Harmonic Balance Analysis and Experimental Validation of a Nonlinear Broadband Piezoelectric Energy Harvester for Low Ambient Vibrations

Abstract

It has been shown by several research groups over the past few years that vibration energy harvesters with intentionally designed nonlinear stiffness components can be used for frequency bandwidth enhancement under harmonic excitation for sufficiently strong vibration amplitudes. In order to overcome the need for high excitation intensities that are required to exploit nonlinear dynamic phenomena, we have developed an M-shaped piezoelectric energy harvester configuration that can exhibit a nonlinear frequency response under low vibration levels. This configuration is made from a continuous bent spring steel with piezoelectric laminates and a proof mass, and no magnetic components. Careful design of this nonlinear architecture that minimizes piezoelectric softening further enables the possibility of achieving the jump phenomenon in hardening at base acceleration levels on the order of a few milli-g. In the present work, such a design is explored for both primary and secondary resonance excitations at different vibration levels and for different electrical loads. Following the primary resonance excitation case that offers more than 600 % increase in the half-power bandwidth as compared to the linear system at a root-mean-square excitation level as low as 0.04g, secondary resonance behavior is investigated with a focus on 1:2 and 1:3 superharmonic resonance neighborhoods. A multi-term harmonic balance formulation is employed for a computationally effective yet high-fidelity analysis of this high-quality-factor system with quadratic and cubic nonlinearities. In addition to primary resonance and secondary (superharmonic) resonance cases, multi-harmonic excitation is modeled and experimentally validated.