Generation of Love Wave in a Media with Temperature Dependent Properties Over a Heterogeneous Substratum
الموضوعات :
S Gupta
1
(Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India)
P Pati
2
(Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India)
B Prasad
3
(Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India)
الکلمات المفتاحية: Initial-stress, Heterogeneity, Temperature-dependent properties, Love waves,
ملخص المقالة :
The present paper deals with the generation of Love waves in a layer of finite thickness over an initially stressed heterogeneous semi-infinite media. The rigidity and density of the layer are functions of temperature, i.e. they are temperature dependent. The lower substratum is an initially stressed medium and its rigidity and density vary linearly with the depth. The frequency relation of Love waves has been acquired in compact form. Numerical calculations are accomplished and a number of graphs for non-dimensional phase velocity versus non-dimensional wave number are plotted to display the influence of intrinsic parameters like initial stress and inhomogeneity factors on the generation of Love waves. It is initiated that the non-dimensional phase velocity of Love wave decreases with increase in the non-dimensional wave number and is strongly influenced by the initial stress of the substratum and the inhomogeneity factors of the layer and the substratum. This study may provide effective information in the field of industrial engineering, civil engineering as well as geophysics and seismology.
[1]Abd-Alla A.M., Hassan S., Abo-Dahab S., Helmy M.I., 2011, Propagation of S-wave in a non-homogeneous anisotropic incompressible and initially stressed medium under influence of gravity field, Applied Mathematics and Computation 217(9): 4321-4332.
[2] Ahmed S.M., Abo-Dahab S.M., 2010, Propagation of love waves in an orthotropic granular layer under initial stress overlying a semi-infinite granular medium, Journal of Vibration and Control 16(12): 1845-1858.
[3] Alam P., Kundu S., 2017, Influences of heterogeneities and initial stresses on the propagation of love-type waves in a transversely isotropic layer over an inhomogeneous half-space, Journal of Solid Mechanics 9(4): 783-793.
[4] Aouadi M., El-Karamany A.S., 2003, Plane waves in generalized thermo viscoelastic material with relaxation time and temperature-dependent properties, Journal of Thermal Stresses 26(3): 197-222.
[5] Biot M.A., 1940, The influence of initial stress on elastic wave, Journal of Applied Physics 11(8): 522-530.
[6] Biot M.A., 1965, Mechanics of Incremental Deformation, John Wiley and Sons, New York.
[7] Chattaraj R., Samal S.K., Mahanti, N.C., 2013, Dispersion of love wave propagating in irregular anisotropic porous stratum under initial stress, International Journal of Geomechanics 13(4): 402-408.
[8] Czaplewski D.A., Sullivan J.P., Friedmann T.A., Wendt J.R., 2005, Temperature dependence of the mechanical properties of tetrahedrally coordinated amorphous carbon thin films, Applied Physics Letters 87(16): 161915.
[9] Das B., Chakraborty S., Lahiri A., 2018, Generalized magnetothermoelastic interaction for a rotating half space, International Journal of Applied and Computational Mathematics 4: 92.
[10] Deliktas E., Teymur M., 2018, Surface shear horizontal waves in a double-layered nonlinear elastic half space, IMA Journal of Applied Mathematics 83(3): 471-495.
[11] Du J., Jin X., Wang J., 2007, Love wave propagation in layered magneto-electro-elastic structures with initial stress, Acta Mechanica 192(1-4): 169-189.
[12] Gupta S., Majhi D.K., Kundu S., Vishwakarma S.K., 2013, Propagation of love waves in non-homogeneous substratum over initially stressed heterogeneous half-space, Applied Mathematics and Mechanics 34(2): 249-258.
[13] Guz A.N., 2002, Elastic waves in bodies with initial (residual) stresses, International Applied Mechanics 38(1): 23-59.
[14] Hata T., 1979, Thermoelastic problem for a Griffith crack in a plate with temperature-dependent properties under a linear temperature distribution, Journal of Thermal Stresses 2: 353-366.
[15] Kakar R., Kakar S., Narang R.K., 2017, Propagation of love-type wave in a temperature dependent crustal layer, Smart Structures and Systems 19(3): 237-241.
[16] Kern H., 1982, P-and S-wave velocities in crustal and mantle rocks under the simultaneous action of high confining pressure and high temperature and the effect of the rock microstructure, High-Pressure Researches in Geoscience 1982: 15-45.
[17] Kundu S., Gupta S., Manna S., 2014, Propagation of love wave in fiber-reinforced medium lying over an initially stressed orthotropic half-space, International Journal for Numerical and Analytical Methods in Geomechanics 38(11): 1172-1182.
[18] Kundu S., Kumari A., Gupta S., Pandit D.K.., 2016, Effect of periodic corrugation, reinforcement, heterogeneity and initial stress on Love wave propagation, Waves in Random and Complex Media 26(4): 485-515.
[19] Lee H.J., Saravanos D.A., 1998, The effect of temperature dependent material properties on the response of piezoelectric composite materials, Journal of Intelligent Material Systems and Structures 9(7): 503-508.
[20] Lokajı´cˇek T., Rudajev V., Dwivedi R.D., Goel R.K., Swarup A., 2012, Influence of thermal heating on elastic wave velocities in granulite, International Journal of Rock Mechanics and Mining Sciences 54: 1-8.
[21] Love A.E.H., 1944, A Treatise on Mathematical Theory of Elasticity, Dover Publication, New York.
[22] Matysiak S.J., 1988, Wave fronts in elastic media with temperature dependent properties, Applied Science Research 45(2): 97-106.
[23] Matysiak S.J., Mieszkowski R., Perkowski D.M., 2014, SH waves in a layer with temperature dependent properties, Acta Geophysica 62(6): 1203-1213.
[24] Nowinski J., 1960, A betti–rayleigh theorem for elastic bodies exhibiting temperature dependent properties, Applied Science Research 9(1): 429-436.
[25] Pal P.C., Prasad B., Kumar S., 2016, Reflection and transmission of SH-waves through a self-reinforced elastic layer embedded between two transversely isotropic inhomogeneous elastic half-spaces, Journal of the Geological Society of India 4: 62-69.
[26] Prasad B., Pal P.C., Kundu S., Prasad N., 2017, Effect of inhomogeneity due to temperature on the propagation of shear waves in an anisotropic layer, AIP Conference Proceedings 1860: 020053-1–020053-7.
[27] Sarkar N., Lahiri A., 2012, A three-dimensional thermoelastic problem for a half-space without energy dissipation, International Journal of Engineering Science 51: 310-325.
[28] Schreiber E., Anderson O.L., Soga N., 1973, Elastic Constants and Their Measurement, McGraw-Hill, New York.
[29] Sethi M., Sharma A., Sharma A., 2016, Propagation of SH-waves in a double non-homogeneous crustal layers of finite depth lying over an homogeneous half-space, Latin American Journal of Solids and Structures 13(14): 2628-2642.
[30] Sun D., Luo S.N., 2011, Wave propagation of functionally graded material plates in thermal environments, Ultrasonics 51(8): 940-952.
[31] Tao L.N., 1989, The heat conduction problem with temperature-dependent material properties, International Journal of Heat and Mass Transfer 32(3): 487-491.
[32] Tomar S.K., Khurana A., 2013, Wave propagation in thermo-chiral elastic medium, Applied Mathematical Modelling 37(22): 9409-9418.
[33] Tillmann A.R., Borges V.L., Guimaraes G., Silva A.L.F.V., Silva S.M.M.L., 2008, Identification of temperature- dependent thermal properties of solid materials, Journal of the Brazilian Society of Mechanical Sciences and Engineering 30(4): 269-278.
[34] Whittaker E.T., Watson G.N., 1990, A Course in Modern Analysis, Cambridge University Press, U.K.
[35] Xu F., Wang W., Hou J., Liu, M., 2012, Temperature effects on the propagation characteristics of love waves along multi-guide layers of SiO2/Su-8 on ST-90 X quartz, Sensors 12(6): 7337-7349.
