Abstract
It is generally known that surface acoustic waves, or Rayleigh waves, have different mode shapes in infinite plates. To be precise, there are both exponentially decaying and growing components in plates appearing in pairs, representing symmetric and antisymmentric modes in a plate. As the plate thickness increases, the combined modes will approach the Rayleigh mode in a semi-infinite solid, exhibiting surface acoustic wave deformation and velocity. In this study, the two-dimensional theory for surface acoustic waves in finite plates is extended to include the exponentially growing modes in the expansion function. With these extra equations, we study the surface acoustic waves in a plate with different thickness to examine the coupling of the exponentially decaying and growing modes. It is found that for small thickness, the two groups of waves are strongly coupled, showing the significance of including the effect of thickness in analysis. As the thickness increases to certain values, such as more than five wavelengths, the exponentially decaying modes alone will be able to predict vibrations of surface acoustic wave modes accurately, thus simplifying the equations and solutions significantly.
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References
Auld B A. Acoustic Fields and Waves in Solids. 2nd ed. Malabar, Florida: Krieger Publishing Company, 1990
Royer D, Dieulesaint E. Elastic Waves in Solids (vols. I and II). Berlin: Springer, 2000
Hashimoto K Y. Surface Acoustic Wave Devices in Telecommunications: Modelling and Simultions. Berlin: Springer, 2000
Victorov I A. Rayleigh and Lamb Waves: Physical Theory and Applications. New York: Plenum Press, 1967
Liu G R, Xi Z C. Elastic Waves in Anisotropic Laminates. Boca Raton, Florida: CRC Press, 2001
Tiersten H F. Elastic surface waves guided by thin films. J Appl Phys, 1969, 40(2): 770–789
Liu G R, Tani J. Surface waves in functionally gradient piezoelectric plates. ASME J Vibr Acoust, 1993, 36: 440–447
Bövik P. A comparison between the Tiersten model and O(H) boundary conditions for elastic surface acoustic waves guided by thin layers. ASME J Appl Mech, 1996, 63: 162–167
Liang W, Shen Y P. Gradient surface ply model of SH wave propagation in SAW sensors. Acta Mech Sin, 1999, 15: 155–164
Fang H Y, Yang J S, Jiang Q. Surface acoustic waves propagating over a rotating piezoelectric half-space. IEEE Trans Ultrason Ferroelect Freq Contr, 2001, 48(4): 998–1044
Alshits V I, Maugin G A. Dynamics of multilayers: Elastic waves in an anisotropic graded or stratifield plate. Wave Motion, 2005, 41: 357–394
Wang Q, Quek S T, Varadan V K. Analytical solution for shear horizontal wave propagation in piezoelectric coupled media by interdigital transducer. ASME J Appl Mech, 2005, 72: 341–350
Song B, Hong W. A new algorithm for the extraction of the surface waves for the Green’s function in layered dielectrics. Sci China Ser F-Inf Sci, 2002, 45(2): 143–151
Wang X M, Zhang H L. Modeling of elastic wave propagation on a curved free surface using an improved finite-difference algorithm. Sci China Ser G-Phys Mech Astron, 2004, 47(5): 633–648
Chen Z J, Han T, Ji X J, et al. Lamb wave sensors array for nonviscous liquid sensing. Sci China Ser G-Phys Mech Astron, 2006, 49(4): 461–472
Wang J, Hashimoto K Y. A two-dimensional theory for the analysis of surface acoustic waves in anisotropic elastic solids. In: Proceedings of 2003 IEEE International Ultrasonics Symposium, Oct 5–8. Hawaii: IEEE Inc, 2003. 637–640
Wang J, Hashimoto K Y. A two-dimensional theory for the analysis of surface acoustic waves in finite elastic solids. J Sound Vibr, 2006, 295: 838–855
Wang J, Lin J B. A two-dimensional theory for surface acoustic wave analysis in finite piezoelectric solids. J Intell Mater Syst Struct, 2005, 16(7–8): 623–629
Wang J, Lin J B, Wan Y P, et al. A two-dimensional analysis of surface acoustic waves in finite solids with considerations of electrodes. Int J Appl Electromagn Mech, 2005, 22(1–2): 53–68
Mindlin R D. An Introduction to the Mathematical Theory of Vibrations of Elastic Plates, Fort Monmouth. New Jersey: US Army Signal Corps Engineering Laboratories, 1955
Lee P C Y, Yu J D, Lin W S. A new two-dimensional theory for vibrations of piezoelectric crystal plates with electroded faces. J Appl Phys, 1998, 83(3): 1213–1223
Peach R C. A normal mode expansion for the piezoelectric plates and certain of its applications. IEEE Trans Ultrason Ferroelec Freq Contr, 1988, 35: 593–611
Wang J, Yang J S. Higher-order theories of piezoelectric plates and applications. Appl Mech Rev, 2000, 53(4): 87–99
Wang J, Yong Y K, Imai T. Finite element analysis of the piezoelectric vibrations of quartz plate resonators with higher-order plate theory. Int J Solids Struct, 1999, 36(15): 2303–2319
Wang J, Yu J D, Yong Y K, et al. A new theory for electroded piezoelectric plates and its finite element application for the forced vibrations of quartz crystal resonators. Int J Solids Struct, 2000, 37: 5653–5673
Tiersten H F. Linear Piezoelectric Plate Vibrations. New York: Plenum Press, 1969
Yang J S. An Introduction to the Theory of Piezoelectricity. Berlin: Springer, 2005
ANSI/IEEE std 176–1987. IEEE Standard on Piezoelectricity. Piscataway, New Jersey: IEEE Inc, 1988
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Supported by Qianjiang River Fund established by Zhejiang Provincial Government and Ningbo University and administered by Ningbo University and the National Natural Science Foundation of China (Grant No. 10572065)
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Wang, J., Du, J. & Pan, Q. A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions. SCI CHINA SER G 50, 631–649 (2007). https://doi.org/10.1007/s11433-007-0059-1
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DOI: https://doi.org/10.1007/s11433-007-0059-1