压电纳米板中SH型导波的传播特性

张乐乐; 刘响林; 刘金喜

doi:10.6052/0459-1879-18-413

压电纳米板中SH型导波的传播特性

doi: 10.6052/0459-1879-18-413

* 石家庄铁道大学工程力学系,石家庄 050043
?? 石家庄铁道大学数理系,石家庄 050043

基金项目: 国家自然科学基金资助项目(11472182);国家自然科学基金资助项目(11802185)

详细信息

作者简介:
2) 刘金喜,教授,主要研究方向：压电和磁电弹多场耦合材料与结构的力学行为.E-mail： liujx02@hotmail.com

中图分类号: O343
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出版历程
- 收稿日期: 2018-12-07
- 刊出日期: 2019-03-18

PROPAGATION CHARACTERISTICS OF SH GUIDED WAVES IN A PIEZOELECTRIC NANOPLATE

* Department of Engineering Mechanics, Shijiazhuang Tiedao University,Shijiazhuang 050043,China
?? Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043,China

摘要

摘要: 压电纳米材料具有机电耦合性强、功耗低和反应灵敏等独特性能,且能满足工程对压电器件微型化的要求,从而在传感、微纳米机电系统和柔性电子器件等领域展现出了广阔的应用前景. 高比表面积引起的表面效应是压电纳米材料最重要的结构特征之一,其对材料的整体力学性质起着决定性的作用.表面效应会导致应力和电位移在压电表面的两侧出现间跃,故传统的力电场连续性条件将不再适用.考虑表面为不计厚度却拥有独立材料参数的薄层,采用表面压电模型计及表面弹性、表面压电性、表面介电性和表面密度的影响,本文研究了压电纳米板中SH型导波的传播特性,给出了板边界处的非典型力电平衡条件,得到了频散方程的解析表达,并结合数值算例详细讨论了表面材料参数和结构尺寸对对称和反对称频散模态的影响.结果表明：SH型导波在压电纳米板中的传播具有明显的尺寸相关性,即当板厚很小时,表面效应会显著改变其频散行为,而随着板厚的增大,表面效应的影响会不断减弱直至可忽略不计.
- 压电材料 /
- 表面效应 /
- 表面压电模型 /
- SH波 /
- 纳米板 /
- 频散特性
Abstract: Piezoelectric nanomaterials have many unique properties, such as enhanced electromechanical coupling, low power dissipation and sensitive response, etc. Also such materials can meet the demand of microminiaturization of piezoelectric devices. These advantages make them strong candidates for applications in the fields of sensing, nanoelectromechanical systems (NEMS), flexible electronic device, and so on. As one of the most important features of nanomaterials, surface effect which resulted from the high ratio of surface to volume commonly plays a dominant role in the overall mechanical properties of piezoelectric nanomaterials. Due to the presence of surface effect, the bulk stress and bulk electric displacement jump across the piezoelectric surface, thus the classical continuity conditions are invalid. In this paper, the dispersion characteristics of SH guided waves propagating in a monolayer piezoelectric nanoplate are investigated with consideration of the surface effect. A surface is regarded as a two-dimensional continuum of zero thickness which possesses own material properties, and the influences of surface elasticity, surface piezoelectricity, surface permittivity and surface density are accounted into the non-classical boundary conditions of the piezoelectric nanoplate via the surface piezoelectricity model. The analytical expressions of dispersion relations are derived, and the numerical examples are provided to discuss the impacts of surface material parameters and nanoplate thickness on the symmetric and antisymmetric modes. Analysis results show that the propagation characteristics of SH guided waves exhibit obvious size-dependence. The surface effect has a significant impact on dispersion behaviors when the nanoplate thickness is small enough, while they may become more and more negligible as the thickness increases.
- piezoelectric material /
- surface effect /
- surface piezoelectricity model /
- SH waves /
- nanoplate /
- dispersion characteristics

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参考文献(1)

[1]	Jing GY, Duan HL, Sun XM , et al. Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy. Physical Review B, 2006,73(23):235409
[2]	Tan EPS, Zhu Y, Yu T , et al. Crystallinity and surface effects on Young's modulus of CuO nanowires. Applied Physics Letters, 2007,90(16):163112
[3]	周伟建, 陈伟球 . 具有表面效应的压电半空间中的表面波. 力学学报, 2017,49(3):597-604
[3]	( Zhou Weijian, Chen Weiqiu . Surface waves in a piezoelectric half-space with surface effect. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(3):597-604 (in Chinese))
[4]	肖俊华, 韩彬, 徐耀玲等. 考虑表面弹性效应时正三角形孔边裂纹反平面剪切问题的断裂力学分析. 固体力学学报, 2017,38(6):530-536
[4]	( Xiao Junhua, Han Bin, Xu Yaoling , et al. Fracture analysis of cracked equilateral triangular hole with surface elasticity effect under antiplane shear. Chinese Journal of Solid Mechanics, 2017,38(6):530-536 (in Chinese))
[5]	Wang JX, Huang JP, Duan HL , et al. Surface stress effect in mechanics of nanostructured materials. Acta Mechanica Solida Sinica, 2011,24(1):52-82
[6]	Duan HL, Wang J, Karihaloo BL . Theory of elasticity at the nanoscale. Advances in Applied Mechanics, 2009,42:1-68
[7]	Pirota KR, Silva EL, Zanchet D , et al. Size effect and surface tension measurements in Ni and Co nanowires. Physical Review B, 2007,76(23):233410
[8]	王帅, 姚寅, 杨亚政等. 双层金属纳米板界面能密度的尺寸效应. 力学学报, 2017,49(5):978-984
[8]	( Wang Shuai, Yao Yin, Yang Yazheng , et al. Size effect of the interface energy density in bi-nano-scaled-metallic plates. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(5):978-984 (in Chinese))
[9]	许新, 李世荣 . 功能梯度材料微梁的热弹性阻尼研究. 力学学报, 2017,49(2):308-316
[9]	( Xu Xin, Li Shirong . Analysis of thermoelastic damping for functionally graded material micro-beam. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(2):308-316 (in Chinese))
[10]	Gurtin ME, Murdoch AI . Surface stress in solids. International Journal of Solids and Structures, 1978,14(6):431-440
[11]	Gurtin ME, Murdoch AI . A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 1975,57(4):291-323
[12]	Wang ZL, Song JH . Piezoelectric nanogenerators based on zinc oxide nanowire arrays. Science, 2006,312(5771):242-246
[13]	Lao CS, Kuang Q, Wang ZL , et al. Polymer functionalized piezoelectric-FET as humidity/chemical nanosensors. Applied Physics Letters, 2007,90(26):262107
[14]	Xu S, Yeh Y, Poirier G , et al. Flexible piezoelectric PMN-PT nanowire-based nanocomposite and device. Nano Letters, 2013,13(6):2393-2398
[15]	Fang XQ, Liu JX, Gupta V . Fundamental formulations and recent achievements in piezoelectric nano-structures: A review. Nanoscale, 2013,5(5):1716-1726
[16]	Huang GY, Yu SW . Effect of surface piezoelectricity on the electromechanical behavior of a piezoelectric ring. Physica Status Solidi (b), 2006,243(4):R22-R24
[17]	Pan XH, Yu SW, Feng XQ . A continuum theory of surface piezoelectricity for nanodielectrics. Science China: Physics, Mechanics and Astronomy, 2011,54(4):564-573
[18]	Yan Z, Jiang LY . The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects. Nanotechnology, 2011,22(24):245703
[19]	Yan Z, Jiang LY . Surface effects on the vibration and buckling of piezoelectric nanoplates. Europhysics Letters, 2012,99(2):27007
[20]	Yan Z, Jiang LY . Surface effects on the electroelastic responses of a thin piezoelectric plate with nanoscale thickness. Journal of Physics D: Applied Physics, 2012,45(25):255401
[21]	Chen T . Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects. Acta Mechanica, 2008,196(3-4):205-217
[22]	Wang KF, Wang BL . Surface effects on the energy-generating performance of piezoelectric circular nanomembrane energy-harvesters under pressure loading. Europhysics Letters, 2014,108(1):17001
[23]	Zhang CL, Zhang CZ, Chen WQ . Modeling of piezoelectric bimorph nano-actuators with surface effects. Journal of Applied Mechanics, 2013,80(6):061015
[24]	Chen T, Chiu MS, Weng CN . Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. Journal of Applied Physics, 2006,100(7):074308
[25]	Zhang LL, Liu JX, Fang XQ , et al. Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects. Physica E: Low-dimensional Systems and Nanostructures, 2014,57:169-174
[26]	Murdoch AI . The propagation of surface waves in bodies with material boundaries. Journal of the Mechanics and Physics of Solids, 1976,24(2-3):137-146
[27]	Gurtin ME, Murdoch AI . Effect of surface stress on wave propagation in solids. Journal of Applied Physics, 1976,47(10):4414-4421