Effect of initial stress on reflection at the free surface of anisotropic elastic medium

Abstract

The propagation of plane waves is considered in a general anisotropic elastic medium in the presence of initial stress. The Christoffel equations are solved into a polynomial of degree six. The roots of this polynomial represent the vertical slowness values for the six quasi-waves resulting from the presence of a discontinuity in the medium. Three of these six values are identified with the three quasi-waves traveling in the medium but away from its boundary. Reflection at the free plane surface is studied for partition of energy among the three reflected waves. For post-critical incidence, the reflected waves are inhomogeneous (evanescent) waves. Numerical examples are considered to exhibit the effects of initial stress on the phase direction, attenuation and reflection coefficients of the reflected waves. The phase velocities and energy shares of the reflected waves change significantly with initial stress as well as anisotropic symmetry. The presence of initial stress, however, has a negligible effect on the phase directions of reflected waves.

Effect of Rotation, Magnetic Field and Initial Stresses on Propagation of Plane Waves in Transversely Isotropic Dissipative Half Space

“…Material parameter for copper-alloy is chos numerical model of magneto-elastic medium are given by [8,11] mum in the range of 50˚ < θ < 85˚ for Z PP and 20˚ < θ < 80˚ for Z PS .…”

“…Borejko [3] introduced the reflection and transmission coefficients for three dimensional plane waves in elastic media. By using the Biot's theory [4] several researchers [5][6][7][8][9] have studied extensively the propagation of elastic waves. The problem related to reflection and refraction of qP and qSV waves at the interface of Fiber-reinforced medium has been discussed by Chattopadhyay and Venkateswarlu [10].…”

Rotation Effect on Reflection of Plane Elastic Waves at a Free Surface Under Initial Stress, Magnetic Field and Temperature Field

“…Kumar and Pratap 22 studied reflection of plane waves in a heat flux dependent microstretch thermoelastic solid half space. Sharma 23 investigated the effect of initial stress on reflection at the free surfaces of an isotropic elastic medium. Some researchers in past have investigated different problem of rotating media.…”

Reflection of plane waves in an initially stressed perfectly conducting transversely isotropic solid half-space

“…The problems on reflection and refraction phenomena in media with initial stresses, anisotropy, thermal, electric and magnetic fields are studied by many researchers, for example, Knott (1899); Gutenberg (1944); Tooly et al (1965); Yu and Tang (1966); Acharya (1970); De and Sengupta (1972); Auld (1973); Achenbach (1976); Keith and Crampin (1977); Dey and Addy (1979); Tolstoy (1982); Norris (1983); Pal and Chattopadhyay (1984); Das et al (1994); Rakshit and Sengupta (1998); Ahmad and Khan (2001); Chattopadhyay and Rogerson (2001); Selim and Ahmed (2006); Sharma (2007); Singh (2010) and many more.…”