非理想界面压电层状结构中SH波的传播性能
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摘要
由于能够实现电能和机械能的相互转换,压电材料被广泛用于制作传感器、滤波器、换能器和执行器等各种压电装置。这些器件通常是层状的,而且他们的许多应用以弹性波的传播知识为理论基础。因此,压电层状结构中弹性波的传播性能一直是应用物理、力学和声学等领域内的重要研究内容。
假定界面是非理想粘接的,本文研究了两种层状压电结构中的SH波传播问题,一种是平面层状的,另一种是层状复合柱体。压电材料具有横观各向同性的性能,而纯弹性材料是各向同性和正交各向异性的。
对于所考虑的层状结构,推导了它们的频散方程,并对几种不同的材料组合计算了相速度随波数的变化规律。数值结果表明：
(a)与理想界面比较,波数较小时,非理想界面降低了SH波传播的相速度；
(b)当波数较小和界面较为理想时,压电层和纯弹性基底(或纯弹性柱)的厚度比越大,相应的相速度越小；
(c)压电材料性能之间的差异对频散特性有显著的影响,而且其影响由压电材料B-G波或剪切体波的速度来反映；
(d)对于正交各向异性层/压电半空间耦合结构,各向异性程度越高,相应的相速度越低。
上述结果对改进层状压电结构在压电器件中的应用以及通过实验测定界面的性能具有参考价值。
Due to the capability of conversion between mechanical and electrical energy, piezoelectric materials have widely been used in technology as sensors, filters, transducers and actuators, and so on. These devices are commonly constructed in layered form and many applications of them are related to the knowledge of elastic wave propagation. Therefore, studies of the propagation of elastic waves accompanied by electrical waves have long been of interesting to researchers in the fields of applied physics, mechanics and acoustics.
This dissertation deals with the propagation of shear horizontal (SH) waves in two kinds of layered structures consisting of piezoelectric and purely elastic media:one being the plane layered structure, and the other being the layered cylinder. The interface is assumed to be imperfect. Piezoelectric materials are transversely isotropic, while pure elastic materials are isotropic or orthotropic.
The dispersion equations for the considered layered structures are derived and then the phase velocities are calculated for different material combinations. The numerical results show that:(a) In comparison with the case of the perfect interface, the imperfect degree of the interface reduces the phase velocities at the lower wave number. (b) When the wave number is lower and the imperfect degree of the interface is weaker, the phase velocities decrease as the ratio of the thickness of the piezoelectric layer to the purely elastic substrate or cylinder increases. (c) The difference between piezoelectric material properties has substantial influences on the dispersion characteristics, and their influences are reflected by velocities of the B-G surface wave and SH bulk wave. (d) For the piezoelectric half-space carrying a purely elastic orthotropic layer, the phase velocity decrease with the increase of the anisotropic degree. These findings may useful for improvement of piezoelectric devices or structures as well the experimental determination of interface property.
假定界面是非理想粘接的,本文研究了两种层状压电结构中的SH波传播问题,一种是平面层状的,另一种是层状复合柱体。压电材料具有横观各向同性的性能,而纯弹性材料是各向同性和正交各向异性的。
对于所考虑的层状结构,推导了它们的频散方程,并对几种不同的材料组合计算了相速度随波数的变化规律。数值结果表明：
(a)与理想界面比较,波数较小时,非理想界面降低了SH波传播的相速度；
(b)当波数较小和界面较为理想时,压电层和纯弹性基底(或纯弹性柱)的厚度比越大,相应的相速度越小；
(c)压电材料性能之间的差异对频散特性有显著的影响,而且其影响由压电材料B-G波或剪切体波的速度来反映；
(d)对于正交各向异性层/压电半空间耦合结构,各向异性程度越高,相应的相速度越低。
上述结果对改进层状压电结构在压电器件中的应用以及通过实验测定界面的性能具有参考价值。
Due to the capability of conversion between mechanical and electrical energy, piezoelectric materials have widely been used in technology as sensors, filters, transducers and actuators, and so on. These devices are commonly constructed in layered form and many applications of them are related to the knowledge of elastic wave propagation. Therefore, studies of the propagation of elastic waves accompanied by electrical waves have long been of interesting to researchers in the fields of applied physics, mechanics and acoustics.
This dissertation deals with the propagation of shear horizontal (SH) waves in two kinds of layered structures consisting of piezoelectric and purely elastic media:one being the plane layered structure, and the other being the layered cylinder. The interface is assumed to be imperfect. Piezoelectric materials are transversely isotropic, while pure elastic materials are isotropic or orthotropic.
The dispersion equations for the considered layered structures are derived and then the phase velocities are calculated for different material combinations. The numerical results show that:(a) In comparison with the case of the perfect interface, the imperfect degree of the interface reduces the phase velocities at the lower wave number. (b) When the wave number is lower and the imperfect degree of the interface is weaker, the phase velocities decrease as the ratio of the thickness of the piezoelectric layer to the purely elastic substrate or cylinder increases. (c) The difference between piezoelectric material properties has substantial influences on the dispersion characteristics, and their influences are reflected by velocities of the B-G surface wave and SH bulk wave. (d) For the piezoelectric half-space carrying a purely elastic orthotropic layer, the phase velocity decrease with the increase of the anisotropic degree. These findings may useful for improvement of piezoelectric devices or structures as well the experimental determination of interface property.
引文
[1]张福学,王丽坤.现代压电学(下)[M].北京：科学出版社,2002
[2]栾桂冬,张金铎,王人乾.压电换能器和换能器阵[M].北京：北京大学出版社,2005.93-96
[3]Bleustein J L. A new surface wave in piezoelectric materials[J]. Applied Physics Letters, 1968,3(12):412-413,
[4]Gulyaev Yu V. Electroacoustic surface waves in solids[J]. Sov Phys Jetp Lett,1969,9(1): 37-38.
[5]Love A E H. Some problems of Geodynamics[D]. Cambridge:Cambridge University Press, London,1911
[6]Fischler C. Propagation and amplification of shear-horizontal waves in piezoelectric plates[J]. J Appl Phys,1971,42(3):919-924
[7]Curtis R G, Redwood M. Transverse surface waves on a piezoelectric material carrying a metal layer of finite thickness[J]. Journal of Applied Physics,1973,44(5):2002-2007
[8]Kielczynski P J, Pajewski W, Szalewski M. Shear-horizontal surface waves on piezoelectric ceramics with depolarized surface layer[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,1989,36(2):287-293
[9]Feng H H, Li X J. Shear-horizontal surface waves in a layered structure of piezo-electric ceramics[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,1993, 40(2):167-170
[10]王子昆,刘华,刘永超,等.层状压电介质中一种奇特的电声波[J].力学学报,2000,32(1)：25-33
[11]金峰,王子昆,王铁军.覆盖层与基底极化方向相反时压电层状半空间中的B-G波[J].固体力学学报,2000,21(2)：95-101
[12]Wang Q, Quek S T, Varadan V K. Love waves in piezoelectric coupled solid media[J]. Smart Materials and Structures,2001,10(2):380-388
[13]Wang Q, Varadan V K. Wave propagation in piezoelectric coupled plates by use of interdigital transducer. Part 1:Dispersion characteristics[J]. International Journal of Solids and Structures,2002,39(5):1119-1130
[14]Wang Q, Varadan V K. Wave propagation in piezoelectric coupled plates by use of interdigital transducer. Part 2:Wave excitation by interdigital transducer[J]. International Journal of Solids and Structures,2002,39(5):1131-1144
[15]Wang Q. SH wave propagation in piezoelectric coupled plates[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,2002,49(5):596-603
[16]Chen S, Tang T T, Wang Z H. Shear-horizontal acoustic wave propagation in piezoelectric bounded plates with metal gratings[J]. Journal of the Acoustical Society of America,2005, 117(6):3609-3615
[17]黄旭涛,严密.功能梯度材料回顾与展望[J].材料科学与工程,1997,15(4)：35-38
[18]刘华,匡震邦,蔡正敏.非均匀压电层状结构中Love波的传播[J].力学学报,2003,35(4)：485-488
[19]Liu J, Wang Z K. The propagation behavior of Love waves in a functionally graded layered piezoelectric structure[J]. Smart Materials and Structures,2005,14:137-146
[20]Qian Z H, Jin F, Wang Z K, et al. Transverse surface waves on a piezoelectric material carrying a functionally graded layer of finite thickness[J]. International Journal of Engineering Science,2007,45(2-8):455-466
[21]Liu H, Wang Z K, Wang T J. Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure[J]. International Journal of Solids and Structures, 2001,38(1):37-51
[22]Jin F, Wang Z K, Kishimoto K. The propagation behavior of Bleustein-Gulyaev waves in a pre-stressed piezoelectric layered structure[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2003,4(2):125-138
[23]Liu H, Kuang Z B, Cai Z M. Propagation of Bleustein-Gulyaev waves in a prestressed layered piezoelectric structure[J]. Ultrasonics,2003,41(5):397-405
[24]Qian Z, Jin F, Wang Z K, et al. Love waves propagation in a piezoelectric layered structure with initial stresses[J]. Acta Mechanica,2004,171(1-2):41-57
[25]Jin F, Qian Z H, Wang Z K, et al. Propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress[J]. Smart Materials and Structures,2005, 14(4):515-523
[26]Su J, Kuang Z B, Liu H. Love wave in ZnO/SiO2/Si structure with initial stresses[J]. Journal of Sound and Vibration,2005,286(4-5):981-999
[27]Fan H, Yang J S, Xu L M. Piezoelectric waves near an imperfectly bonded interface between two half-spaces[J]. Applied Physics Letters,2006,88(20):203509
[28]Fan H, Yang J S, Xu L M. Antiplane piezoelectric surface waves over a ceramic half-space with an imperfectly bonded layerjJ]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,2006,53(9):1695-1698
[29]Chen C L. On the electroacoustic waves guided by a cylindrical piezoelectric interface[J]. Journal of Applied Physics,1973,44(9):3841-3847
[30]Sun C T, Cheng N C. Piezoelectric waves on a layered cylinder[J]. Journal of Applied Physics,1974,45(10):4288-4294
[31]Srinivasamoorthy V R, Anandam C. Torsional wave propagation in an infinite piezo-electric cylinder (622) crystal class[J]. J. Acoust. Soc. Am.1980,67(6):2034-2035
[32]Wang Q, Jin J, Quek S T. Propagation of a shear direction acoustic wave in piezoelectric coupled cylinders[J]. Journal of Applied Mechanics,2002,69(3):391-394
[33]Du J, Jin X, Wang J, et al. SH wave propagation in a cylindrically layered piezoelectric structure with initial stress[J]. Acta Mechanica,2007,191(1-2):59-74
[34]Wang X, Pan E, Roy A K. Scattering of antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface[J]. Acta Mechanica,2007,193(3-4):177-195
[35]Shul C W, Lee K Y. Dynamic response of subsurface interface crack in multi-layered orthotropic half-space under anti-plane shear impact loading[J]. International Journal of Solids and Structures,2001,38(20):3563-3574
[36]Pramanik R, Pal S C, Ghosh M L. High frequency scattering due to a pair of time-harmonic antiplane forces on the faces of a finite interface crack between dissimilar anisotropic materials[J]. European Journal of Mechanics A-Solids,1999,18(6):1013-1026
[37]Jiang S N, Jiang Q, Li X F, et al. Piezoelectromagnetic waves in a ceramic plate between two ceramic half-spaces[J]. International Journal of Solids and Structures,2006,43(18-19): 5799-5810
[2]栾桂冬,张金铎,王人乾.压电换能器和换能器阵[M].北京：北京大学出版社,2005.93-96
[3]Bleustein J L. A new surface wave in piezoelectric materials[J]. Applied Physics Letters, 1968,3(12):412-413,
[4]Gulyaev Yu V. Electroacoustic surface waves in solids[J]. Sov Phys Jetp Lett,1969,9(1): 37-38.
[5]Love A E H. Some problems of Geodynamics[D]. Cambridge:Cambridge University Press, London,1911
[6]Fischler C. Propagation and amplification of shear-horizontal waves in piezoelectric plates[J]. J Appl Phys,1971,42(3):919-924
[7]Curtis R G, Redwood M. Transverse surface waves on a piezoelectric material carrying a metal layer of finite thickness[J]. Journal of Applied Physics,1973,44(5):2002-2007
[8]Kielczynski P J, Pajewski W, Szalewski M. Shear-horizontal surface waves on piezoelectric ceramics with depolarized surface layer[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,1989,36(2):287-293
[9]Feng H H, Li X J. Shear-horizontal surface waves in a layered structure of piezo-electric ceramics[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,1993, 40(2):167-170
[10]王子昆,刘华,刘永超,等.层状压电介质中一种奇特的电声波[J].力学学报,2000,32(1)：25-33
[11]金峰,王子昆,王铁军.覆盖层与基底极化方向相反时压电层状半空间中的B-G波[J].固体力学学报,2000,21(2)：95-101
[12]Wang Q, Quek S T, Varadan V K. Love waves in piezoelectric coupled solid media[J]. Smart Materials and Structures,2001,10(2):380-388
[13]Wang Q, Varadan V K. Wave propagation in piezoelectric coupled plates by use of interdigital transducer. Part 1:Dispersion characteristics[J]. International Journal of Solids and Structures,2002,39(5):1119-1130
[14]Wang Q, Varadan V K. Wave propagation in piezoelectric coupled plates by use of interdigital transducer. Part 2:Wave excitation by interdigital transducer[J]. International Journal of Solids and Structures,2002,39(5):1131-1144
[15]Wang Q. SH wave propagation in piezoelectric coupled plates[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,2002,49(5):596-603
[16]Chen S, Tang T T, Wang Z H. Shear-horizontal acoustic wave propagation in piezoelectric bounded plates with metal gratings[J]. Journal of the Acoustical Society of America,2005, 117(6):3609-3615
[17]黄旭涛,严密.功能梯度材料回顾与展望[J].材料科学与工程,1997,15(4)：35-38
[18]刘华,匡震邦,蔡正敏.非均匀压电层状结构中Love波的传播[J].力学学报,2003,35(4)：485-488
[19]Liu J, Wang Z K. The propagation behavior of Love waves in a functionally graded layered piezoelectric structure[J]. Smart Materials and Structures,2005,14:137-146
[20]Qian Z H, Jin F, Wang Z K, et al. Transverse surface waves on a piezoelectric material carrying a functionally graded layer of finite thickness[J]. International Journal of Engineering Science,2007,45(2-8):455-466
[21]Liu H, Wang Z K, Wang T J. Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure[J]. International Journal of Solids and Structures, 2001,38(1):37-51
[22]Jin F, Wang Z K, Kishimoto K. The propagation behavior of Bleustein-Gulyaev waves in a pre-stressed piezoelectric layered structure[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2003,4(2):125-138
[23]Liu H, Kuang Z B, Cai Z M. Propagation of Bleustein-Gulyaev waves in a prestressed layered piezoelectric structure[J]. Ultrasonics,2003,41(5):397-405
[24]Qian Z, Jin F, Wang Z K, et al. Love waves propagation in a piezoelectric layered structure with initial stresses[J]. Acta Mechanica,2004,171(1-2):41-57
[25]Jin F, Qian Z H, Wang Z K, et al. Propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress[J]. Smart Materials and Structures,2005, 14(4):515-523
[26]Su J, Kuang Z B, Liu H. Love wave in ZnO/SiO2/Si structure with initial stresses[J]. Journal of Sound and Vibration,2005,286(4-5):981-999
[27]Fan H, Yang J S, Xu L M. Piezoelectric waves near an imperfectly bonded interface between two half-spaces[J]. Applied Physics Letters,2006,88(20):203509
[28]Fan H, Yang J S, Xu L M. Antiplane piezoelectric surface waves over a ceramic half-space with an imperfectly bonded layerjJ]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,2006,53(9):1695-1698
[29]Chen C L. On the electroacoustic waves guided by a cylindrical piezoelectric interface[J]. Journal of Applied Physics,1973,44(9):3841-3847
[30]Sun C T, Cheng N C. Piezoelectric waves on a layered cylinder[J]. Journal of Applied Physics,1974,45(10):4288-4294
[31]Srinivasamoorthy V R, Anandam C. Torsional wave propagation in an infinite piezo-electric cylinder (622) crystal class[J]. J. Acoust. Soc. Am.1980,67(6):2034-2035
[32]Wang Q, Jin J, Quek S T. Propagation of a shear direction acoustic wave in piezoelectric coupled cylinders[J]. Journal of Applied Mechanics,2002,69(3):391-394
[33]Du J, Jin X, Wang J, et al. SH wave propagation in a cylindrically layered piezoelectric structure with initial stress[J]. Acta Mechanica,2007,191(1-2):59-74
[34]Wang X, Pan E, Roy A K. Scattering of antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface[J]. Acta Mechanica,2007,193(3-4):177-195
[35]Shul C W, Lee K Y. Dynamic response of subsurface interface crack in multi-layered orthotropic half-space under anti-plane shear impact loading[J]. International Journal of Solids and Structures,2001,38(20):3563-3574
[36]Pramanik R, Pal S C, Ghosh M L. High frequency scattering due to a pair of time-harmonic antiplane forces on the faces of a finite interface crack between dissimilar anisotropic materials[J]. European Journal of Mechanics A-Solids,1999,18(6):1013-1026
[37]Jiang S N, Jiang Q, Li X F, et al. Piezoelectromagnetic waves in a ceramic plate between two ceramic half-spaces[J]. International Journal of Solids and Structures,2006,43(18-19): 5799-5810