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

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.