Nonlinear M-shaped broadband piezoelectric energy harvester for very low base accelerations: primary and secondary resonances

Abstract

It has been well demonstrated 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 high 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 very low vibration levels. This configuration is made from a continuous bent spring steel with piezoelectric laminates and a proof mass but 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 few milli-g base acceleration levels. In the present work, such a design is explored for both primary and secondary resonance excitations at different vibration levels and load resistance values. Following the primary resonance excitation case that offers a 660% 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.