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In the study of piezoelectric cantilever energy harvesting system, a bi-stable nonlinear cantilever with magnets added to the structure has a wider frequency band response and a higher energy output efficiency. Hence, the calculation accuracy of the magnetic force on which the potential function and dynamics of the system depend is essential to predicting the output response and energy harvesting effect. In this work, we use a shape function to describe the relation between the deflections of an arbitrary point and the free-end point on the beam, and then calculate the trace and deflection angle of the beam's free-end by integrating the entire slope of the cantilever beam. The magnetic force is consequently derived from the magnets' real-time relative positions and postures by using the magnetizing current method. With comprehensively considering the axial magnetic force and the lateral magnetic force, the simulation results demonstrate that when the displacement of the magnet at the end of the beam is large enough, the directions of axial and lateral magnetic force change from repulsive to attractive, which leads to a large veer of the resultant magnetic force across two quadrants. So, it means that a smaller interval between magnets may not cause a larger deflection of the beam, and the magnetic force existing as attractive force could diminish the well space of potential function (that is, the distance between two equilibrium positions of the system). The experimental data in this work are nicely consistent with the simulation results. And in this work, we also make a comparison of the simulation results with those from our method and existing method, showing that the accuracy of the proposed method is much higher than that from the existing calculation method, especially in the scenario where the magnet at the end of the beam is far from the horizontal axis.
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Keywords:
- vibration energy harvesting /
- bi-stable cantilever system /
- calculation of magnetic force /
- magnetizing current
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[2] Sun J, Li Y G, Liu J Q, Yang C S, He D N (in Chinese) [孙健, 李以贵, 刘景全, 杨春生, 何丹农 2009 微纳电子技术 46 673]
[3] Gao Y J, Leng Y G, Fan S B, Lai Z H 2014 Smart Mater. Struct. 23 095003
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[11] Tang L H, Yang Y W 2012 Appl. Phys. Lett. 101 094102
[12] Akoun G, Yonnet J P 1984 IEEE Trans. Magn. 20 1962
[13] Tan D, Leng Y G, Fan S B, Gao Y J 2015 Acta Phys. Sin. 64 060502 (in Chinese) [谭丹, 冷永刚, 范胜波, 高毓璣 2015 物理学报 64 060502]
[14] Lin J T, Lee B, Alphenaar B 2010 Smart Mater. Struct. 19 126
[15] Chen Z S, Yang Y M 2011 Acta Phys. Sin. 60 074301(in Chinese) [陈仲生, 杨拥民 2011 物理学报 60 074301]
[16] Ferrari M, Ba M, Guizzetti M, Ferrari V 2011 Sens. Actuators A 172 287
[17] Zhou S, Cao J, Erturk A, J Lin Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Adhikari S, Litak G 2012 J. Intell. Mater. Syst. Struct. 23 1505
[18] Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Adhikari S, Litak G 2012 J. Intell. Mater. Syst. Struct. 23 1505
[19] Esmailzadeh E, Nakhaie-Jazar G 1998 Int. J. Non-Linear Mech. 33 567
[20] Ali S F, Padhi R 2009 P. I. Mech. Eng. I-J. Sys. Contr. Eng. 223 657
[21] Nayfeh A H, Pai P F 2007 Linear and Nonlinear Structural Mechanics (Hoboken:Wiley) pp65-110
[22] Agashe J S, Arnold D P 2008 J. Phys. D:Appl. Phys. 41 1586
[23] Bobbio S, Delfino F, Girdinio P, Molfino P 2000 IEEE Trans. Magn. 36 663
[24] Furlani E P, Reznik S, Kroll A 1995 IEEE Trans. Magn. 31 844
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[1] Roundy S J 2003 Ph. D. Dissertation (Berkeley: University of California, Berkeley)
[2] Sun J, Li Y G, Liu J Q, Yang C S, He D N (in Chinese) [孙健, 李以贵, 刘景全, 杨春生, 何丹农 2009 微纳电子技术 46 673]
[3] Gao Y J, Leng Y G, Fan S B, Lai Z H 2014 Smart Mater. Struct. 23 095003
[4] Wang Q, Luo Y, Gu J Z (in Chinese) [王强, 骆英, 顾建祖 2008 电子元件与材料 27 47]
[5] Cottone F, Vocca H, Gammaitoni L 2009 Phys. Rev. Lett. 102 080601
[6] And B, Baglio S, Trigona C, Dumas N, Latorre L, Nouet P 2010 J. Micromech. Microeng. 20 125020
[7] Stanton S C, McGehee C C, Mann B P 2010 Physica D 239 640
[8] Fan K Q, Xu C H, Wang W D, Fang Y 2014 Chin. Phys. B 23 084501
[9] Yung K W, Landecker P B, Villani D D 1998 Magn. Electric. Separat. 9 39
[10] Neubauer M, Twiefel J, Westermann H, Wallaschek J 2012 Small-Scale Energy Harvesting (Rijeka: InTech) p303
[11] Tang L H, Yang Y W 2012 Appl. Phys. Lett. 101 094102
[12] Akoun G, Yonnet J P 1984 IEEE Trans. Magn. 20 1962
[13] Tan D, Leng Y G, Fan S B, Gao Y J 2015 Acta Phys. Sin. 64 060502 (in Chinese) [谭丹, 冷永刚, 范胜波, 高毓璣 2015 物理学报 64 060502]
[14] Lin J T, Lee B, Alphenaar B 2010 Smart Mater. Struct. 19 126
[15] Chen Z S, Yang Y M 2011 Acta Phys. Sin. 60 074301(in Chinese) [陈仲生, 杨拥民 2011 物理学报 60 074301]
[16] Ferrari M, Ba M, Guizzetti M, Ferrari V 2011 Sens. Actuators A 172 287
[17] Zhou S, Cao J, Erturk A, J Lin Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Adhikari S, Litak G 2012 J. Intell. Mater. Syst. Struct. 23 1505
[18] Friswell M I, Ali S F, Adhikari S, Lees A W, Bilgen O, Adhikari S, Litak G 2012 J. Intell. Mater. Syst. Struct. 23 1505
[19] Esmailzadeh E, Nakhaie-Jazar G 1998 Int. J. Non-Linear Mech. 33 567
[20] Ali S F, Padhi R 2009 P. I. Mech. Eng. I-J. Sys. Contr. Eng. 223 657
[21] Nayfeh A H, Pai P F 2007 Linear and Nonlinear Structural Mechanics (Hoboken:Wiley) pp65-110
[22] Agashe J S, Arnold D P 2008 J. Phys. D:Appl. Phys. 41 1586
[23] Bobbio S, Delfino F, Girdinio P, Molfino P 2000 IEEE Trans. Magn. 36 663
[24] Furlani E P, Reznik S, Kroll A 1995 IEEE Trans. Magn. 31 844
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