Metamaterial beam for flexural wave resonance rainbow trapping and piezoelectric energy harvesting

The rainbow trapping effect demonstrates great potential in multiple-band energy harvesting. However, the existing finite-size devices with the rainbow trapping phenomenon hardly harvest energy efficiently due to the mismatch between rainbow trapping frequencies and resonance frequencies of the devices. In this study, for the first time, we report a periodically perforated metamaterial beam, which achieves both the flexural wave rainbow trapping and resonance simultaneously for the multiple-band and multiple-position energy harvesting. The band structure of the unit cell in the metamaterial beam is analyzed to illustrate its ability to realize strong dispersion and energy concentration. The study first indicates that the rainbow trapping effect activated by resonance frequencies causes much more intense spatial separation and localization of flexural waves compared with that by cutoff frequencies for the periodically perforated bare beam. We, then, demonstrate that the resonance rainbow trapping phenomenon allows the proposed design to show superiority in piezoelectric energy harvesting compared with the counterpart with off-resonance rainbow trapping. Simulations indicate that the optimal resistance and the highest output power vary much for different pairs of piezoelectric patches at the corresponding resonance rainbow frequencies; by contrast, the positions of piezoelectric patches have little influence on the performance of the device. The design concept of on-resonance rainbow trapping in metamaterials in this study will help engineers to open a new venue for high-performance piezoelectric energy harvesters.