}$$

(39)

Also the integral for the transfer function in equation is

$$\int\limits_{ - \infty }^{ + \infty } {\left| {\frac{{i\omega B_{1} + (i\omega )^{2} B_{2} }}{{A_{0} + i\omega A_{1} + (i\omega )^{2} A_{2} + (i\omega )^{3} A_{3} }}} \right|^{2} d\omega } = \pi \frac{{B_{2}^{2} A_{1} + B_{1}^{2} A_{3} }}{{A_{3} (A_{1} A_{2} - A_{0} A_{3} )}}$$

(40)