Design of phononic crystals using superposition of defect and gradient-index for enhanced wave focusing

This paper introduces a novel design strategy for phononic crystals (PnCs) that significantly enhances their wave amplification and focusing capabilities, making them highly suitable for energy harvesting applications. The strategy is based on the combination of two distinct wave tuning techniques: defect PnCs implementation and gradient-index (GRIN) structure designs. The two techniques are based on different mechanisms and are commonly considered independently for wave manipulation applications. In particular, defect PnCs incorporate structural or material irregularities within periodic PnCs, enabling waves of certain frequencies, typically blocked by the bandgap, to pass through and emerge with amplified amplitude at the defect location. In contrast, the gradient-index technique utilizes gradient structures that induce refractive effect to the wave propagation, focusing the wave at a pre-determined location. The PnC design strategy that we propose combines the wave amplifying effect of defect PnCs in conjunction with the wave focusing effect of the gradient-index mechanism. This combination leads to substantial performance improvement, with enhancement factors of 2.6 and 4.1, in comparison with individually implemented defect or gradient models, respectively. These results open up new possibilities for the development of PnCs with the goal of tuning wave propagations for optimized vibration energy harvesters.