Reflection of Plane Wave at Traction-Free Surface of a Pre-Stressed Functionally Graded Piezoelectric Material (FGPM) Half-Space

Document Type: Research Paper

Authors

Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad-826004,India

Abstract

This paper is devoted to study a problem of plane waves reflection at a traction-free surface of a pre-stressed functionally graded piezoelectric material (FGPM). The effects of initial stress and material gradient on the reflection of plane waves are studied in this paper. Secular equation has been derived analytically for the pre-stressed FGPM half-space and used to show the existence of two coupled waves namely and  Continuity condition of stress, electrical potential and electrical displacement at traction free surface is used to obtain the reflection coefficient of  and waves. Results of the problem are shown graphically and effects of initial stress and material gradient are discussed for a particular case of Lithium niobate material.

Keywords


[1] Shana Z., Josse F., 1992, Reflection of bulk wave at a piezoelectric crystal-viscous conductive liquid interface, Journal of the Acoustical Society of America 91: 854-860.
[2] Noorbehesht B., Wade G., 1980, Reflection and transmission of plane elastic-wave at the boundary between piezoelectric materials and water, Journal of the Acoustical Society of America 67: 1947-1953.
[3] Chattopadhyay A., Saha S., 1996, Reflection and refraction of P wave at the interface of two monoclinic media, International Journal of Engineering Science 34 (11): 1271-1284.
[4] Kaur J., Tomar S. K., 2004, Reflection and refraction of SH-wave at a corrugated interface between two monoclinic elastic half-spaces, International Journal for Numerical and Analytical Methods in Geomechanics 28(15): 1543-1575.
[5] Kyame J.J., 1949, Wave propagation in piezoelectric crystals, Journal of the Acoustical Society of America 21: 159-167.
[6] Yang J.S., 2006, A review of a few topics in piezoelectricity, Applied Mechanics Reviews 59: 335-345.
[7] Fang H., Yang J., Jiang Q., 2001, Surface acoustic wave propagating over a rotating piezoelectric half-space, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 48: 998-1004.
[8] Wang Q., 2002, Wave propagation in a piezoelectric coupled solid medium, Journal of Applied Mechanics 69: 819-824.
[9] Yang J.S., Zhou H.G., 2005, An interface wave in piezoelectromagnetic materials, International Journal of Applied Electromagnetics and Mechanics 21: 63-68.
[10] Pang Y., Yue-Sheng W., 2008, Reflection and refraction of plane wave at the interface between piezoelectric and piezomagnetic media, International Journal of Engineering Science 46: 1098-1110.
[11] Sharma J.N., Walia V., Gupta S.K., 2008, Reflection of piezothermoelastic wave from the charge and stress free boundary of a transversely isotropic half space, International Journal of Engineering Science 46: 131-146.
[12] Chattopadhyay A., Saha S., Chakraborty M., 1997, Reflection and transmission of shear wave in monoclinic media, International Journal for Numerical and Analytical Methods in Geomechanics 21(7): 495-504.
[13] Sharma J.N., Walia V., 2007, Further investigations on rayleigh wave in piezothermoelastic materials, Journal of Sound and Vibration 301: 189-206.
[14] Abd-alla A.N., Alsheikh F.A., 2009, Reflection and refraction of plane quasilongitudinal wave at an interface of two piezoelectric media under initial stresses, Archive of Applied Mechanics 79: 843-857.
[15] Singh B., 2010, Wave propagation in a pre-stressed piezoelectric half-space, Acta Mechanica 211: 337-344.
[16] Guo X., Wei P., 2014, Effect of initial stress on the reflection and transmission wave at the interface between two piezoelectric half-spaces, International Journal of Solids and Structures 51: 3735-3751.
[17] Wang Z. K., Shang, F. L., 1997, Cylindrical buckling of piezoelectric laminated plates, Acta Mechanica Solida Sinica 18: 101-108.
[18] Weis R.S., Gaylord, T.K., 1985, Lithium niobate: summary of physical properties and crystal structure, Applied Physics A 37: 191-203.