Influence of Rigid Boundary and Initial Stress on the Propagation of Love Wave
ABSTRACT
In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density. The dispersion equation of the phase velocity has been derived. It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space. The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs.
In the present paper we study the effect of rigid boundary on the propagation of Love waves in an inhomogeneous substratum over an initially stressed half space, where the heterogeneity is both in rigidity and density. The dispersion equation of the phase velocity has been derived. It has been found that the phase velocity of Love wave is considerably influenced by the rigid boundary, inhomogeneity and the initial stress present in the half space. The velocity of Love waves have been calculated numerically as a function of KH (where K is a wave number H is a thickness of the layer) and are presented in a number of graphs.
Cite this paper
nullS. Gupta, A. Chattopadhyay, S. Vishwakarma and D. Majhi, "Influence of Rigid Boundary and Initial Stress on the Propagation of Love Wave," Applied Mathematics, Vol. 2 No. 5, 2011, pp. 586-594. doi: 10.4236/am.2011.25078.
nullS. Gupta, A. Chattopadhyay, S. Vishwakarma and D. Majhi, "Influence of Rigid Boundary and Initial Stress on the Propagation of Love Wave," Applied Mathematics, Vol. 2 No. 5, 2011, pp. 586-594. doi: 10.4236/am.2011.25078.
References
[1] S. Stein and M. Wysession, “An Introduction to Seismology, Earthquakes and Earth Structure,” Blackwell Publishing, Oxford, 2003. [2] P. M. Shearer, “Introduction to Seismology,” 2nd Edition, Cambridge University Press, Cambridge, 2009. [3] Y. Sat?, “Study on Surface Waves VI: Generation of Love and Other Type of SH-Waves,” Departmental Bulletin Paper, Bulletin Earthquake Research Institute, University of Tokyo, Tokyo, 1952, pp.101-120. [4] J. D. Noyer, “The Effect of Variations in Layer Thickness on Love Waves,” Bulletin of Seismology Society of America, Vol. 51, No. 2, 1961, pp. 227-235. [5] A. E. H. Love, “A Treatise on Mathematical Theory of Elasticity,” 4th Edition, Dover Publication, New York, 1944. [6] M. A. Biot, “The Influence of Initial Stress on Elastic Wave,” Journal of Applied Physics, Vol. 11, No. 8, 1940, pp. 522-530. doi:10.1063/1.1712807 [7] M. A. Biot, “Mechanics of Incremental Deformation,” John Wiley and Sons, New York, 1965. [8] A. M. Abd-Alla and S. M. Ahmed, “Propagation of Love Waves in a Non-Homogeneous Orthotropic Elastic Layer under Intial Stress Overlying Semi-Infinite Medium,” Applied Mathematics and Computation, Vol. 106, No. 2, 1999, pp. 265-275. doi:10.1016/S0096-3003(98)10128-5 [9] P. Khurana, “Love Wave Propagation in a Prestressed Medium,” Indian Journal of Pure and Applied Mathematics, Vol. 32, No. 8, 2001, pp. 1201-1207. [10] M. D. Sharma and N. Garg, “Wave Velocities in a Prestressed Anisotropic Elastic Medium,” Journal of Earth System Science, Vol. 115, No. 2, 2007, pp. 257-265. [11] S. C. Das and S. Dey, “Note on Gravity Waves,” Indian Journal of Engineering Mathematics, Vol. 1, No. 2, 1968, pp. 155-160. [12] S. C. Das and S. Dey, “Edge Waves under Initial Stress,” Applied Scientific Research, Vol. 22, No. 1, 1970, pp. 382-389. [13] S. Dey, “Wave Propagation in Two-Layered Medium under Initial Stresses,” Journal of Pure and Applied Geophysics Switzerland, Vol. 90, No. 1, 1971, pp. 38-52. doi:10.1007/BF00875507 [14] S. Dey and S. K. Addy, “Love Waves under Initial Stresses in a Visco-Elastic Medium Overlying an Elastic Half-Space,” Gerlands Beitr ge Zur Geophysik, Vol. 87, No. 4, 1978, pp. 306-311. [15] A. Chattopadhyay and R. K. De, “Propagation of Love Type Waves in a Visco Elastic Initially Stressed Layer Overlying a Visco-Elastic Half-Space with Irregular Interface,” Revue Roumaine Des Sciences Techniques-Series De Mechanique Appliquee, Vol. 26, No. 3, 1981, pp. 449-460. [16] A. Chttopadhyay and B. K. Kar, “On the Dispersion Cur- ves of Love Type Waves in an Initially Stressedcrustal Layer Having an Irregular Interface,” Geophysical Research Bulletin, Vol. 16 No. 1, 1978, pp. 13-23. [17] J. Pujole, “Elastic Wave Propagation and Generation in Seismology,” Cambridge University Press, Cambridge, 2003. doi:10.1017/CBO9780511610127 [18] C. Chapman, “Fundamentals of Seismic Wave Propagation,” Cambridge University Press, Cambridge, 2004. doi:10.1017/CBO9780511616877
[1] S. Stein and M. Wysession, “An Introduction to Seismology, Earthquakes and Earth Structure,” Blackwell Publishing, Oxford, 2003. [2] P. M. Shearer, “Introduction to Seismology,” 2nd Edition, Cambridge University Press, Cambridge, 2009. [3] Y. Sat?, “Study on Surface Waves VI: Generation of Love and Other Type of SH-Waves,” Departmental Bulletin Paper, Bulletin Earthquake Research Institute, University of Tokyo, Tokyo, 1952, pp.101-120. [4] J. D. Noyer, “The Effect of Variations in Layer Thickness on Love Waves,” Bulletin of Seismology Society of America, Vol. 51, No. 2, 1961, pp. 227-235. [5] A. E. H. Love, “A Treatise on Mathematical Theory of Elasticity,” 4th Edition, Dover Publication, New York, 1944. [6] M. A. Biot, “The Influence of Initial Stress on Elastic Wave,” Journal of Applied Physics, Vol. 11, No. 8, 1940, pp. 522-530. doi:10.1063/1.1712807 [7] M. A. Biot, “Mechanics of Incremental Deformation,” John Wiley and Sons, New York, 1965. [8] A. M. Abd-Alla and S. M. Ahmed, “Propagation of Love Waves in a Non-Homogeneous Orthotropic Elastic Layer under Intial Stress Overlying Semi-Infinite Medium,” Applied Mathematics and Computation, Vol. 106, No. 2, 1999, pp. 265-275. doi:10.1016/S0096-3003(98)10128-5 [9] P. Khurana, “Love Wave Propagation in a Prestressed Medium,” Indian Journal of Pure and Applied Mathematics, Vol. 32, No. 8, 2001, pp. 1201-1207. [10] M. D. Sharma and N. Garg, “Wave Velocities in a Prestressed Anisotropic Elastic Medium,” Journal of Earth System Science, Vol. 115, No. 2, 2007, pp. 257-265. [11] S. C. Das and S. Dey, “Note on Gravity Waves,” Indian Journal of Engineering Mathematics, Vol. 1, No. 2, 1968, pp. 155-160. [12] S. C. Das and S. Dey, “Edge Waves under Initial Stress,” Applied Scientific Research, Vol. 22, No. 1, 1970, pp. 382-389. [13] S. Dey, “Wave Propagation in Two-Layered Medium under Initial Stresses,” Journal of Pure and Applied Geophysics Switzerland, Vol. 90, No. 1, 1971, pp. 38-52. doi:10.1007/BF00875507 [14] S. Dey and S. K. Addy, “Love Waves under Initial Stresses in a Visco-Elastic Medium Overlying an Elastic Half-Space,” Gerlands Beitr ge Zur Geophysik, Vol. 87, No. 4, 1978, pp. 306-311. [15] A. Chattopadhyay and R. K. De, “Propagation of Love Type Waves in a Visco Elastic Initially Stressed Layer Overlying a Visco-Elastic Half-Space with Irregular Interface,” Revue Roumaine Des Sciences Techniques-Series De Mechanique Appliquee, Vol. 26, No. 3, 1981, pp. 449-460. [16] A. Chttopadhyay and B. K. Kar, “On the Dispersion Cur- ves of Love Type Waves in an Initially Stressedcrustal Layer Having an Irregular Interface,” Geophysical Research Bulletin, Vol. 16 No. 1, 1978, pp. 13-23. [17] J. Pujole, “Elastic Wave Propagation and Generation in Seismology,” Cambridge University Press, Cambridge, 2003. doi:10.1017/CBO9780511610127 [18] C. Chapman, “Fundamentals of Seismic Wave Propagation,” Cambridge University Press, Cambridge, 2004. doi:10.1017/CBO9780511616877