超胞周期性对花瓣形点缺陷声子晶体压电能量收集性能的影响
Effect of Supercell Periodicity on Piezoelectric Energy Harvesting Performance of Petal-Shaped Point Defect Phononic Crystals
摘要: 声子晶体点缺陷能够在带隙内形成局域缺陷态，并将弹性波能量限制在压电片附近，是提高压电能量收集性能的重要途径。除缺陷模态和压电片尺寸外，有限超胞的周期数直接影响带隙约束能力、倏逝波衰减程度以及缺陷模态的稳定性。本文基于一种花瓣形点缺陷声子晶体压电能量收集系统，在压电片直径为10 mm、厚度为2.3 mm的优化参数基础上，固定点缺陷位置，分别研究x方向和y方向周期数对系统振动模态、输出电压和输出功率的影响。结果表明，x方向周期数对系统性能起主导作用，随着超胞由5 × 7增加至9 × 7，峰值输出电压由26.495 V提高至86.302 V，最大输出功率由17.228 mW提高至32.257 mW；继续增加至10 × 7后，输出性能基本趋于饱和。y方向周期数起调节优化作用，输出性能随周期数增加呈现先增大后减小的非单调变化，其中9 × 7超胞取得最佳结果。在该尺寸下，系统在100 MΩ负载条件下获得86.302 V峰值输出电压、32.257 mW最大输出功率，机电能量转换效率达到30.36%。研究结果表明，合理的超胞周期数能够在保证能量局域效果的同时避免结构冗余，为点缺陷声子晶体压电能量收集器的尺寸设计提供依据。
Abstract: Phononic crystal point defects can form localized defect modes within the bandgap, and confine elastic wave energy in the vicinity of piezoelectric patches, which serves as a critical approach to improving the performance of piezoelectric energy harvesting. In addition to defect modes and the dimensions of piezoelectric patches, the number of periods of a finite supercell directly affects the bandgap confinement capability, the attenuation degree of evanescent waves, and the stability of defect modes. Based on a petal-shaped point defect phononic crystal piezoelectric energy harvesting system, this paper fixes the position of the point defect on the basis of the optimized parameters that the piezoelectric patch has a diameter of 10 mm and a thickness of 2.3 mm, and investigates the effects of the number of periods in the x-direction and y-direction on the vibration mode, output voltage and output power of the system, respectively. The results show that the number of periods in the x-direction plays a dominant role in the system performance. As the supercell increases from 5 × 7 to 9 × 7, the peak output voltage increases from 26.495 V to 86.302 V, and the maximum output power increases from 17.228 mW to 32.257 mW; when the supercell is further increased to 10 × 7, the output performance basically tends to be saturated. The number of periods in the y-direction functions for adjustment and optimization, and the output performance exhibits a non-monotonic variation that first increases and then decreases as the number of periods increases, with the 9 × 7 supercell achieving the optimal performance. Under this dimension, the system obtains a peak output voltage of 86.302 V and a maximum output power of 32.257 mW at a load resistance of 100 MΩ, and the electromechanical energy conversion efficiency reaches 30.36%. The research findings indicate that a reasonable number of supercell periods can avoid structural redundancy while guaranteeing the energy localization effect, which provides a reference for the dimension design of point defect phononic crystal piezoelectric energy harvesters.
文章引用：杨伊漫, 田苗. 超胞周期性对花瓣形点缺陷声子晶体压电能量收集性能的影响[J]. 凝聚态物理学进展, 2026, 15(3): 59-69. https://doi.org/10.12677/cmp.2026.153007

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