**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31103

##### The Effect of the Initial Stresses on the Reflection and Transmission of Plane Quasi-Vertical Transverse Waves in Piezoelectric Materials

**Authors:**
Abo-El-Nour N. Abd-Alla,
Fatimah A. Alsheikh

**Abstract:**

This study deals with the phenomena of reflection and transmission (refraction) of qSV-waves, for an incident of quasi transverse vertically waves, at a plane interface of two semi-infinite piezoelectric elastic media under the influence of the initial stresses. The relations governing the reflection and transmission coefficients of these reflected waves for various suitable boundary conditions are derived. We have shown analytically that reflection and transmission coefficients of (qP) and (qSV) waves depend upon the angle of incidence, the parameters of electric potential, the material constants of the medium as will as the initial stresses presented in the media. The numerical calculations of the reflection and transmission amplitude ratios for different values of initial stresses have been carried out by computer for different materials as examples and the results are given in the form of graphs. Finally, some of particular cases are considered.

**Keywords:**
Piezoelectricity,
Quasi plane vertical transverse waves,
reflection and transmission coefficients,
initial stresses,
PZT-5H Ceramic,
Aluminum Nitride (AlN)

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1062324

**References:**

[1] Abd-alla A. and Al-sheikh F.A. "Reflection and refraction of plane quasi-longitudinal waves at an interface of two piezoelectric media under initial stresses," Archive of Applied Mechanics, Springer-Verlag (2008), DOI 10.1007/S00419=008=0257-y.

[2] Achenbach J.D., "Wave propagation in elastic solids", North- Holland Publishing Company- Amsterdam, Vol. 16, (1973).

[3] Auld B. A., "Acoustic Field and Waves in Solids," V. I,II, Robert E. Kriger Publishing Company, Malabar, Florida (1990).

[4] Chattopadhyay, A., Venhateswarla, R., and Saha, S., "Reflection of quasi-P waves and quasi-SV waves at free and rigid boundaries of a fibre-reinforced medium", Sadhana 27(6), 613-630, (2002).

[5] Dey, S., and Addy, S., "Reflection and refraction of plane waves under initial stresses at an interface", Int. J. Non-Linear. Mech. 14 (2), 101-110, (1979).

[6] Hussain W. and Ogden R.W., "The effect of pre-strain on the reflection and transmission of plane waves at an elastic interface," Int. J. Eng. Sci., V.39(8), pp.929-950 (2001).

[7] Khurana A. and Tomar S.K., "Propagation of plane elastic waves at a plane interface between two electro-microelastic solid halfspaces," Int. J. Solids Struct. 44, pp.3773-3795 (2007).

[8] Kumar R. and Singh M., "Reflection/transmission of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic half-spaces," Materials Science and Engineering: A, V.472(1-2),pp. 83-96 (2008).

[9] Othman M. I.A. and Song Y., "Reflection of magneto-thermoelastic waves from a rotating elastic half-space," Int. J. Eng. Sci., 46(5), pp.459-474 (2008),

[10] Othman M. I.A. and Song Y., "Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation," Int. J. Solids and Structures, 44 (17), pp.5651-5664 (2007).

[11] Pang Y., Wang Y. S., Liu J.X. and Fang D. N., "Reflection and refraction of plane waves at the interface between piezoelectric and piezomagnetic media," Int. J. Eng. Sci., In Press, Corrected Proof, Available online 6 June (2008).

[12] Singh, B., "Reflection of SV waves from the free surface of an elastic solid in generalized thermoelastic diffusion", J. Sound Vib. 291(3-5), 764-778, (2006).

[13] Singh S.J. and Khurana S., "Reflection and transmission of P- and SV-waves at the interface two between monoclinic elastic halfspaces," Proc. Natl. Acad. Sci. India 71A (IV), pp.305-319(2001).

[14] Singh, B., and Khurana, S., "Reflection of P and SV waves the interface of a monoclinic elastic half-space", Proc. Indian Acad. Sci. (Earth Planet. Sci.) 14, 401-412, (2002).

[15] Singh J. and Tomar S.K., "Reflection and transmission of transverse waves at a plane interface between two different porous elastic solid half-spaces," Applied Mathematics and Computation, 176, (1),pp.364-378( 2006).

[16] Tomar S.K. and Garg M., "Reflection and transmission of waves from a plane interface between two microstretch solid halfspaces," Int. J. Eng. Sci. 43 (1-2) (2005), pp. 139-169 Erratum, ibid, 44(3-4) (2006) 285-287.

[17] Tomar S.K. and Singh J., "Transmission of longitudinal waves through a plane interface between two dissimilar porous elastic solid half-spaces," Applied Mathematics and Computation, 169,(1), pp.671-688( 2005).