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

ABSTRACT

The problem regarding the reflection of plane waves in a transversely isotropic dissipative medium is considered, in which we are studying about the reflection of incidence waves in initially stressed dissipative half space. After solving the governing equations, we find the two complex quasi-*P* (*qP*) and quasi-*SV* (*qSV*) waves. The occurrence of reflected waves is studied to calculate the reflection coefficient and the energy partition of incidence wave at the plane boundary of the dissipative medium. Numerical example is considered for the reflection coefficient and the partition of incident energy, in which we study about the effect of rotation, initial stresses and magnetic field.

Cite this paper

S. Shekhar and I. Parvez, "Effect of Rotation, Magnetic Field and Initial Stresses on Propagation of Plane Waves in Transversely Isotropic Dissipative Half Space,"*Applied Mathematics*, Vol. 4 No. 8, 2013, pp. 107-113. doi: 10.4236/am.2013.48A015.

S. Shekhar and I. Parvez, "Effect of Rotation, Magnetic Field and Initial Stresses on Propagation of Plane Waves in Transversely Isotropic Dissipative Half Space,"

References

[1] M. A. Biot, “The Influence of Initial Stress on Elastic Waves,” Journal of Applied Physics, Vol. 11, No. 8, 1940, pp. 522-530. doi:10.1063/1.1712807

[2] J. D. Achenbach, “Wave Propagation in Elastic Solids,” North-Holland Pub. Co., New York, 1973.

[3] P. Borejko, “Reflection and Transmission Coefficients for Three-Dimensional Plane Waves in Elastic Media,” Wave Motion, Vol. 24, No. 4, 1996, pp. 371-393. doi:10.1016/S0165-2125(96)00026-1

[4] M. A. Biot, “Mechanics of Incremental Deformation,” Wiley, New York, 1965.

[5] S. Dey and D. Dutta, “Propagation and Attenuation of Seismic Body Waves in Initially Stressed Dissipative Me dium,” Acta Geophysica, Vol. 46, No. 3, 1998, pp. 351-366.

[6] R. W. Ogden and D. Sotirropoulos, “Reflection of Plane Waves from the Boundary of a Pre-Stressed Compressi ble Elastic Half-Space,” IMA Journal of Applied Mathe matics, Vol. 61, No. 1, 1998, pp. 61-90. doi:10.1093/imamat/61.1.61

[7] S. K. Roychoudhuri and S. Banerjee, “Magneto-Thermo elastic Interaction in an Infinite Viscoelastic Cylinder of Temperature-Rate Dependent Material Subjected to a Pe riodic Loading,” International Journal of Engineering Science, Vol. 36, No. 5-6, 1998, pp. 635-643. doi:10.1016/S0020-7225(97)00096-7

[8] M. D. Sharma, “Effect of Initial Stress on Reflection at the Free Surfaces of Anisotropic Elastic Medium,” Journal of Earth System Science, Vol. 116, No. 6, 2007, pp. 537-551. doi:10.1007/s12040-007-0049-8

[9] R. D. Tooly, T. W. Spencer and H. F. Sagoci, “Reflection and Transmission of Plane Compressional Waves,” Geo physics, Vol. 30, No. 4, 1965, pp. 552-570. doi:10.1190/1.1439622

[10] A. Chattopadhyay and R. L. K. Venkateswarlu, “Reflec tion and Refraction of Quasi P and SV Waves at the In terface of Fiber-Reinforced Media,” Advanced Studies in Theoretical Physics, Vol. 1, No. 2, 2007, pp. 57-73.

[11] A. N. Norris, “Propagation of Plane Waves in a Pre Stressed Elastic Media,” Journal of the Acoustical Society of America, Vol. 74, No. 5, 1983, pp. 1642-1643. doi:10.1121/1.390131

[12] B. Singh and J. Arora, “Reflection of Plane Waves from a Free Surface of an Initially Stressed Transversely Iso tropic Dissipative Medium,” Applied Mathematics, Vol. 2, 2011, pp. 115-125.

[13] B. Singh and J. Arora, “Reflection of Plane Waves from Free Surface of an Initially Stressed Rotating Orthotropic Dissipative Solid Half Space,” Engineering, Vol. 4, No. 3, 2012, pp. 170-175. doi:10.4236/eng.2012.43022

[14] M. M. Selim, “Reflection of Plane Waves at Free Surface of an Initially Stressed Dissipative Medium,” World Academy of Science, Engineering and Technology, Vol. 30, 2008, pp. 120-127.

[15] T. Kong, D. X. Li and X. Wang, “Thermo-Magneto-Dy namic Stresses and Perturbation of Magnetic Field Vector in a Non-Homogeneous Hollow Cylinder,” Applied Ma thematical Modelling, Vol. 33, No. 11, 2009, pp. 2939-2950. doi:10.1016/j.apm.2008.10.003

[1] M. A. Biot, “The Influence of Initial Stress on Elastic Waves,” Journal of Applied Physics, Vol. 11, No. 8, 1940, pp. 522-530. doi:10.1063/1.1712807

[2] J. D. Achenbach, “Wave Propagation in Elastic Solids,” North-Holland Pub. Co., New York, 1973.

[3] P. Borejko, “Reflection and Transmission Coefficients for Three-Dimensional Plane Waves in Elastic Media,” Wave Motion, Vol. 24, No. 4, 1996, pp. 371-393. doi:10.1016/S0165-2125(96)00026-1

[4] M. A. Biot, “Mechanics of Incremental Deformation,” Wiley, New York, 1965.

[5] S. Dey and D. Dutta, “Propagation and Attenuation of Seismic Body Waves in Initially Stressed Dissipative Me dium,” Acta Geophysica, Vol. 46, No. 3, 1998, pp. 351-366.

[6] R. W. Ogden and D. Sotirropoulos, “Reflection of Plane Waves from the Boundary of a Pre-Stressed Compressi ble Elastic Half-Space,” IMA Journal of Applied Mathe matics, Vol. 61, No. 1, 1998, pp. 61-90. doi:10.1093/imamat/61.1.61

[7] S. K. Roychoudhuri and S. Banerjee, “Magneto-Thermo elastic Interaction in an Infinite Viscoelastic Cylinder of Temperature-Rate Dependent Material Subjected to a Pe riodic Loading,” International Journal of Engineering Science, Vol. 36, No. 5-6, 1998, pp. 635-643. doi:10.1016/S0020-7225(97)00096-7

[8] M. D. Sharma, “Effect of Initial Stress on Reflection at the Free Surfaces of Anisotropic Elastic Medium,” Journal of Earth System Science, Vol. 116, No. 6, 2007, pp. 537-551. doi:10.1007/s12040-007-0049-8

[9] R. D. Tooly, T. W. Spencer and H. F. Sagoci, “Reflection and Transmission of Plane Compressional Waves,” Geo physics, Vol. 30, No. 4, 1965, pp. 552-570. doi:10.1190/1.1439622

[10] A. Chattopadhyay and R. L. K. Venkateswarlu, “Reflec tion and Refraction of Quasi P and SV Waves at the In terface of Fiber-Reinforced Media,” Advanced Studies in Theoretical Physics, Vol. 1, No. 2, 2007, pp. 57-73.

[11] A. N. Norris, “Propagation of Plane Waves in a Pre Stressed Elastic Media,” Journal of the Acoustical Society of America, Vol. 74, No. 5, 1983, pp. 1642-1643. doi:10.1121/1.390131

[12] B. Singh and J. Arora, “Reflection of Plane Waves from a Free Surface of an Initially Stressed Transversely Iso tropic Dissipative Medium,” Applied Mathematics, Vol. 2, 2011, pp. 115-125.

[13] B. Singh and J. Arora, “Reflection of Plane Waves from Free Surface of an Initially Stressed Rotating Orthotropic Dissipative Solid Half Space,” Engineering, Vol. 4, No. 3, 2012, pp. 170-175. doi:10.4236/eng.2012.43022

[14] M. M. Selim, “Reflection of Plane Waves at Free Surface of an Initially Stressed Dissipative Medium,” World Academy of Science, Engineering and Technology, Vol. 30, 2008, pp. 120-127.

[15] T. Kong, D. X. Li and X. Wang, “Thermo-Magneto-Dy namic Stresses and Perturbation of Magnetic Field Vector in a Non-Homogeneous Hollow Cylinder,” Applied Ma thematical Modelling, Vol. 33, No. 11, 2009, pp. 2939-2950. doi:10.1016/j.apm.2008.10.003