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Variational principle, uniqueness and reciprocity theorems in porous magneto-piezothermoelastic medium. (English) Zbl 1438.74059
Summary: The basic governing equations for an anisotropic porous magneto-piezothermoelastic medium are presented. The variational principle, uniqueness theorem and theorem of reciprocity in this model are established under the assumption of positive definiteness of magnetic and piezoelectric fields. Particular cases of interest are also deduced and compared with the known results.
MSC:
74F15 Electromagnetic effects in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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[1] Alshaikh, F. A., 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, 03, 819-832, (2012)
[2] Aouadi, M., Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion, Journal of Thermal Stresses, 30, 665-678, (2007)
[3] Arai, T.; Ayusawa, K.; Sato, H.; Miyata, T.; Kawamura, K.; Kobayashi, K., Properties of hydrophone with porous piezoelectric ceramics, Japanese Journal of Applied Physics, 30, 2253-2255, (1991)
[4] Banno, H., Effects of porosity on dielectric, elastic and electromechanical properties of Pb(Zr, Ti)O_3 ceramics with open pores: a theoretical approach, Japanese Journal of Applied Physics, 32, 4214-4217, (1993)
[5] Biot, M. A., Thermoelasticity and Irreversible Thermodynamics, Journal of Applied Physics, 27, 240-253, (1956) · Zbl 0071.41204
[6] Biot, M. A., Mechanics of deformation and acoustic propagation in porous media, Journal of Applied Physics, 33, 1482-1498, (1962) · Zbl 0104.21401
[7] Biot, M. A., Generalized theory of acoustic propagation in porous dissipative media, The Journal of the Acoustical Society of America, 34, 1254-1264, (1962)
[8] Chandrasekharaiah, D. S., A generalised linear thermoelasticity theory of piezoelectric media, Acta Mechanica, 71, 293-349, (1984)
[9] Chen, W. Q., On the general solution for piezothermoelasticity for transverse isotropy with application, Journal of Applied Mechanics, 67, 705-711, (2000) · Zbl 1110.74379
[10] Ezzat, M. A.; El Karamany, A. S., The uniqueness and reciprocity theorems for generalized thermoviscoelasticity for anisotropic media, Journal of Thermal Stresses, 25, 507-522, (2002)
[11] Gómez Alvarez-Arenas, T. E.; Montero de Espinosa, F., Highly coupled dielectric behavior of porous ceramics embedding a polymer, Applied Physics Letters, 68, 263-265, (1996)
[12] Hashimoto, K. V.; Yamaguchi, M., Piezoelectric and dielectric properties of composite materials, Proceedings of the IEEE Ultrasonics Symposium, 2, 697-702, (1986)
[13] Hayashi, T., Processing of porous 3-3 PZT ceramics using capsule-free O 2 -HIP, Japanese Journal of Applied Physics, 30, 2243-2246, (1991)
[14] Ieşan, D., Reciprocity, uniqueness and minimum principles in the linear theory of piezoelectricity, International Journal of Engineering Science, 28, 1139-1149, (1990) · Zbl 0718.73071
[15] Ignaczak, J., Uniqueness in generalized thermoelasticity, Journal of Thermal Stresses, 2, 171-175, (1979)
[16] Kuang, Z. B., Variational principles for generalized thermodiffusion theory in pyroelectricity, Acta Mechanica, 214, 275, (2010) · Zbl 1261.74013
[17] Kumar, R.; Gupta, V., Uniqueness and reciprocity theorem and plane waves in thermoelastic diffusion with a fractional order derivative, Chinese Physics B, 22, 074601, (2013)
[18] Kumar, R.; Kansal, T., Variational principle, uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion material, Qscience Connect, 27, (2013)
[19] Li, J. Y., Uniqueness and reciprocity theorems for linear thermo-electro-magneto-elasticity, The Quarterly Journal of Mechanics and Applied Mathematics, 56, 35-43, (2003) · Zbl 1043.74015
[20] Li, J. Y.; Dunn, M. L., Micromechanics of magnetoelectroelastic composite materials: Average fields and effective behavior, Journal of Intelligent Material Systems and Structures, 9, 404-416, (1998)
[21] Li, L.; Wei, P. J., The piezoelectric and piezomagnetic effect on the surface wave velocity of magneto-electro-elastic solids, Journal of Sound and Vibration, 333, 2312-2326, (2014) · Zbl 1308.93073
[22] Majhi, M. C., Discontinuities in generalized thermo elastic wave propagation in a semi-infinite piezoelectric rod, Journal of Technical Physics, 36, 269-278, (1995)
[23] Mindlin, R. D., Equations of high frequency vibrations of thermopiezoelectric crystal plates, International Journal of Solids and Structures, 10, 625-637, (1974) · Zbl 0282.73068
[24] Nowacki, W., Dynamical problem of thermodiffusion in solid-1, Bull. Of polish Academy of Science Series. Science and Technology, 22, 56-64, (1974)
[25] Nowacki, W., Some general theorems of thermopiezoelectricity, Journal of Thermal Stresses, 1, 171-182, (1978)
[26] Nowacki, W.; Parkus, H., Interactions in elastic solids, Foundation of linear piezoelectricity, (1979), Wein: Springer, Wein
[27] Oatao, Y.; Ishihara, M., Transient thermoelastic analysis of a laminated hollow cylinder constructed of isotropic elastic and magneto-electro-thermoelastic material, Advances in Materials Science and Applications, 2, 48-59, (2013)
[28] Othman, M. I. A., The uniqueness and reciprocity theorems for generalised thermoviscoelasticity with thermal relaxation times, Mechanics and Mechanical Engineering, 7, 77-87, (2004)
[29] Pang, Y.; Li, J. X., SH interfacial waves between piezoelectric/piezomagnetic half-spaces with magneto-electro-elastic imperfect bonding, Piezoelectricity, Acoustic Waves, and Device Applications (SPAWDA), 226-230, (2014)
[30] Rao, S. S.; Sunar, M., Analysis of thermopiezoelectric sensors and acutators in advanced intelligent structures, American Institute of Aeronautics and Astronautics Journal, 31, 1280-1286, (1993)
[31] Sharma, M. D., Three-dimensional wave propagation in a general anisotropic poroelastic medium: Phase velocity, group velocity and polarization, Geophysical Journal International, 156, 329-344, (2004)
[32] Sharma, M. D., 3-D wave propagation in a general anisotropic poroelastic medium: Reflection and refraction at an interface with fluid, Geophysical Journal International, 157, 947-958, (2004)
[33] Sharma, M. D., Polarisations of quasi-waves in a general anisotropic porous solid saturated with viscous fluid, Journal of Earth System Science, 114, 411-419, (2005)
[34] Sharma, M. D., Wave propagation in thermoelastic saturated porous medium, Journal of Earth System Science, 117, 951-958, (2008)
[35] Sharma, M. D., Boundary conditions for porous solids saturated with viscous fluid, Applied Mathematics and Mechanics, 30, 821-832, (2009) · Zbl 1173.74347
[36] Sharma, M. D., Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media, Acta Mechanica, 215, 307-318, (2010) · Zbl 1398.74174
[37] Sharma, M. D.; Gogna, M. L., Wave propagation in anisotropic liquid-saturated porous solids, The Journal of the Acoustical Society of America, 90, 1068-1073, (1991)
[38] Sharma, J. N.; Kumar, M., Plane harmonic waves in piezothermoealstic materials, Indian Journal of Engineering and Materials Sciences, 7, 434-442, (2000)
[39] Sharma, J. N.; Walia, V., Further investigations on Rayleigh waves in piezothermoelastic materials, Journal of Sound and Vibration, 301, 189-206, (2007)
[40] Sharma, J. N.; Pal, M.; Chand, D., Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials, Journal of Sound and Vibration, 284, 227-248, (2005)
[41] Sherie, H. H.; Dhaliwa, R. S., A uniqueness theorem and a variational principle for generalized thermoelasticity, Journal of Thermal Stresses, 3, 223-230, (1980)
[42] Van Run, A. M. J. G.; Terrell, D. R.; Scholing, J. H., An in situ grown eutectic magnetoelectric composite material, Journal of Materials Science, 9, 1710-1714, (1974)
[43] Vashishth, A. K.; Gupta, V., Vibrations of porous piezoelectric ceramic plates, Journal of Sound and Vibration, 325, 781-797, (2009)
[44] Vashishth, A. K.; Gupta, V., Uniqueness theorem, theorem of reciprocity, and eigenvalue problems in linear theory of porous piezoelectricity, Applied Mathematics and Mechanics, 32, 479-494, (2011) · Zbl 1213.74119
[45] Xia, Z.; Ma, S.; Qiu, X.; Wu, Y.; Wang, F., Influence of porosity on the stability of charge and piezoelectricity for porous polytetrafluoroethylene film electrets, Journal of Electrostatics, 59, 57-69, (2003)
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