Variational Principle, Uniqueness and Reciprocity Theorems in Porous Piezothermoelastic with Mass Diffusion
محورهای موضوعی : Engineering
R Kumar
1
(Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India)
P Sharma
2
(Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India)
کلید واژه: Porous, Variational principle, Piezothermoelastic, Uniqueness, Reciprocity,
چکیده مقاله :
The basic governing equations in anisotropic elastic material under the effect of porous piezothermoelastic are presented. Biot [1], Lord & Shulman [4] and Sherief et al. [5] theories are used to develop the basic equations for porous piezothermoelastic with mass diffusion material. The variational principle, uniqueness theorem and theorem of reciprocity in this model are established under the assumption of positive definiteness of elastic, porousthermal, chemical potential and electric field.
[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.
