Nonlinear Resonance-based Piezoelectric Vibration Energy Harvesting

R. Xu, S. G. Kim

Linear resonance-based energy harvesters have been popular for vibration energy harvesting, due to their simplicity of micro-fabrication and high power efficiency at resonance. Nevertheless, the narrow frequency bandwidths that linear energy harvesters suffer prevent the technology from applying in the real frequency-changing ambient environment. As a promising potential solution, nonlinear resonance widens the power bandwidth by one order of magnitude, which shows the great potential of nonlinear designs. We built an electromechanically coupled, lumped model to provide a comprehensive analysis of nonlinear resonance-based energy harvesting. The model was based on the configuration of a doubly clamped beam with a thin film piezoelectric element working in d33 mode. The static indeterminate structure problem was solved with the Euler-Bernoulli beam theory and energy method. By considering the simple case of inputting a sinusoidal force and connecting the harvester to a resistor, we employed Kirchhoff’s laws and the Harmonic Balance Method (HBM) to build and solve the nonlinear differential equations. Closed form expressions of the system’s parameters were obtained from the analysis. The coupled, lumped model has verified varying electrical loads at each frequency to generate maximum power at that frequency by showing a power spectrum with a much wider bandwidth. Furthermore, the optimal electrical damping at each frequency was obtained; it shows that the electrical damping should be much higher than the mechanical damping to increase the power at low frequencies, and the maximum power is obtained when the electrical damping matches the mechanical damping.

Figure 1: The normalized electrical damping and deflection amplitude vs. electrical resistance. The insensitivity of the deflection to the change of damping explains the wide power bandwidth.

Figure 2: The maximum power envelope and the normalized optimal electrical damping at each frequency. The optimal electrical damping condition at each frequency could be useful to further widen the power bandwidth.

Further Reading

· A. Hajati and S.-G. Kim, “Ultra-wide bandwidth piezoelectric energy harvesting,” *Appl. Phys. Lett.*, vol. 99, no. 8, p. 083105, 2011.

· G. Gafforelli, R. Xu, A Corigliano and S. G. Kim,"Modelling of a bridge-shaped nonlinear piezoelectric energy harvester," *Journal of Physics: Conference Series*,vol. 476, 012100. 1. IOP Publishing, 2013.

· G. Gafforelli , R. Xu, A. Corigliano and S. G. Kim, “Modeling of a bridge-shaped nonlinear piezoelectric energy harvester, J. Energy Harvesting, in press, 2014

· G. Gafforelli, A. Corigliano, R. Xu and S. G. Kim, “Experimental verification of a bridge-shaped nonlinear vibration energy harvester, Applied Physics Letters, **105**, 203901 (2014)