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標題: 電磁感應之雙穩態振動獵能系統實驗設計與研究
Experimental Design and Study on Electromagnetic Induction in Bi-stable vibration Energy Harvesting
作者: 葉展嘉
Chan-Chia Yeh
關鍵字: 雙穩態;獵能;電磁感應發電;非線性振動系統;Bi-stable;Nonlinear vibration;Energy harvesting;electromagnetic induction
引用: [1] Erturk, A., Hoffmann, J., and Inman, D. J., 'A piezomagnetoelastic structure for broadband vibration energy harvesting.' Applied Physics Letters, Vol. 94, pp.254102, 2009. [2] Ivana Kovacic,Michael J. Brennan. The Duffing equation: nonlinear oscillators and their behaviour. John Wiley & Sons, 2011. [3] Liu, H., Lee, C., Kobayashi, T., Tay, C. J., and Quan, C., 'A new S-shaped MEMS PZT cantilever for energy harvesting from low frequency vibrations below 30 Hz.' Microsystem technologies, Vol. 18, pp. 497-506, 2012. [4] Zhou, S., Cao, J., Inman, D. J., Lin, J., Liu, S., Wang, Z., 'Broadband tristable energy harvester: Modeling and experiment verification.' Applied Energy, Vol. 133, pp. 33-39, 2014. [5] Wu, H., Tang, L., Yang, Y., and Soh, C. K., 'Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester.' Journal of Intelligent Material Systems and Structures, Vol. 25, pp. 1875-1889, 2014. [6] Cottone, F., Gammaitoni, L., Vocca, H., Ferrari, M., and Ferrari, V., 'Piezoelectric buckled beams for random vibration energy harvesting.' Smart materials and structures, Vol. 21, pp. 035021, 2012. [7] Andò, B., Baglio, S., Bulsara, A. R., and Marletta, V., 'A bistable buckled beam based approach for vibrational energy harvesting.' Sensors and Actuators A: Physical, Vol. 211, pp. 153-161, 2014. [8] Leadenham, S., and Erturk, A., 'M-shaped asymmetric nonlinear oscillator for broadband vibration energy harvesting: Harmonic balance analysis and experimental validation.' Journal of Sound and Vibration, Vol. 333, pp. 6209-6223, 2014. [9] Zhou, S., Cao, J., Inman, D. J., Lin, J., Liu, S., and Wang, Z., 'Broadband tristable energy harvester: modeling and experiment verification.' Applied Energy, Vol. 133, pp. 33-39, 2014. [10] Saha, C. R., O'Donnell, T., Loder, H., Beeby, S., and Tudor, J., 'Optimization of an electromagnetic energy harvesting device.' IEEE Transactions on Magnetics, Vol. 42, pp. 3509-3511, 2006. [11] Yang, B., Lee, C., Xiang, W., Xie, J., He, J. H., Kotlanka, R. K., and Feng, H., 'Electromagnetic energy harvesting from vibrations of multiple frequencies.' Journal of Micromechanics and Microengineering, Vol. 19, pp. 035001, 2009. [12] Shu, Y. C., and Lien, I. C., 'Analysis of power output for piezoelectric energy harvesting systems.' Smart materials and structures, Vol. 15, pp. 1499, 2006. [13] Adhikari, S., Friswell, M. I., and Inman, D. J., 'Piezoelectric energy harvesting from broadband random vibrations.' Smart Materials and Structures, Vol. 18, pp. 115005, 2009. [14] Wu, Y., Badel, A., Formosa, F., Liu, W., and Agbossou, A. E., 'Piezoelectric vibration energy harvesting by optimized synchronous electric charge extraction.' Journal of Intelligent Material Systems and Structures, Vol. 24, pp. 1445-1458, 2013. [15] Vasic, Dejan, Chen, Y. Y., and François, Costa., 'Design of self-powering part of SSHI interface for piezoelectric energy harvesting.' Electronics Letters, Vol. 49, pp. 288-290, 2013. [16] Chao, P. J., 'Bi-Stable Vibration Structure for Energy Harvesting and Its Parameters Study.' Master Thesis, National Chung Hsing University, 2016. [17] Chuang, H. T., 'Experimental Vibration of Piezoelectric Bi-stable Vibration System for Energy Harvesting.' Master Thesis, National Chung Hsing University, 2017. [18] Harne, R. L., and Wang, K. W., 'A review of the recent research on vibration energy harvesting via bistable systems.' Smart materials and structures, Vol. 22, pp. 023001, 2013. [19] Johnson, D. R., Thota, M., Semperlotti, F., and Wang, K. W., 'On achieving high and adaptable damping via a bistable oscillator.' Smart Materials and Structures, Vol. 22, pp. 115027,2013. [20] Galili, I., Dov, K., and Yaron, L., 'Teaching Faraday's law of electromagnetic induction in an introductory physics course' American journal of physics, Vol. 74, pp. 337-343, 2016. [21] Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Heng, Q. Z., Yen, N.-C., Tung, C. C., Liu, H. H., 'The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.' Proceeding of the Royal Society of London A, Vol. 454, pp. 903-995, 1998.
線性振動獵能系統一般在共振頻率下才有最大位移,此時的獵能效果較好,因此有頻寬之限制;對於非線性振動獵能系統而言,獵能的有效頻帶較寬,且獵能效能普遍高於線性系統。利用Duffing equation可描述特定之非線性系統;在滿足Duffing equation的非線性系統中,因為非線性剛性的關係,從位移位能圖可看出兩個穩定平衡點與一個不穩定平衡點,在所有現象中,以其中一個穩定點做週期性振動為單穩態現象,能跨越不穩定平衡點之不規律振動為渾沌現象,在兩個穩定平衡點與一個不穩定平衡點之間做大幅度週期性振動為snap-through現象。本實驗主要透過彈簧對質量塊產生非線性力,在質量塊裝上磁鐵,透過激振器帶動主結構,使質量塊與磁鐵做直線變加速度,而磁鐵在運動過程中感應線圈產生電能。實驗中改變不同彈力係數、穩定平衡點位置、激發頻率與激發振幅,討論單穩態、snap-through、渾沌等現象對獵能效能的影響,也比較線性系統與非線性系統的獵能效能。

Linear vibration energy harvesting systems generally have magnified displacements at resonant frequencies. In case of vibration resonance, the energy harvesting performance will outperform at the certain frequencies, and thus the effectiveness of electric energy harvesting is limited within a narrow bandwidth. The nonlinear vibration systems normally have wider bandwidth of effective energy harvesting and larger collected electric energy than the linear systems. The Duffing equation can be utilized to describe specific nonlinear vibration systems. For such a nonlinear system, the displacement-potential energy plot shows that there exists two stable equilibrium points and one unstable equilibrium point due to the nonlinear stiffness. The phenomenon that the response oscillates around one of the stable equilibrium point periodically is called the monostable state. While the system vibrates across the unstable equilibrium point irregularly, it is named as the chaotic phenomenon. Once the system has large periodical vibration amplitude across the two stable equilibrium points, it is the so-called snap-through phenomenon. In this study, the oblique spring is used to produce a nonlinear stiffness on the vibrating electromagnet. The shaker is used to excite the host structure of the energy harvester and then results in the electric energy that is introduced by the vibrating electromagnet. In the experiment, different parameters of spring stiffness, stable equilibrium positions, excitation frequencies and amplitude were investigated. The effects of monostable, snap-through, and chaotic states to energy harvesting efficiency are discussed. The results are also compared with the linear systems.
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