Dispersion of Love Wave in a Fiber-Reinforced Medium Lying Over a Heterogeneous Half-Space with Rectangular Irregularity
محورهای موضوعی : Engineering
R.M Prasad
1
(Department of Mathematics, S.N. Sinha College, Tekari, Gaya, Bihar-824236, India)
S Kundu
2
(Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand-826004 ,India)
کلید واژه: Phase velocity, Fiber reinforcement, Rectangular irregularity, Heterogeneous half-space,
چکیده مقاله :
This paper concerned with the dispersion of Love wave in a fiber-reinforced medium lying over a heterogeneous half-space. The heterogeneity is caused by the consideration of quadratic variation in density and directional rigidity of lower half-space. The irregularity has been considered in the form of rectangle at the interface of the fiber-reinforced layer and heterogeneous half-space. The dispersion equation of Love wave has been deduced for existing geometry of the problem under suitable boundary conditions using variable separation method. It has also been observed that for a homogeneous layer with rigidity lying over a regular homogeneous isotropic half-space, the velocity equation coincides with the classical results of Love wave. The effect of the medium characteristics on the dispersion of Love waves has been discussed and the results are displayed with graphs by means of MATLAB programming to clear the physical significance. The study of Love wave dispersion with irregular interface helps civil engineers in building construction, analysis of earthquake in mountain roots, continental margins, and so on. It is also beneficial for the study of seismic waves generated by artificial explosions.
Raoofian Naeeni M., Eskandari-Ghadi M., 2016, A potential method for body and surface wave propagation in transversely isotropic half- and full-spaces, Civil Engineering Infrastructures Journal 49: 263-288.
[2] Raoofian Naeeni M., Eskandari-Ghadi M., 2016, Analytical solution of the asymmetric transient wave in a transversely isotropic half-space due to both buried and surface impulses, Soil Dynamics and Earthquake Engineering 81: 42-57.
[3] Achenbach J.D., 1973, Wave Propagation in Elastic Solid, North Holland, Publishing Company American Elsevier, Amsterdam, New York.
[4] Spencer A.J.M., 1972, Deformation of Fiber-Reinforced Material, Oxford University Press, London.
[5] Richter C.F., 1958, Elementary Seismology, W. H. Freeman and Company, San Francisco and Bailey Bros, Swinfen Ltd, London.
[6] Meissner E., 1921, Elastic Oberflachenwellen mit dispersion in einem inhomogeneous medium, Viertelgahrsschriftden Naturforschender Ge-Sellschaft in Zurich 66: 181-185.
[7] Chattopadhyay A., Choudhury S., 1990, Propagation, reflection and transmission of magneto elastic shear waves in a self-reinforced medium, International Journal of Engineering Science 28: 485-495.
[8] Abd-Alla A.M., Nofal T.A., Abo-Dahab S.M., Al-Mullise A., 2013, Surface waves propagation in fibre-reinforced anisotropic elastic media subjected to gravity field, International Journal of Physical Sciences 8: 574-584.
[9] Singh B., 2006, Wave propagation in thermally conducting linear fibre-reinforced composite materials, Archive of Applied Mechanics 75: 513-520.
[10] Singh B., Singh S.J., 2004, Reflection of plane waves at the free surface of a fiber-reinforced elastic half-space, Sadhana 29: 249-257.
[11] Kumar R., Gupta R.R., 2009, Deformation due to various sources in a fibre-reinforced anisotropic generalized thermoelastic medium, Canadian Journal of Physics 87: 179-187.
[12] Chattopadhyay A., Singh A.K., 2012, Propagation of magneto elastic shear waves in an irregular self-reinforced layer, Journal of Engineering Mathematics 75: 139-155.
[13] Singh S.S., 2010, Love wave at a layer medium bounded by irregular boundary surfaces, Journal of Vibration and Control 17: 789-795.
[14] Chattaraj R., Samal S.K., Mahanti N., 2013, Dispersion of love wave propagating in irregular anisotropic porous stratum under initial stress, International Journal of Geomechanics 13: 402-408.
[15] Chattopadhyay A., Gupta S., Sharma V.K., Kumari P., 2010, Effects of irregularity and anisotropy on the propagation of shear waves, International Journal of Engineering, Science and Technology 2: 116-126.
[16] Gupta S., Chattopadhyay A., Kundu S., 2010, Influence of irregularity and rigidity on the propagation of torsional wave, Applied Mathematical Sciences 4: 805-816.
[17] Gupta S., Majhi D.K., Vishwakarma S.K., Kundu S., 2011, Propagation of torsional surface waves under the effect of irregularity and initial stress, Applied Mathematics 2: 1453-1461.
[18] Selim M.M., 2007. Propagation of torsional surface waves in heterogeneous half-space with irregular free surface, Applied Mathematical Sciences 1: 1429-1437.
[19] Gupta S., Chattopadhyay A., Majhi D.K., 2010, Effect of irregularity on the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer, Applied Mathematics and Mechanics 31: 481-492.
[20] Abd-Alla A.M., Ahmed S.M., 1999, Propagation of Love waves in a non-homogeneous orthotropic elastic layer under initial stress overlying semi-infinite medium, Applied Mathematics and Computation 106: 265-275.
[21] Vaishnav P.K., Kundu S., Abo-Dahab S.M., Saha A., 2017, Torsional surface wave propagation in anisotropic layer sandwiched between heterogeneous half-space, Journal of Solid Mechanics 9: 213-224.
[22] Vishwakarma S.K., Gupta S., 2013, Existence of torsional surface waves in an earth’s crustal layer lying over a sandy mantle, Journal of Earth System Science 122: 1411-1421.
[23] Wang C.D., Lin Y.T., Jeng Y.S, Ruan Z.W., 2010, Wave propagation in an inhomogeneous cross-anisotropic medium, International Journal for Numerical and Analytical Methods in Geomechanics 34: 711-732.
[24] Dey S., Gupta S., 1987, Longitudinal and shear waves in an elastic medium with void pores, Proceedings of the Indian National Science Academy 53: 554-563.
[25] Gupta S., Sultana R., Kundu S., 2015, Influence of rigid boundary on the propagation of torsional surface wave in an inhomogeneous layer, Journal of Earth System Science 124: 161-170.
[26] Biot M.A., 1965, Mechanics of Incremental Deformation, John Wiley and Sons, New York.
[27] Love A.E. H., 1911, Some Problems of Geodynamics, Cambridge University Press, London.
[28] Chattopadhyay A., Choudhury S., 1995, Magneto elastic shear waves in an infinite self-reinforced plate, International Journal for Numerical and Analytical Methods in Geomechanics 19: 289-304.
[29] Gubbins D., 1990, Seismology and Plate Tectonics, Cambridge University Press, Cambridge, New York.
