Multi-frequency responses of compliant orthoplanar spring designs for widening the bandwidth of piezoelectric energy harvesters

This paper compares the performance of three nonlinear compliant orthoplanar springs, namely, bi-leg, quad-leg and pent-leg designs to study the vibration mode interaction effect for widening the operational bandwidth of piezoelectric vibration energy harvester. All the designs have three or more vibration modes below 150 Hz with the addition of multiple masses. Finite element analysis results of spring designs and vibration mode shapes are presented and compared with experiments. The prototypes were manufactured and experimentally tested to analyze their dynamic voltage-frequency responses and operational bandwidths under sinusoidal and band-limited excitations. The experimental results demonstrate that the operational bandwidth is significantly broadened by the geometric nonlinearity of the structure. The addition of multiple masses brings the vibration modes of the system closer, and thus further helps to extend the operational bandwidth. In addition, we introduce multiple piezoelectric plates into harvesters to enable energy harvesting in all vibration modes. The quad-leg design shows the largest frequency bandwidth of 35 Hz, maintaining a peak-to-peak voltage of 4 V under the forward frequency-sweep excitations. Under the reverse frequency-sweep excitations, the voltage response and the operational bandwidth are comparable to those of the forward-sweep ones as a result of continuous overlapping of linear and nonlinear voltage peaks. Random excitation experiments demonstrate the effectiveness of the proposed mutli-leg structure in harvesting energy from wideband environmental vibrations.