SURFACE WAVES IN A PIEZOELECTRIC HALF-SPACE WITH SURFACE EFFECT
-
摘要: 纳米科技的快速发展使压电纳米结构在纳米机电系统中得到广泛应用，形成了诸如纳米压电电子学等新的研究方向。与传统的宏观压电材料相比，在纳米尺度下压电材料往往呈现出不同的力学特性，而造成这种差异的原因之一便是表面效应。本文基于Stroh公式、Barnett-Lothe积分矩阵及表面阻抗矩阵，研究计入表面效应的任意各向异性压电半空间中的表面波传播问题，导出了频散方程。针对横观各向同性压电材料，假设矢状平面平行于材料各向同性面，发现Rayleigh表面波和B-G波解耦，并得到各自的显式频散方程。结果表明，Rayleigh表面波的波速小于偏振方向垂直于表面的体波，而B-G波的波速小于偏振方向垂直于矢状平面的体波。以PZT-5H材料为例，用数值方法考察表面残余应力和电学边界条件对表面波频散特性的影响发现：表面残余应力只对第一阶Rayleigh波有明显的影响；电学开路情形的B-G波比电学闭路情形的B-G波传播快。本文工作可为纳米表面声波器件的设计或压电纳米结构的无损检测提供理论依据。Abstract: The fast developments in nanotechnology enable the wide applications of piezoelectric nano-structures in nano-electromechanical systems, forming new research directions such as nanopiezotronics. Compared with the traditional macroscopic piezoelectric materials, nano-scaled piezoelectric materials present different mechanical properties, possibly due to the existence of surface effect, one of the main reasons for explaining the difference. This paper concerns the propagation of surface waves in a generally anisotropic piezoelectric half-space with surface effect. Stroh formalism, Barnett-Lothe integral matrices, and surface impedance matrices are adopted to theoretically derive the dispersion equations of surface waves. For transversely isotropic piezoelectric materials with the isotropic basal plane parallel with the sagittal plane, Rayleigh waves and B-G waves are found to be decoupled from each other, and their dispersion equations are derived in an explicit and compact form. It is rigorously shown that the velocity of Rayleigh waves should be smaller than that of the bulk waves polarized in the depth direction, whilst the velocity of B-G waves should be smaller than that of the bulk waves polarized in the direction perpendicular to the sagittal plane. In the numerical simulations, PZT-5H is taken as an example to numerically illustrate the influences of surface residual stress and electrical boundary conditions on the dispersion properties of surface waves. It is found that surface residual stress has a significant effect only on the first-order Rayleigh wave, and the B-G wave under the electric open-circuit condition propagates faster than under the electric closed-circuit condition. The theoretical predictions and numerical results presented in the paper should be helpful in understanding size-dependent dynamic behaviors of piezoelectric structures with surface effect and may provide a solid basis for the design of nano-sized surface acoustic wave devices as well as for the nondestructive testing of nano-sized piezoelectric structures.
-
Key words:
- surface waves /
- surface effect /
- piezoelectric material /
- Stroh formlism /
- dispersion relation
-
[1] Fang XQ, Liu JX, Gupta V. Fundamental formulations and recent achievements in piezoelectric nano-structures:A review. Nanoscale, 2013, 5(5):1716-1726 doi: 10.1039/c2nr33531j [2] Voon LC, Willatzen M. Electromechanical phenomena in semi-conductor nanostructures. Journal of Applied Physics, 2011, 109:031101 doi: 10.1063/1.3533402 [3] Lao CS, Kuang Q, Wang ZL. Polymer functionalized piezoelectricFET as humidity/chemical nanosensors. Applied Physics Letters, 2007, 90(26):262107 doi: 10.1063/1.2748097 [4] Wang XD, Zhou J, Song JH, et al. Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire. Nano Letters, 2006, 6(12):2768-2772 doi: 10.1021/nl061802g [5] 孔艳平, 刘金喜. PMN-PT层/弹性基底结构中声表面波特性分析.力学学报, 2015, 47(3):493-502 doi: 10.6052/0459-1879-14-299Kong Yanping, Liu Jinxi. Surface acoustic wave propagation in the PMN-PT layer/elastic substrate. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(3):493-502 (in Chinese) doi: 10.6052/0459-1879-14-299 [6] Stan G, Ciobanu CV, Parthangal PM, et al. Diameter-dependent radial and tangential elastic moduli of ZnO nanowires. Nano Letters, 2007, 7(12):3691-3697 doi: 10.1021/nl071986e [7] Chen CQ, Shi Y, Zhang YS, et al. Size dependence of Young's modulus in ZnO nanowires. Physical Review Letters, 2006, 96(7):075505 doi: 10.1103/PhysRevLett.96.075505 [8] 徐巍, 王立峰, 蒋经农.基于应变梯度中厚板单元的石墨烯振动研究.力学学报, 2015, 47(5):751-761 doi: 10.6052/0459-1879-15-074Xu Wei, Wang Lifeng, Jiang Jingnong. Finite element analysis of strain gradient middle thick plate model on the vibration of graphene sheets. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5):751-761 (in Chinese) doi: 10.6052/0459-1879-15-074 [9] 唐宇帆, 任树伟, 辛锋先等. MEMS系统中微平板结构声振耦合性能研究.力学学报, 2016, 48(4):907-916 http://lxxb.cstam.org.cn/CN/abstract/abstract145761.shtmlTang Yufan, Ren Shuwei, Xin Fengxian, et al. Scale effect analysis for the vibroacoustic performance of a micro-plate. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4):907-916 (in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract145761.shtml [10] 陈玲, 沈纪苹, 李成等.梯度型非局部高阶梁理论与非局部弯曲新解法.力学学报, 2016, 48(1):127-134 doi: 10.6052/0459-1879-15-170Chen Ling, Shen Jiping, Li Cheng, et al. Gradient type of nonlocal higher-order beam theory and new solution methodology of nonlocal bending deflection. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1):127-134 (in Chinese) doi: 10.6052/0459-1879-15-170 [11] 杨刚, 张斌.类石墨烯二维原子晶体的微态理论模型.力学学报, 2015, 47(3):451-457 doi: 10.6052/0459-1879-14-282Yang Gang, Zhang Bin. Micromorphic model of graphene-like two-dimensional atomic crystals. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(3):451-457 (in Chinese) doi: 10.6052/0459-1879-14-282 [12] Miller RE, Shenoy VB. Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 2000, 11(3):139-147 doi: 10.1088/0957-4484/11/3/301 [13] Cammarata RC. Surface and interface stress effects in thin films. Progress in Surface Science, 1994, 46(1):1-38 doi: 10.1016/0079-6816(94)90005-1 [14] Murdoch AI. The propagation of surface waves in bodies with material boundaries. Journal of the Mechanics and Physics of Solids, 1976, 24(2):137-146 https://www.researchgate.net/publication/222087105_The_propagation_of_surface_waves_in_bodies_with_material_boundaries [15] Gurtin ME, Murdoch AI. A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 1975, 57(4):291-323 https://www.researchgate.net/publication/225935208_A_Continuum_Theory_of_Elastic_Material_Surfaces [16] Chen WQ, Wu B, Zhang CL, et al. On wave propagation in anisotropic elastic cylinders at nanoscale:surface elasticity and its effect. Acta Mechanica, 2014, 225(10):2743-2760 doi: 10.1007/s00707-014-1211-4 [17] Huang GY, Yu SW. Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring. Physica Status Solidi (b), 2006, 243(4):R22-R24 doi: 10.1002/(ISSN)1521-3951 [18] Yan Z, Jiang LY. Surface effects on the electromechanical coupling and bending behaviours of piezoelectric nanowires. Journal of Physics D:Applied Physics, 2011, 44(7):075404 doi: 10.1088/0022-3727/44/7/075404 [19] Yan Z, Jiang LY. The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects. Nanotechnology, 2011, 22(24):245703 doi: 10.1088/0957-4484/22/24/245703 [20] Yan Z, Jiang LY. Electromechanical response of a curved piezoelectric nanobeam with the consideration of surface effects. Journal of Physics D:Applied Physics, 2011, 44(36):365301 doi: 10.1088/0022-3727/44/36/365301 [21] Zhang CL, Chen WQ, Zhang C. On propagation of anti-plane shear waves in piezoelectric plates with surface effect. Physics Letters A, 2012, 376(45):3281-3286 doi: 10.1016/j.physleta.2012.09.027 [22] 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 doi: 10.1016/j.physe.2013.11.007 [23] Chen WQ. Surface effect on Bleustein-Gulyaev wave in a piezoelectric half-space. Theoretical and Applied Mechanics Letters, 2011, 1(4):041001 doi: 10.1063/2.1104101 [24] Bleustein JL. A new surface wave in piezoelectric materials. Applied Physics Letters, 1968, 13(12):412-413 doi: 10.1063/1.1652495 [25] Gulyaev YV. Electroacoustic surface waves in solids. Soviet Physics JETP, 1969, 9:37-38 doi: 10.1007/BF00818735 [26] Stroh AN. Dislocations and cracks in anisotropic elasticity. Philosophical Magazine, 1958, 3(25):625-646 https://www.researchgate.net/publication/239064714_Dislocations_and_Cracks_in_Anisotropic_Elasticity [27] Stroh AN. Steady state problems in anisotropic elasticity. Journal of Mathematical Physics, 1962, 41(2):77-103 [28] Lothe J, Barnett DM. Integral formalism for surface waves in piezoelectric crystals. Existence considerations. Journal of Applied Physics, 1976, 47(5):1799-1807 doi: 10.1063/1.322895 [29] Barnett DM, Lothe J. Free surface (Rayleigh) waves in anisotropic elastic half-spaces:the surface impedance method. Proceedings of the Royal Society of London A, 1985, 402(1822):135-152 doi: 10.1098/rspa.1985.0111 [30] Lothe J, Barnett D M. Further development of the theory for surface waves in piezoelectric crystals. Physica Norvegica, 1977, 8(4):239-254 [31] Abbudi M, Barnett DM. On the existence of interfacial (Stoneley) waves in bonded piezoelectric half-spaces. Proceedings of the Royal Society of London A, 1990, 429(1877):587-611 doi: 10.1098/rspa.1990.0075 [32] Tiersten HF. Wave propagation in an infinite piezoelectric plate. Journal of the Acoustical Society of America, 1963, 35(2):234-239 doi: 10.1121/1.1918438 [33] Ding HJ, Chen WQ. Three Dimensional Problems of Piezoelasticity. New York:Nova Science Publishers, 2001 [34] Soh AK, Liu J, Lee KL, et al. Moving dislocations in general anisotropic piezoelectric solids. Physica Status Solidi (b), 2005, 242(4):842-853 doi: 10.1002/(ISSN)1521-3951 [35] Ding HJ, Liang J. The fundamental solutions for transversely isotropic piezoelectricity and boundary element method. Computers & Structures, 1999, 71(4):447-455 https://www.researchgate.net/publication/256919242_Fundamental_solutions_for_transversely_isotropic_piezoelectricity_and_boundary_element_method [36] Sezawa K, Kanai K. Discontinuity in dispersion curves of Rayleighwaves. Bulletin of the Earthquake Research Institute, 1935, 13:237-244 https://www.researchgate.net/publication/29774476_Discontinuity_in_the_Dispersion_Curves_of_Rayleigh_Waves -
下载:
点击查看大图
图(2)
计量
- 文章访问数: 1004
- HTML全文浏览量: 179
- PDF下载量: 772
- 被引次数: 0
