Analysis of Plane Waves in Anisotropic Magneto-Piezothermoelastic Diffusive Body with Fractional Order Derivative
محورهای موضوعی : Engineering
1 - Department of Mathematics, Kurukshetra University Kurukshetra-136119, Haryana , India
2 - Department of Mathematics, Kurukshetra University Kurukshetra-136119, Haryana , India
کلید واژه: Phase velocity, Attenuation coefficient, Piezothermoelastic, Magneto, Harmonic plane wave,
چکیده مقاله :
In this paper the propagation of harmonic plane waves in a homogeneous anisotropic magneto-piezothermoelastic diffusive body with fractional order derivative is studied. The governing equations for a homogeneous transversely isotropic body in the context of the theory of thermoelasticity with diffusion given by Sherief et al. [1] are considered as a special case. It is found that three types of waves propagate in one dimension anisotropic magneto-piezothermoelastic diffusive body, namely quasi-longitudinal wave (QP), quasi-thermal wave (QT) and quasi-diffusion wave (QD). The different characteristics of waves like phase velocity, attenuation coefficient, specific heat loss and penetration depth are computed numerically and presented graphically for Cadmium Selenide (CdSe) material. The effect of fractional order parameter on phase velocity, attenuation coefficient, specific heat loss and penetration depth has been studied.
[1] Sherief H. H., Hamza F.A., Saleh H.A., 2004, The theory of generalised thermoelastic diffusion, International Journal of Engineering Science 42(5): 591-608.
[2] Sherief H.H., El-Sayed A.M., El-Latief A.M., 2010, Fractional order theory of thermoelasticity, International Journal of Solids and Structures 47: 269-275.
[3] Mindlin R.D.,1974, Equation of high frequency of thermopiezoelectric crystals plates, International Journal of Solids and Structures 10: 625-637.
[4] Nowacki W., 1978, Some general theorems of thermo-piezoelectricity, Journal of Thermal Stresses 1:171-182.
[5] Nowacki W., 1979 , Foundation of Linear Piezoelectricity, In Parkus, Interactions in Elastic Solids, Springer, Wein.
[6] Chandrasekharaiah D.S., 1984, A generalised linear thermoelasticity theory of piezoelectric media, Acta Mechanica 71: 293-349.
[7] Sharma M.D., 2010, Propagation of inhomogeneous waves in anisotropic piezothermoelastic media, Acta Mechanica 215: 307-318.
[8] Sharma J .N., Kumar M., 2000, Plane harmonic waves in piezothermoelastic materials, Indian Journal of Engineering & Materials Sciences 7: 434-442.
[9] Sharma J.N., Walia V., 2007, Further investigation on Rayleigh waves in piezothermoelastic materials, Journal of Sound and Vibration 301:189-206.
[10] Sharma J.N., Pal M., Chand D., 2005, Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials, Journal of Sound and Vibration 284: 227-248.
[11] Alshaikh F. A., 2012, The mathematical modelling for studying the influence of the initial stresses and relaxation times on reflection and refraction waves in piezothermoelastic half-space, Applied Mathematics 3: 819-832.
[12] Singh B., 2005, Reflection of P and SV waves from free surface of an elastic solid with generalized thermodiffusion, Journal of Earth System Science 114(2): 159-168.
[13] Singh B., 2006, Reflection of SV waves from free surface of an elastic solid in generalized thermodiffusion, Journal of Sound and Vibration 291: 764-778.
[14] Aouadi M., 2006, Variable electrical and thermal conductivity in the theory of generalized thermodiffusion, Zeitschrift für Angewandte Mathematik und Physik 57(2): 350-366.
[15] Aouadi M., 2006, A generalized thermoelastic diffusion problem for an infinitely long solid cylinder, International Journal of Mathematics and Mathematical Sciences 2006:1-15.
[16] Aouadi M., 2007, A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 44: 5711-5722.
[17] Aouadi M., 2007, Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion, Journal of Thermal Stresses 30: 665-678.
[18] Aouadi M.,2008, Generalized theory of thermoelastic diffusion for anisotropic media, Journal of Thermal Stresses 31: 270-285.
[19] Sharma J.N., Singh D., Sharma R., 2003, Generalized thermoelastic waves in transversely isotropic plates, Indian Journal of Pure and Applied Mathematics 34(6): 841-852.
[20] Sharma J.N., 2007, Generalized thermoelastic diffusive waves in heat conducting materials, Journal of Sound and Vibration 301: 979-993.
[21] Sharma J.N., Sharma Y.D., Sharma P.K., 2008, On the propagation elasto-thermodiffusive surface waves in heat-conducting materials, Journal of Sound and Vibration 315(4): 927-938.
[22] Kumar R., Kansal T., 2012, Analysis of plane waves in anisotropic thermoelastic diffusive body, Mechanics of solids 47(3): 337-352.
[23] Van Run A. M. J. G., Terrell D.R., Scholing J.H., 1974, An in situ grown eutectic magnetoelectric composite material, Journal of Materials Science 9: 1710-1714.
[24] Li J.Y., Dunn M.L., 1998, Micromechanics of mgnetoelectrostatic composites: average fields and effective behaviour, Journal of Intelligent Material Systems and Structures 9: 404-416.
[25] Oatao Y., Ishihara M., 2013, Transient thermoelastic analysis of a laminated hollow cylinder constructed of isotropic elastic and magneto-electro-thermoelastic material, Advances in Materials Science and Applications 2(2): 48-59.
[26] Pang Y., Li J. X., 2014, SH interfacial waves between piezoelectric/piezomagnetic half-spaces with magneto-electro-elastic imperfect bonding, Piezoelectricity, Acoustic Waves, and Device Applications .
[27] Li L., Wei P.J., 2014, The piezoelectric and piezomagnetic effect on the surface wave velocity of magneto-electro-elastic solids, Journal of Sound and Vibration 333(8): 2312-2326.
[28] Abd-alla Abo-el-nour N., Alshaikh F., Giorgio I., Della Corte A., 2015, A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress, Mathematics and Mechanics of Solids 21: 104-118.
[29] Kumar R., Gupta V., 2013, Plane wave propagation in an anisotropic thermoelastic body with fractional order derivative and void, Journal of Thermoelasticity 1(1): 21-34.
[30] Bassiouny E., Sabry R., 2013, Fractional order two temperature thermo-elastic behavior of piezoelectric materials, Journal of Applied Mathematics and Physics 1(5):110-120 .
[31] Meerschaert M. M., McGough R. J., 2014, Attenuated fractional wave equations with anisotropy, Journal of Vibration and Acoustics 136:051004.
[32] Kumar R., Gupta V., 2015, Plane wave propagation and domain of influence in fractional order thermoelastic materials with three phase lag heat transfer, Mechanics of Advanced Materials and Structures 23(8): 896-908.
[33] Meral F. C., Royston T.J., Magin R.L., 2009, Surface response of a fractional order viscoelastic halfspace to surface and subsurface sources, Journal of the Acoustical Society of America 126(6): 3278-3285.
[34] Meral F.C., Royston T. J., Magin R. L., 2011, Rayleigh-Lamb wave propagation on a fractional order viscoelastic plat, Journal of the Acoustical Society of America 129(2): 1036-1045.
[35] Li J. Y., 2003, Uniqueness and reciprocity theorems for linear thermo-electro-magneto-elasticity, Journal of Mechanics and Applied Mathematics 56(1): 35-43.
[36] Kuang Z.B., 2010, Variational principles for generalised thermodiffusion theory in pyroelectricity, Acta Mechanica 214: 275-289.
[37] Slaughter W.S., 2002, The Linearized Theory of Elasticity, Birkhauser Boston.
