The Effect of the Initial Stresses on the Reflection and Transmission of Plane Quasi-Vertical Transverse Waves in Piezoelectric Materials
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.
[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).
[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).
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55215", author = "Abo-El-Nour N. Abd-Alla and Fatimah A. Alsheikh", title = "The Effect of the Initial Stresses on the Reflection and Transmission of Plane Quasi-Vertical Transverse Waves in Piezoelectric Materials", 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 = "Quasi plane vertical transverse waves, reflection and transmission coefficients, initial stresses, PZT-5H Ceramic, Aluminum Nitride (AlN), Piezoelectricity", volume = "3", number = "2", pages = "105-8", }
