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| 基于Timoshenko梁模型的非对称三稳态压电能量采集器性能分析 |
| Performance Analysis of an Asymmetric Tri-Stable Piezoelectric Energy Harvester Based on the Timoshenko Beam Model |
| 投稿时间：2025-07-31 修订日期：2026-01-01 |
| DOI： |
| 中文关键词: 压电能量采集器 三稳态 多尺度法 解析解 Timoshenko梁理论 |
| 英文关键词: Piezoelectric energy harvester Tri-stable Method of multiple scales Analytical solution Timoshenko beam theory |
| 基金项目:安徽省自然科学基金面上项目；安徽省高校自然科学基金重点项目 |
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| 中文摘要: |
| 本文通过Timoshenko梁理论与Lagrange变分原理建立了一种基于五层压电悬臂叠合梁的非对称磁力式三稳态压电能量采集器的力电耦合运动方程，并采用多尺度法对该方程进行求解，获得了系统动力响应的解析表达式。通过理论方法和数值模拟的对比分析，重点探讨了负载电阻、磁铁非对称间距、基层厚度配置比等参数对系统输出功率的影响。结果表明：系统输出功率随负载电阻变化呈现双峰特性；随着磁铁非对称间距d0和基层厚度配置比rs的增大，系统的峰值功率显著提高而其对应的局部最优负载电阻则降低；增大d0和rs可有效拓宽系统工作频带。在高频激励下，Timoshenko梁模型计算的输出功率幅值明显高于Euler梁模型，而在低频段两者结果基本一致，且这种一致性频带范围随rs的增大而显著拓宽。通过对比解析解与数值解，验证了理论模型的准确性。 |
| 英文摘要: |
| This paper establishes the electromechanical coupled motion equations of an asymmetric tri-stable piezoelectric energy harvester based on a five-layer piezoelectric cantilever composite beam using Timoshenko beam theory and the Lagrange variational principle. The equations are solved using the method of multiple scales, yielding analytical expressions for the dynamic response of the system. Through comparative analysis of theoretical methods and numerical simulations, the effects of parameters such as load resistance, asymmetric magnet spacing, and substrate thickness ratio on the system's output power is investigated. The results indicate that the system's output power shows dual-peak characteristics with varying load resistance. With the increase in the asymmetric magnet spacing d0 and the thickness ratio rs of the substrate layer, the peak power of the system improves significantly, while the corresponding optimal load resistance decreases. Increasing d0 and rs can effectively broaden the system's operating bandwidth. Under high-frequency excitation, the output power amplitude calculated using the Timoshenko beam model is significantly higher than that obtained with the Euler beam model, while both models yield essentially identical results in the low-frequency range. Moreover, this frequency range of consistency expands significantly with increasing rs. The accuracy of the theoretical model is verified by comparing the analytical and numerical solutions. |
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