Abstract
This paper is devoted to study a problem of reflection and refraction of quasi-longitudinal waves under initial stresses at an interface of two anisotropic piezoelectric media with different properties. One of the two media is aluminum nitride, which is considered the down piezoelectric medium and the above medium is chosen as PZT-5H ceramics. The two piezoelectric media welded are assumed to be anisotropic of a type of a transversely isotropic crystals (hexagonal crystal structure, class 6 mm). The equations of motion and constitutive relations for the piezoelectric media have been written. Suitable boundary conditions are used to obtain the reflection and refraction coefficients. For an incidence of quasi-longitudinal plane waves, four independent-type amplitude ratios of elastic displacement components for plane waves, called quasi-longitudinal (qP) and quasi-shear vertical (qSV) waves, are shown to exist. Also, it is observed that there exist four dependent amplitude ratios of electric potential, which are proportional to the previous four types. Finally, it is found that the coefficients of reflection and refraction are functions of angle of incidence, elastic constants, piezoelectric potential parameters and the initial stresses. Numerical computations and the results obtained are depicted graphically. In the end, a particular case has been reduced from the present study. This investigation is considered important because the initial stresses in such practical problems are inevitable and may result in frequency shift, a change in the velocity of surface waves and controlling the selectivity of a filter compensation of the devices.
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Abd-alla, A.N., Abo-dahab, A.M.: The influence of the viscosity and the magnetic field on reflection and transmission of waves at interface between magneto-viscoelastic materials. MECCANICA, On line (2008)
Achenbach J.D.: Wave propagation in elastic solids, vol. 16. North-Holland, Amsterdam (1973)
Auld B.A.: Acoustic Field and Waves in Solids, vol. I, II. Robert E. Kriger Publishing Company, Malabar (1990)
Chattopadhyay A., Saha S.: Reflection and refraction of P waves at the interface of two monoclinic media. Int. J. Eng. Sci. 34(11), 1271–1284 (1996)
Dey S., Addy S.K.: Reflection and refraction of plane waves under initial stresses at an interface. Int. J. Non-Linear Mech. 14(2), 101–110 (1997)
Dieulesaint E., Royer D.: Elastic Waves in Solids. Wiley, New York (1980)
Eringen A.C., Suhubi E.S.: Elastodynamics, vol. II. Academic press, New York (1975)
Henneke E.G.: Reflection-refraction of stress waves at a plane boundary between anisotropic media. J. Acoust. Soc. Am. 51, 210–217 (1972)
Hussain W., Ogden R.W.: The effect of pre-strain on the reflection and transmission of plane waves at an elastic interface. Int. J. Eng. Sci. 39, 929–950 (2001)
Khurana A., Tomar S.K.: Propagation of plane elastic waves at a plane interface between two electro-microelastic solid half-spaces. Int. J. Solids Struct. 44(11–12), 3773–3795 (2007)
Khurana A., Tomar S.K.: Transmission of longitudinal wave at a plane interface between micropolar elastic and chiral solid half-spaces: incidence from micropolar half-space. J. Sound Vib. 311(3–5), 973–9908 (2008)
Kumar R., Singh M.: Reflection/transmission of plane waves at an imperfectly bonded of interface of two orthotropic generalized thermoelastic half-space. Mater. Sci. Eng. A 472(1–2), 83–96 (2008)
Kumar R., Sharma N., Ram P.: Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media. Theor. Appl. Fract. Mech. 49(3), 305–312 (2008)
Mandal B.: Reflection and transmission properties of elastic waves on a plane interface for general anisotropic media. J. Acoust. Soc. Am. 90(2), 1106–1118 (1991)
Osipov I.O.: Reflection and refraction of plane longitudinal waves at the interface of a liquid and an anomalous anisotropic medium. J. Appl. Math. Mech. 61(2), 203–213 (1997)
Parton V.Z., Kudryavtsev B.A.: Electromagnetoelasticity: Piezoelectrics and Electrically Conductive Solids. Gordon & Breach, New York (1988)
Qian Z., Jin F., Kishimoto K., Wang Z.: Effect of initial stress on the propagation behavior of SH-waves in multilayered piezoelectric composite structures. Sens. Actuat. A 112, 368–375 (2004)
Rokhlin S.I., Bolland T.K., Adler L.: Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media. J. Acoust. Soc. Am. 79, 906–918 (1986)
Singh B.: Reflection and refraction of plane waves at a liquid thermo-microstretch elastic solid interface. Int. J. Eng. Sci. 39, 583–598 (2001)
Tomar S.K., Singh J.: Transmission of longitudinal waves through a plane interface between two dissimilar porous elastic solid half-spaces. Appl. Math. Comput. 169(1), 671–688 (2005)
Tomar S.K., Garg M.: Reflection and transmission of waves from a plane interface between two microstretch solid half-space. Int. J. Eng. Sci. 43, 139–169 (2005) (Erratam in Int. J. Eng. Sci. 44, 285–287, 2006)
Tomar S.K., Arora A.: Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids. Int. J. Solids Struct. 43(7–8), 1991–2013 (2006)
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Abd-alla, Aen.N., Alsheikh, F.A. Reflection and refraction of plane quasi-longitudinal waves at an interface of two piezoelectric media under initial stresses. Arch Appl Mech 79, 843–857 (2009). https://doi.org/10.1007/s00419-008-0257-y
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DOI: https://doi.org/10.1007/s00419-008-0257-y