ON THE MAGNETICALLY INDUCED ELECTROMECHANICAL COUPLING OF CENTROSYMMETRIC FLEXOELECTRIC SANDWICH PLATE
-
摘要: 现代工业的发展对材料性能和结构尺寸提出更高的要求, 机电器件的设计越来越偏向于小型化、高频化和智能化. 最新研究成果表明, 磁电耦合复合材料不仅能够以较强的磁电转换效率实现磁能、机械能和电能之间的相互转换, 还可以避免结构与机械驱动源的直接接触, 实现非接触调控, 这对于制备多功能微纳米器件具有重要意义. 文章基于Mindlin所发展的多物理场结构理论分析方法, 结合宏观压磁理论和偶应力挠曲电理论, 研究由单个挠曲电电介质层和两个对称压磁层构成的三明治型夹层板在外部横向磁场驱动下的动态力电耦合响应, 其中通过引入曲率将经典力电耦合理论拓宽到中心对称材料. 夹层板在正弦型全局磁场和均布局部磁场驱动下的动态数值算例表明: 位移和电势具有一定的频率依赖性, 当激振频率达到固有频率时, 振幅达到最大值; 此外, 对称式驱动压磁层分布方式趋于提高多层复合板的力电耦合性能. 文章理论模型和研究结果可为磁控机电器件的优化设计提供新的改进思路.Abstract: The development of modern industry inspires higher requirements for material properties and structural dimensions. The design of electromechanical devices is increasingly biased towards miniaturization, high frequency and intelligence. The most recent studies demonstrate that composite materials with magnetoelectric coupling can not only achieve mutual conversion of magnetic, mechanical, and electrical energy with high magnetoelectric conversion efficiencies, but can also avoid direct contact between the structure and the mechanical driving source to achieve non-contact control, which is crucial for the creation of multifunctional micro and nanoscale devices. Based on the multi-physics structural analysis framework developed by Mindlin, this paper studies the dynamic electromechanical coupling response of a sandwich plate composed of a flexoelectric dielectric layer and two symmetric piezomagnetic layers induced by external transverse magnetic fields. The macroscopic piezomagnetic and curvature-induced flexoelectric theories are employed and the classical electromechanical coupling theory is extended to centrosymmetric materials. The dynamic numerical examples of the sandwich plate driven by a sinusoidal global magnetic field and a uniformly distributed local magnetic field show that the magnitudes of displacement and potential are frequency dependent. When the excitation frequency reaches the natural frequency, the amplitude reaches the maximum. In addition, the distribution of symmetrical piezomagnetic layer tends to improve the electromechanical coupling performance of multilayer composite plates. Both the theoretical model and numerical results provide new ideas for the optimization design of magnetic-controlled electromechanical devices.
-
图 3 横向磁场驱动下夹层板的边界配置
Figure 3. Boundary configuration of sandwich plate under a transverse magnetic field
图 4 全局磁场驱动下的一阶电势幅频关系对比
Figure 4. Comparison of amplitude-frequency curve of first-order potential under the global magnetic field
图 6 局部磁场驱动下夹层板的挠度幅频关系
Figure 6. Deflection amplitude-frequency curve of the sandwich plate under local magnetic field
图 7 局部磁场驱动下夹层板的前两阶挠度、转角和一阶电势振型
Figure 7. The first two order deflection, rotation angle and first-order potential mode of the sandwich plate under the local magnetic field
7 局部磁场驱动下夹层板的前两阶挠度、转角和一阶电势振型 (续)
7. The first two order deflection, rotation angle and first-order potential mode of the sandwich plate under the local magnetic field (continued)
表 1 CoFe2O4和Si的材料参数
Table 1. Material parameters of CoFe2O4 and Si
Property/Unit CoFe2O4 Si elastic constants/GPa ${ {C'_{11}} } = 286 \\$ ${ {C'_{1{\text{2} }} } } = {\text{173} }$ $ {C_{11}} = 165.7 $ ${ {C'_{13}} } = 170 \\$ $ {C_{12}} = 63.9 \\ $ ${ {C'_{33} }} = 269.5 \\$ $ {C_{44}} = 79.56 $ ${ {C'_{44}} } = 45.3$ dielectric constants/(C2·(N·m2)−1)×10−9 ${ {s'_{11}} } = 0.{\text{08} } \\$ ${s_{11} } = 0.1035$ ${ {s'_{33}} } = 0.{\text{093} }$ piezomagnetic constants/(N·(A·m)−1) ${ {h'_{31}} } = 580.3$ — ${ {h'_{33} }} = 699.7$ flexoelectric coefficient/(nC·m−1) — $ {f_{16}} = 0.4 $ mass density/(kg·m−3) $\rho ' = 5300$ $\rho = 2332$ 
下载: 导出CSV
-
[1] 李东, 袁惠群. 磁致伸缩换能器耦合磁弹性模型与振动特性分析. 固体力学学报, 2011, 32(4): 365-371 (Li Dong, Yuan Huiqun. Analysis on coupling magneto-elastic characteristic of a giant magnetostrictive transducer. Chinese Journal of Solid Mechanics, 2011, 32(4): 365-371 (in Chinese) [2] 王歆钰, 储瑞江, 魏胜男等. 应力作用下EuTiO3铁电薄膜电热效应的唯象理论研究. 物理学报, 2015, 64(11): 117701 (Wang Xinyu, Chu Ruijiang, Wei Shengnan, et al. Phenomenological theory for investigation on stress tunable electrocaloric effect in ferroelectric EuTiO3 films. Acta Physica Sinica, 2015, 64(11): 117701 (in Chinese) doi: 10.7498/aps.64.117701 [3] Qu Y, Jin F, Yang J. Temperature-induced potential barriers in piezoelectric semiconductor films through pyroelectric and thermoelastic couplings and their effects on currents. Journal of Applied Physics, 2022, 131: 094502 doi: 10.1063/5.0083759 [4] 张伟, 刘爽, 毛佳佳等. 磁耦合式双稳态宽频压电俘能器的设计和俘能特性. 力学学报, 2022, 54(4): 1102-1112 (Zhang Wei, Liu Shuang, Mao Jiajia, et al. Design and energy capture characteristics of magnetically coupled bistable wide band piezoelectric energy harvester. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(4): 1102-1112 (in Chinese) doi: 10.6052/0459-1879-21-676 [5] Qu Y, Pan E, Zhu F, et al. Modeling thermoelectric effects in piezoelectric semiconductors: New fully coupled mechanisms for mechanically manipulated heat flux and refrigeration. International Journal of Engineering Science, 2023, 182: 103775 doi: 10.1016/j.ijengsci.2022.103775 [6] Kagawa Y, Yamabuchi T. Finite element simulation of two-dimensional electromechanical resonators. IEEE Trans. Sonics Ultrason., 1974, 21(4): 275-282 doi: 10.1109/T-SU.1974.29826 [7] Devoe DL. Piezoelectric thin film micromechanical beam resonators. Sensors and Actuators A-Physical, 2001, 88(3): 263-272 doi: 10.1016/S0924-4247(00)00518-5 [8] Jiang X, Huang W, Zhang S. Flexoelectric nano-generator: Materials, structures and devices. Nano Energy, 2013, 2(6): 1079-1092 doi: 10.1016/j.nanoen.2013.09.001 [9] Ray MC. Analysis of smart nanobeams integrated with a flexoelectric nano actuator layer. Smart Materials and Structures, 2016, 25(5): 055011 doi: 10.1088/0964-1726/25/5/055011 [10] Chu Z, Pourhosseiniasl M, Dong S. Review of multi-layered magnetoelectric composite materials and devices applications. Journal of Physics D: Applied Physics, 2018, 51(24): 243001 doi: 10.1088/1361-6463/aac29b [11] Bhaskar UK, Banerjee N, Abdollahi A, et al. A flexoelectric microelectromechanical system on silicon. Nature Nanotechnology, 2016, 11(3): 263-266 doi: 10.1038/nnano.2015.260 [12] Deng Q, Lv S, Li Z, et al. The impact of flexoelectricity on materials, devices, and physics. Journal of Applied Physics, 2020, 128(8): 080902 doi: 10.1063/5.0015987 [13] Lan M, Yang W, Liang X, et al. Vibration modes of flexoelectric circular plate. Acta Mechanica Sinica, 2022, 38: 422063 [14] Sun L, Zhang Z, Gao C, et al. Effect of flexoelectricity on piezotronic responses of a piezoelectric semiconductor bilayer. Journal of Applied Physics, 2021, 129(24): 244102 doi: 10.1063/5.0050947 [15] Yan Z, Jiang LY. Flexoelectric effect on the electroelastic responses of bending piezoelectric nanobeams. Journal of Applied Physics, 2013, 113(19): 194102 doi: 10.1063/1.4804949 [16] Liang X, Hu S, Shen S. Size-dependent buckling and vibration behaviors of piezoelectric nanostructures due to flexoelectricity. Smart Materials and Structures, 2015, 24: 105012 doi: 10.1088/0964-1726/24/10/105012 [17] Qu Y, Jin F, Yang J. Flexoelectric effects in second-order extension of rods. Mechanics Research Communications, 2021, 111: 103625 doi: 10.1016/j.mechrescom.2020.103625 [18] Zhang R, Liang X, Shen S. A Timoshenko dielectric beam model with flexoelectric effect. Meccanica, 2016, 51: 1181-1188 doi: 10.1007/s11012-015-0290-1 [19] Liang X, Yang W, Hu S, et al. Buckling and vibration of flexoelectric nanofilms subjected to mechanical loads. Journal of Physics D: Applied Physics, 2016, 49(11): 115307 doi: 10.1088/0022-3727/49/11/115307 [20] 曹彩芹, 陈晶博, 李东波. 考虑电场梯度的挠曲电纳米板弯曲性能分析. 力学学报, 2022, 54(11): 3088-3098 (Cao Caiqin, Chen Jingbo, Li Dongbo. Bending performance analysis of flexoelectric nanoplate considering electric field gradients. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 3088-3098 (in Chinese) doi: 10.6052/0459-1879-22-282 [21] 宋铭, 鄢之. 考虑挠曲电效应的压电纳米薄板力-电-热耦合特性研究. 固体力学学报, 2020, 41(5): 444-454 (Song Ming, Yan Zhi. Thermo-electro-mechanical properties of piezoelectric nanoplates with flexoelectricity. Chinese Journal of Solid Mechanics, 2020, 41(5): 444-454 (in Chinese) doi: 10.19636/j.cnki.cjsm42-1250/o3.2020.025 [22] Fu Y, Wang J, Mao Y. Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment. Applied Mathematical Modelling, 2012, 36(9): 4324-4340 doi: 10.1016/j.apm.2011.11.059 [23] Cui N, Wu W, Zhao Y, et al. Magnetic force driven nanogenerators as a noncontact energy harvester and sensor. Nano Letters, 2012, 12(7): 3701-3705 doi: 10.1021/nl301490q [24] Peng M, Zhang Y, Liu Y, et al. Magnetic-mechanical-electrical-optical coupling effects in GaN-based LED/rare-earth terfenol-D structures. Advanced Materials, 2014, 26(39): 6767-6772 doi: 10.1002/adma.201402824 [25] Scott JF. Applications of modern ferroelectrics. Science, 2007, 315(5814): 954-959 doi: 10.1126/science.1129564 [26] Chen XZ, Hoop M, Shamsudhin N, et al. Hybrid magnetoelectric nanowires for nanorobotic applications: fabrication, magnetoelectric coupling, and magnetically assisted in vitro targeted drug delivery. Advanced Materials, 2017, 29(8): 1605458 doi: 10.1002/adma.201605458 [27] Tan K, Wen X, Deng Q, et al. Soft rubber as a magnetoelectric material—Generating electricity from the remote action of a magnetic field. Materials Today, 2021, 43: 8-16 doi: 10.1016/j.mattod.2020.08.018 [28] Van Den Boomgaard J, Van Run A, Suchtelen JV. Magnetoelectricity in piezoelectric-magnetostrictive composites. Ferroelectrics, 1976, 10(1): 295-298 doi: 10.1080/00150197608241997 [29] Ryu J, Carazo AV, Uchino K, et al. Magnetoelectric properties in piezoelectric and magnetostrictive laminate composites. Japanese Journal of Applied Physics, 2001, 40(8R): 4948 doi: 10.1143/JJAP.40.4948 [30] Li DB, Yan JQ, Chen JB, et al. Magnetically-induced flexoelectric effects in the second-order extension of a composite fiber with piezomagnetic and flexoelectric layers. International Journal of Applied Mechanics, 2021, 13(7): 2150083 doi: 10.1142/S1758825121500836 [31] Mindlin RD. High frequency vibrations of piezoelectric crystal plates. International Journal of Solids and Structures, 1972, 8(7): 895-906 doi: 10.1016/0020-7683(72)90004-2 [32] Yang J. The Mechanics of Piezoelectric Structures. Singapore: World Scientific, 2006 [33] Mindlin RD, Tiersten HF. Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis, 1962, 11: 415-448 doi: 10.1007/BF00253946 [34] Toupin R. Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis, 1962, 11(1): 385-414 doi: 10.1007/BF00253945 [35] Koiter WT. Couple-stresses in the theory of elasticity. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen. Series B, 1964, 67: 17-44 [36] Qu YL, Zhang GY, Fan YM, et al. A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects. Part I: Reconsideration of curvature-based flexoelectricity theory. Mathematics and Mechanics of Solids, 2022, 26(11): 1647-1659 [37] Li A, Zhou S, Qi L, et al. A flexoelectric theory with rotation gradient effects for elastic dielectrics. Modelling and Simulation in Materials Science and Engineering, 2016, 24: 015009 doi: 10.1088/0965-0393/24/1/015009 [38] Qu Y, Guo Z, Jin F, et al. A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects. Part II: Variational formulations and applications in plates. Mathematics and Mechanics of Solids, 2022, 27(12): 2567-2587 doi: 10.1177/10812865221075768 [39] Zhang G, Qu Y, Guo, Z, et al. Magnetically induced electric potential in first-order composite beams incorporating couple stress and its flexoelectric effects. Acta Mechanica Sinica, 2021, 37: 1509-1519 doi: 10.1007/s10409-021-01137-4 [40] Guo Z, Qu Y, Zhang G, et al. Magnetically induced electromechanical fields in a flexoelectric composite microplate. Mathematics and Mechanics of Solids, 2023, 28(4): 1091-1110 doi: 10.1177/10812865221112172 [41] Gao XL, Zhang GY. A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2016, 472(2191): 20160275 doi: 10.1098/rspa.2016.0275 [42] Sze SM, Ng KK. Physics of Semiconductor Devices. 3rd ed. New York: Wiley, 2006 [43] Qu Y, Jin F, Yang J. Magnetically induced charge redistribution in the bending of a composite beam with flexoelectric semiconductor and piezomagnetic dielectric layers. Journal of Applied Physics, 2021, 129: 064503 doi: 10.1063/5.0039686 [44] Jiang S, Li X, Guo S, et al. Performance of a piezoelectric bimorph for scavenging vibration energy. Smart Materials and Structures, 2005, 14: 769-774 doi: 10.1088/0964-1726/14/4/036 -
下载:
点击查看大图
图(8) / 表(1)
计量
- 文章访问数: 77
- HTML全文浏览量: 31
- PDF下载量: 19
- 被引次数: 0
