本研究旨在開發並驗證一套應用於低頻水體運動環境之浮筒—壓電梁能量採集系統，未來可應用於船舶槽體或油罐車之槽液晃盪監測。系統以升頻轉換為核心，透過浮筒運動與槌頭敲擊，將低頻水體晃盪轉換為壓電梁的高頻自由振動，以提升低頻環境下壓電能量採集之可行性。
本系統由水平激振水槽、錨纜約束浮筒、槌頭與壓電懸臂梁組成。水槽受水平激振後，水體晃盪推動浮筒產生水平位移與俯仰擺動，當擺幅足夠時，槌頭敲擊壓電梁並產生電壓。數值模型以液體晃盪理論描述水體運動，透過壓力分布計算浮筒所受之力與力矩，並結合錨纜拉緊與放鬆、敲擊事件、單自由度梁及壓電機電耦合方程式，建立完整能量傳遞模型。模型所得壓電梁等效剛性為150.73 N/m，與實驗值155.37 N/m之誤差為2.98%，顯示模型可合理描述系統主要動態。
實驗以激振器驅動水槽進行水平往復運動，搭配高速攝影與示波器量測浮筒運動及壓電輸出。掃頻結果顯示，系統於1.89 Hz時產生最大輸出，與理論水槽第一自然頻率1.8921 Hz之相對誤差僅約0.11%，且加入浮筒後共振頻率未明顯改變。而壓電梁自然頻率12.84 Hz約為水槽晃盪頻率的6.8倍，證明浮筒敲擊可將低頻水體運動轉換為高頻梁振動。
機構參數實驗顯示，梁高135至145 mm時輸出電壓介於0.612至0.632 V，差異有限；但是當梁過高時，會因敲擊轉為撥動或發生錯失接觸而使電壓下降。槌頭與壓電梁之水平距離實驗則顯示，距離增加會降低槌頭敲擊時的剩餘動能。激振振幅小於1.5 mm時，輸出隨振幅增加而上升；超過1.5 mm後增幅趨緩，2 mm以上開始出現碎浪，3 mm時則發生少量溢流，說明系統存在適當的激振與敲擊範圍。
負載實驗顯示，輸出電壓隨負載電阻增加而上升，但當電壓接近開路限制後，功率反而下降。當實際負載電阻為1.482 MΩ時，均方根電壓為0.575 V，最大輸出功率為0.223 μW，因此最佳阻抗位於約1至2 MΩ範圍。
數值模擬結果與各項實驗呈現一致變化趨勢，能合理反映浮筒運動、敲擊行為及壓電輸出，顯示模型具備良好預測能力。綜合而言，本研究完成浮筒—壓電梁升頻轉換系統之機構設計、參數識別、數值模擬與實驗驗證，證明其可將低頻水體晃盪轉換為壓電梁振動，並產生可整流與儲存之電能。未來可進一步針對多模組整合、多自由度梁及實際槽體環境測試進行研究，以提升輸出穩定性與監測應用價值。

This study develops a frequency-up conversion piezoelectric harvesting driven by sloshing in water tanks, which is applicable in ship tanks or tanker trucks. Through frequency-up conversion, water sloshing drives a mooring-line-constrained buoy, whose hammer impacts a piezoelectric cantilever beam and excites higher-frequency free vibration.
A coupled numerical model is established to describe water sloshing, buoy motion, mooring constraints, impact events, beam vibration, and voltage output. The predicted voltage closely agrees with the experimental results, indicating that the model captures the primary system dynamics.
Experiments were conducted using a horizontally excited water tank, high-speed imaging, and an oscilloscope. The maximum output occurs at 1.89 Hz, closely matching the theoretical natural frequency of1.8921 Hz. The beam natural frequency is approximately 12.84 Hz, confirming successful frequency-up conversion.
Impact height, hammer-to-beam distance, and excitation amplitude affect the output. Excessive impact height reduces contact stability, while greater horizontal distance decreases the hammer’s remaining kinetic energy. Output increases with excitation amplitude but also be limited by wave breaking, mooring constraints, and unstable buoy motion.
The maximum output power is approximately 0.223 μW at an external resistance of 1.482 MΩ. Numerical and experimental results show consistent trends.
Overall, the system successfully converts low-frequency liquid sloshing into rectifiable and storable electrical energy. Future work may focus on multi-module integration, multi-degree-of-freedom beams, and practical tank testing.

[1] Roundy, S., Wright, P. K., & Rabaey, J. (2003). A study of low level vibrations as a power source for wireless sensor nodes. Computer communications, 26(11), 1131-1144.
[2] Roundy, S., & Wright, P. K. (2004). A piezoelectric vibration based generator for wireless electronics. Smart Materials and structures, 13(5), 1131-1142.
[3] Zhu, D., Roberts, S., Mouille, T., Tudor, M. J., & Beeby, S. P. (2012). General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters. Smart Materials and Structures, 21(10), 105039.
[4] Fu, H., Mei, X., Yurchenko, D., Zhou, S., Theodossiades, S., Nakano, K., & Yeatman, E. M. (2021). Rotational energy harvesting for self-powered sensing. Joule, 5(5), 1074-1118.
[5] Tian, L., Shen, H., Yang, Q., Song, R., & Bian, Y. (2023). A novel outer-inner magnetic two degree-of-freedom piezoelectric energy harvester. Energy Conversion and Management, 283, 116920.
[6] Ferrari, M., Ferrari, V., Guizzetti, M., Marioli, D., & Taroni, A. (2008). Piezoelectric multifrequency energy converter for power harvesting in autonomous microsystems. Sensors and Actuators A: Physical, 142(1), 329-335.
[7] Zhou, S., Lallart, M., & Erturk, A. (2022). Multistable vibration energy harvesters: Principle, progress, and perspectives. Journal of Sound and Vibration, 528, 116886.
[8] Gao, F., Liu, G., Fu, X., Li, L., & Liao, W. H. (2021). Lightweight piezoelectric bending beam-based energy harvester for capturing energy from human knee motion. IEEE/ASME Transactions on Mechatronics, 27(3), 1256-1266.
[9] Zou, H. X., Zhao, L. C., Gao, Q. H., Zuo, L., Liu, F. R., Tan, T., ... & Zhang, W. M. (2019). Mechanical modulations for enhancing energy harvesting: Principles, methods and applications. Applied Energy, 255, 113871.
[10] Deng, F., Cai, Y., Fan, X., Gui, P., & Chen, J. (2019). Pressure-type generator for harvesting mechanical energy from human gait. Energy, 171, 785-794.
[11] Shi, G., Tong, D., Xia, Y., Jia, S., Chang, J., Li, Q., ... & Ye, Y. (2022). A piezoelectric vibration energy harvester for multi-directional and ultra-low frequency waves with magnetic coupling driven by rotating balls. Applied Energy, 310, 118511.
[12] Pozzi, M., Aung M. S., Zhu, M., Jones, R. K., & Goulermas, J. Y. (2012). The pizzicato knee-joint energy harvester: characterization with biomechanical data and the effect of backpack load. Smart Materials and Structures, 21(7), 075023.
[13] Kim, M. O., Pyo, S., Oh, Y., Kang, Y., Cho, K. H., Choi, J., & Kim, J. (2018). Flexible and multi-directional piezoelectric energy harvester for self-powered human motion sensor. Smart Materials and Structures, 27(3), 035001.
[14] Dechant, E., Fedulov, F., Chashin, D. V., Fetisov, L. Y., Fetisov, Y. K., & Shamonin, M. (2017). Low-frequency, broadband vibration energy harvester using coupled oscillators and frequency up-conversion by mechanical stoppers. Smart Materials and Structures, 26(6), 065021.
[15] Haroun, A., Yamada, I., & Warisawa, S. I. (2015). Micro electromagnetic vibration energy harvester based on free/impact motion for low frequency–large amplitude operation. Sensors and Actuators A: Physical, 224, 87-98.
[16] Pillatsch, P., Yeatman, E. M., & Holmes, A. S. (2012). A scalable piezoelectric impulse-excited energy harvester for human body excitation. Smart Materials and Structures, 21(11), 115018.
[17] Pyo, S., Kwon, D. S., Ko, H. J., Eun, Y., & Kim, J. (2022). Frequency up-conversion hybrid energy harvester combining piezoelectric and electromagnetic transduction mechanisms. International Journal of Precision Engineering and Manufacturing-Green Technology, 9(1), 241-251.
[18] Zhang, Y., Cai, C. S., & Zhang, W. (2014). Experimental study of a multi-impact energy harvester under low frequency excitations. Smart Materials and Structures, 23(5), 055002.
[19] Yu, H., Zhou, J., Deng, L., & Wen, Z. (2014). A vibration-based MEMS piezoelectric energy harvester and power conditioning circuit. Sensors, 14(2), 3323-3341.
[20] Yang, B., & Lee, C. K. (2009). A wideband electromagnetic energy harvester for random vibration sources. Advanced Materials Research, 74, 165-168.
[21] Kulah, H., & Najafi, K. (2008). Energy scavenging from low-frequency vibrations by using frequency up-conversion for wireless sensor applications. IEEE Sensors Journal, 8(3), 261-268.
[22] Kim, K. J., Kim, J., & Kim, D. (2023). Slosh-induced piezoelectric energy harvesting in a liquid tank. Renewable Energy, 206, 409-417.
[23] Jing, D., Hu, S., Nan, Y., Ma, C., Zhang, Z., Shao, M., & Shao, S. (2024). Design and test of liquid sloshing piezoelectric energy harvester. Advances in Mechanical Engineering, 16(5), 16878132241248999.
[24] Chen, S. E., Yang, R. Y., Qiu, Z. H., & Wu, C. C. (2021). A piezoelectric wave energy harvester using plucking-driven and frequency up-conversion mechanism. Energies, 14(24), 8441.
[25] Chen, S. E., Hsu, Y. X., Yang, R. Y., & Wu, C. C. (2024). Investigation of the Performance of Piezoelectric Wave Energy Harvesters Using a Buoy Design. Marine Research, 4(2), 1-16.
[26] Du, X., Li, P., Li, Z., Liu, X., Wang, W., Feng, Q., ... & Tang, L. (2024). Multi-pillar piezoelectric stack harvests ocean wave energy with oscillating float buoy. Energy, 298, 131347.
[27] Rosso, M., Nastro, A., Baù, M., Ferrari, M., Ferrari, V., Corigliano, A., & Ardito, R. (2022). Piezoelectric energy harvesting from low-frequency vibrations based on magnetic plucking and indirect impacts. Sensors, 22(15), 5911.
[28] Li, X., Chuai, X., Hu, G., Zhang, D., Cai, M., Wang, C., ... & Liang, J. (2024). Energy and dynamics analysis of a single plucking energy harvester for transient-motion-powered IoT applications. Energy Conversion and Management, 310, 118465.
[29] Yu, H., Zhang, X., Shan, X., Hu, L., Zhang, X., Hou, C., & Xie, T. (2023). A novel bird-shape broadband piezoelectric energy harvester for low frequency vibrations. Micromachines, 14(2), 421.
[30] Babic, S., Sirois, F., Akyel, C., & Girardi, C. (2010). Mutual inductance calculation between circular filaments arbitrarily positioned in space: Alternative to Grover's formula. IEEE transactions on magnetics, 46(9), 3591-3600.
[31] Akoun, G., & Yonnet, J. P. (1984). 3D analytical calculation of the forces exerted between two cuboidal magnets. IEEE Transactions on magnetics, 20(5), 1962-1964.
[32] Cady, W. G. (2018). Piezoelectricity: volume two: an introduction to the theory and applications of electromechanical phenomena in crystals. Courier Dover Publications.
[33] Chen, C. D., Wu, Y. H., & Su, P. W. (2020). Dynamic modeling and experimental validation of an impact-driven piezoelectric energy harvester in magnetic field. Sensors, 20(21), 6170.
[34] Yang, C. L., Chen, K. W., & Chen, C. D. (2018). Model and characterization of a press-button-type piezoelectric energy harvester. IEEE/ASME Transactions On Mechatronics, 24(1), 132-143.
[35] Ibrahim, R. A. (2005). Liquid sloshing dynamics: Theory and applications. / Raouf A. Ibrahim. Cambridge ; New York : Cambridge University Press
[36] 鄭鈞鴻（2025）。應用於低速旋轉機構之雙自由度非接觸磁力升頻轉換壓電能量獵能研究。碩士論文，國立成功大學機械工程學系。https://thesis.lib.ncku.edu.tw/thesis/detail/f262bde2ea3efd267333a897abd2e7ed/
[37] 馮宇為（2025）。具磁吸碰撞升頻轉換之壓電獵能器分析與量測。碩士論文，國立成功大學機械工程學系。https://thesis.lib.ncku.edu.tw/thesis/detail/d02e97453d74cffb9aa7ea081e1d4d11/