Variational Principle, Uniqueness and Reciprocity Theorems in Porous Piezothermoelastic with Mass Diffusion
Subject Areas : Engineering
1 - Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India
2 - Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India
Keywords:
Abstract :
[1] Biot M.A., 1956, Theory of deformation of a porous viscoelastic anisotropic solid, Journal of Applied Physics 27(5): 459-467.
[2] Biot M.A., 1956, The theory of propagation of elastic waves in a fluid saturated porous solid, The Journal of the Acoustical Society of America 28: 168-191.
[3] Biot M.A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[4] Lord H.W., Shulman Y., 1967, The generalised dynamic theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
[5] 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.
[6] Mindlin R.D., 1974, Equation of high frequency of thermopiezoelecteric crystals plates, International Journal of Solids and Structures 10(6): 625-637.
[7] Nowacki W., 1978, Some general theorems of thermo-piezoelectricity, Journal of Thermal Stresses 1:171-182.
[8] Nowacki W., 1979, Foundation of Linear Piezoelectricity, Interactions in Elastic Solids, Springer, Wein, Chapter 1.
[9] Chandrasekharaiah D.S., 1984, A generalised linear thermoelasticity theory of piezoelectric media, Acta Mechanica 71:293-349.
[10] Rao S.S., Sunar M., 1993, Analysis of thermopiezoelectric sensors and acutators in advanced intelligent structures, AIAA Journal 31: 1280-1286.
[11] Majhi M.C., 1995, Discontinuities in generalized thermo elastic wave propagation in a semi- infinite piezoelectric rod, Journal of Technical Physics 36: 269-278.
[12] Chen W.Q., 2000, Three dimensional green’s function for two- phase transversely isotropic piezothermoelastic media, Journal of Applied Mechanics 67:705.
[13] Biot M.A., 1962, Mechanics of deformation and acoustic propagation in porous media, Journal of Applied Physics 33:1482-1498.
[14] Biot M.A., 1962, Generalised theory of acoustic propagation in porous dissipative media, Journal of the Acoustical Society of America 34:1254-1264.
[15] Sharma J.N., Kumar M., 2000, Plane harmonic waves in piezothermoealstic materials, Indian Journal of Engineering and Materials Sciences 7: 434-442.
[16] 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.
[17] Sharma J.N., Walia V., 2007, Further investigationon rayleigh waves in piezothermoelastic materials, Journal of Sound and Vibration 301:189-206.
[18] Sharma M.D., 2010, Propagation of in homogeneous waves in anisotropic piezothermoelastic media, Acta Mechanica 215: 307-318.
[19] 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.
[20] Sharma M. D., Gogna M. L., 1991, Wave propagation in anisotropic liquid-saturated porous solids, Journal of the Acoustical Society of America 89:1068-1073.
[21] Sharma M. D., 2004, 3-D Wave propagation in a general anisotropic poroelastic medium: phase velocity, group velocity and polarization, Geophysical Journal International 156:329-344.
[22] Sharma M. D., 2004, 3-D Wave propagation in a general anisotropic poroelastic medium: reflection and refraction at an interface with fluid, Geophysical Journal International 157(2): 947-958.
[23] Sharma M. D., 2005, Polarisations of quasi-waves in a general anisotropic porous solid saturated with viscous fluid, Journal of Earth System Science 114(4): 411-419.
[24] Sharma M. D., 2008, Wave propagation in thermoelastic saturated porous medium, Journal of Earth System Science 117(6): 951-958.
[25] Sharma M. D., 2009, Boundary conditions for porous solids saturated with viscous fluid, Applied Mathematics and Mechanics 30(7): 821-832.
[26] Hashimoto K. V., Yamaguchi M., 1986, Piezoelectric and dielectric properties of composite materials, Proceedings of the IEEE Ultrasonics Symposium 2: 697-702.
[27] Arai T., Ayusawa K., Sato H., Miyata T., Kawamura K., Kobayashi K., 1991, Properties of hydrophones with porous piezoelectric ceramics, Journal of Applied Physics 30: 2253-2255.
[28] Hayashi T. , Sugihara S., Okazaki K., 1991, Processing of porous 3-3 PZT ceramics using capsule-free O2 –HIP, Japanese Journal of Applied Physics 30: 2243-2246.
[29] Xia Z., Ma Sh., Qiu X., Wu Y., Wang F., 2003, Influence of porosity on the stability of charge and piezoelectricity for porous polytetrafluoroethylene film electrets, Journal of Electrostatics 59: 57-69.
[30] Banno H., 1993, Effects of porosity on dielectric, elastic and electromechanical properties of Pb(Zr,Ti)O3 ceramics with open pores: a theoretical approach, Japanese Journal of Applied Physics 32: 4214-4217.
[31] Gomez T. E., Montero F., 1996, Highly coupled dielectric behaviour of porous ceramics embedding a polymer, Applied Physics Letters 68: 263-265.
[32] Vashishth A. K., Gupta V., 2009, Vibrations of porous piezoelectric ceramic plates, Journal of Sound and Vibration 325: 781-797.
[33] Nowacki W., 1974, Dynamical problem of thermodiffusion in solid-1, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 55-64.
[34] Nowacki W., 1974, Dynamical problem of thermodiffusion in solid-11, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 129-135.
[35] Nowacki W., 1974, Dynamical problem of thermodiffusion in solid-111, Bulletin of the Polish Academy of Sciences: Technical Sciences 22: 275-267.
[36] Nowacki W., 1974, Dynamical problem of thermodiffusion in solids, Proceedings vibration problems 15: 105-128.
[37] Kuang Z.B., 2010, Variational principles for generalised thermodiffusion theory in pyroelectricity, Acta Mechenica 214: 275-289.
[38] Kumar R., Kansal T., 2008, Propagation of lamb waves in transversely isotropic thermoelastic diffusion plate, International Journal of Solids and Structures 45: 5890-5913.
[39] Ezzat M.A., El Karamany A.S., 2002, The uniqueness and reciprocity theorems for generalised thermoviscoelasticity for anisotropic media, Journal of Thermal Stresses 25(6): 507-522.
[40] Li J. Y., 2003, Uniqueness and reciprocity theorems for linear thermo-electro-magneto-elasticity, Journal of Mechanics and Applied Mathematics 56(1): 35-43.
[41] Othman M.I.A., 2004, The uniqueness and reciprocity theorems for generalised thermoviscoelasticity with thermal relaxation times, Mechanics and Mechanical Engineering 7(2): 77-87.
[42] Aouadi M., 2007, Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion, Journal of Thermal Stresses 30(7): 665-678.
[43] Vashishth A. K., Gupta V., 2011, Uniqueness theorem, reciprocity and eigen value problems in linear theory of porous piezoelectricity, Applied Mathematics and Mechanics 32(4): 479-494.
[44] Kumar R., Kansal T., 2013, Variational principle, uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion material, Qscience Connect, DOI: 10.5339/connect.2013.27.
[45] Kumar R., Gupta V., 2013, Uniqueness and reciprocity theorem and plane waves in thermoelastic diffusion with a fractional order derivative, Chinese Physics B 22(7):74601.