Singh, B. (2013). Rayleigh Wave in an Initially Stressed Transversely Isotropic Dissipative Half-Space. Journal of Solid Mechanics, 5(3), 270-277.

B Singh. "Rayleigh Wave in an Initially Stressed Transversely Isotropic Dissipative Half-Space". Journal of Solid Mechanics, 5, 3, 2013, 270-277.

Singh, B. (2013). 'Rayleigh Wave in an Initially Stressed Transversely Isotropic Dissipative Half-Space', Journal of Solid Mechanics, 5(3), pp. 270-277.

Singh, B. Rayleigh Wave in an Initially Stressed Transversely Isotropic Dissipative Half-Space. Journal of Solid Mechanics, 2013; 5(3): 270-277.

Rayleigh Wave in an Initially Stressed Transversely Isotropic Dissipative Half-Space

^{}Department of Mathematics, Post Graduate Government College, Sector 11,Chandigarh

Abstract

The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the surface wave solutions. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the frequency equation of Rayleigh wave. The numerical values of the non-dimensional speed of Rayleigh wave speed are computed for different values of frequency and initial stress parameter. The effects of transverse isotropy and initial stress parameter are observed on the Rayleigh wave speed.

[1] Sinha S.B., 1964, Transmission of elastic waves through a homogenous layer sandwiched in homogenous media, Journal of Physics of the Earth 12:1-4.

[2] Gupta R. N., 1965, Reflection of plane waves from a linear transition layer in liquid media, Geophysics 30:122-131.

[3] Tooly R. D., Spencer T.W., Sagoci H.F., 1965, Reflection and transmission of plane compressional waves, Geophysics 30:552-570.

[4] Gupta R.N., 1966, Reflection of elastic waves from a linear transition layer, The Bulletin of the Seismological Society of America 56:511-526. [5] Gupta R. N.,1967, Propagation of SH-waves in inhomogeneous media, The Journal of the Acoustical Society of America 41:1328-1329.

[6] Acharya H.K., 1970, Reflection from the free surface of inhomogeneous media, The Bulletin of the Seismological Society of America 60:1101-1104. [7] Cerveny V., 1974, Reflection and transmission coefficients for transition layers, Studia Geophysica et Geodaetica 17:59-68.

[8] Singh B. M., Singh S. J., Chopra S. D., 1978, Reflection and refraction of SH-waves at the plane boundary between two laterally and vertically heterogeneous solids, Acta Geophysica Polonica 26:209-216.

[9] Singh B., 2008, Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space, Applied Mathematics and Computation 198:498-505. [10] Sharma M. D., 2007, Effect of initial stress on reflection at the free surfaces of anisotropic elastic medium, Journal of Earth System Science 116:537-551.

[11] Dey S., Dutta D., 1998, Propagation and attenuation of seismic body waves in initially stressed dissipative medium, Acta Geophysica Polonica 46: 351-365.

[12] Selim M. M., Ahmed M. K., 2006, Propagation and attenuation of seismic body waves in dissipative medium under initial and couple stresses, Applied Mathematics and Computation 182:1064-1074.

[13] Biot M. A., 1965, Mechanics of Incremental Deformation, John Wiley and Sons Inc., New York. [14] Selim M. M., 2008, Reflection of plane waves at free surface of an initially stressed dissipative medium, World Academy of Science, Engineering and Technology 30:36-43.

[15] Singh B., Arora J., 2011, Reflection of plane waves from a free surface of an initially stressed transversely iso- tropic dissipative medium, Applied Mathematics 2:1129-1133.

[16] Biot M. A., 1940, The influence of initial stress on elastic waves, Journal of Applied Physics 11:522-530.

[17] Babich S. Y., Guz A. N., Zhuk A. P, 1979 , Elastic waves in bodies with initial stress, Soviet Applied Mechanics 15:277-291.

[18] Guz A.N., 2002, Elastic waves in bodies with initial (residual) stresses, International Applied Mechanics38:23-59.

[19] Fung Y. C., 1965, Foundation of Solid Mechanics, Prentice Hall of India, New Delhi.