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提出了一种基于能量转换原理的磁致伸缩/压电层合材料低频磁电响应模型，并对不同层合结构的磁电响应特性进行了对比研究. 该模型假定层合材料层间能量传递通过层间剪切力来实现，利用应力函数法分析了磁致伸缩层和压电层的应力与应变，求出了磁致伸缩层的应变能和存储磁场能以及压电层的应变能和电场能；利用Hamilton最小能量原理求出了层间剪切力的大小，获得了开路状态下层合材料的低频磁电响应模型. 发现磁电电压系数与磁致伸缩材料的磁导率、泊松比、磁机耦合系数以及压电材料的泊松比、机电耦合系数等有关，并对这些参数的影响进行了分析. 同时对两层和三层结构的层合材料磁电特性进行了对比研究，发现层合结构不同则获得的磁电系数公式不同，用相应的公式计算得到的误差才会最小. 研究结果表明，本文的理论误差小于6.5%，与其他方法相比，本文的理论模型能更好地描述磁电层合材料的低频磁电响应特性.A low frequency magnetoelectric (ME) response model of magnetostrictive/piezoelectric laminate composite is presented based on energy conversion principle, and ME response characteristics of different laminate structures are compared in this paper. In this model it is assumed that the energy transfer between the layers of the composite laminates is achieved by the interlayer shear force. The stresses and strains of the magnetostrictive and piezoelectric layers are analyzed by the stress function method. While the strain and stored magnetic energy of magnetostrictive layers and the strain and electric field energy of piezoelectric layers are solved. Under open-circuit conditions, the interlayer shear force and the low frequency ME response model of laminate composites are obtained by using Hamilton principle of minimum energy. The theoretical results show that the ME voltage coefficient is related to the Poisson ratio, magnetic permeability, magnetomechanical coupling coefficient of magnetostrictive material, Poisson ratio, and electromechanical coupling coefficient of piezoelectric material. The influences of these parameters are analyzed. The magnetoelectric characteristics of two- and three-tier laminated structures are compared in this paper, showing that different laminated structures have different formulas for ME coefficient and calculation errors will be smaller when the corresponding ME coefficient formula is used. The experimental results show that the analytical error is smaller than 6% and the model can better describe the low frequency ME response characteristics of laminated magnetoelectric materials.
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Keywords:
- magnetoelectric laminated material /
- magnetoelectric response /
- energy conversion principle /
- shear stress
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[19] Chang C M, Carman G 2007 Phys. Rev. B 76 134116
[20] Huang Z 2006 J. Appl. Phys. 100 114104
[21] Bichurin M I, Petrov V M, Srinivasan G 2002 J. Appl. Phys. 92 7681
[22] Xu Z L 2006 Elasticity (Vol. 1) (4th Ed.) (Beijing: Higher Education Press) p32 (in Chinese) [徐芝纶 2006 弹性力学 (上册) (第四版) (北京: 高等教育出版社) 第32页]
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[24] Dai X, Zhang Z, Wang Y, Li J, Cheng L 2014 J. Appl. Phys. 115 014104
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[26] Zhai J, Xing Z, Dong S, Li J, Viehland D 2006 Appl. Phys. Lett. 88 062510
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[1] Ryu J, Carazo A V, Uchino K, Kim H E 2001 Jpn. J. Appl. Phys. 40 4948
[2] Chen L, Li P, Wen Y M, Wang D 2011 Acta Phys. Sin. 60 067501 (in Chinese) [陈蕾, 李平, 文玉梅, 王东 2011 60 067501]
[3] Chen L, Li P, Wen Y M, Zhu Y 2013 Chin. Phys. B 22 077505
[4] Dai X Z, Wen Y M, Li P, Yang J, Jiang X F 2010 Acta Phys. Sin. 59 2137 (in Chinese) [代显智, 文玉梅, 李平, 杨进, 江小芳 2010 59 2137]
[5] Yu X J, Wu T Y, Li Z 2013 Acta Phys. Sin. 62 058503 (in Chinese) [于歆杰, 吴天逸, 李臻 2013 62 058503]
[6] Eerenstein W, Mathur N D, Scott J F 2006 Nature 442 759
[7] Li P, Huang X, Wen Y M 2012 Acta Phys. Sin. 61 137504 (in Chinese) [李平, 黄娴, 文玉梅 2012 61 137504]
[8] Zhou H M, Chen Q, Deng J H 2014 Chin. Phys. B 23 047502
[9] Filippov D A 2005 Phys. Solid State 47 1082
[10] Nan C W 1994 Phys. Rev. B 50 6082
[11] Nan C W, Clarke D R 2005 J. Am. Ceram. Soc. 80 1333
[12] Dong S, Li J F, Viehland D 2003 IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 50 1253
[13] Dong S, Li J, Viehland D 2003 IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 50 1236
[14] Zhang L, Wang B W, Li S Y, Wang Z H, Huang W M, Wong L 2010 Chin. J. Sci. Instrum. 31 1528 (in Chinese) [张纳, 王博文, 李淑英, 王志华, 黄文美, 翁玲 2010 仪器仪表学报 31 1528]
[15] Harshe G, Dougherty J P, Newnham R E 1993 Int. J. Appl. Electromagn. Mater. 4 145
[16] Yang J, Wen Y M, Li P, Dai X Z 2009 Proceedings of Micro and Nanotechnology for Power Generation and Energy Conversion Applications Washington, USA, December 1-4, 2009 p352
[17] Cui X, Dong S 2011 J. Appl. Phys. 109 083903
[18] Bichurin M, Petrov V, Srinivasan G 2003 Phys. Rev. B 68 054402
[19] Chang C M, Carman G 2007 Phys. Rev. B 76 134116
[20] Huang Z 2006 J. Appl. Phys. 100 114104
[21] Bichurin M I, Petrov V M, Srinivasan G 2002 J. Appl. Phys. 92 7681
[22] Xu Z L 2006 Elasticity (Vol. 1) (4th Ed.) (Beijing: Higher Education Press) p32 (in Chinese) [徐芝纶 2006 弹性力学 (上册) (第四版) (北京: 高等教育出版社) 第32页]
[23] Dong S, Zhai J, Xing Z, Li J, Viehland D 2007 Appl. Phys. Lett. 91 022915
[24] Dai X, Zhang Z, Wang Y, Li J, Cheng L 2014 J. Appl. Phys. 115 014104
[25] Yang F, Wen Y M, Zheng M, Li P 2006 Chin. J. Sensor. Actuat. 19 2371 (in Chinese) [杨帆, 文玉梅, 郑敏, 李平 2006 传感技术学报 19 2371]
[26] Zhai J, Xing Z, Dong S, Li J, Viehland D 2006 Appl. Phys. Lett. 88 062510
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