542
Views
3
CrossRef citations to date
0
Altmetric
Research Article

Variational principle, uniqueness and reciprocity theorems in porous magneto-piezothermoelastic medium

& | (Reviewing Editor)
Article: 1231947 | Received 30 Nov 2015, Accepted 29 Aug 2016, Published online: 20 Sep 2016

References

  • 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, 03, 819–832.10.4236/am.2012.38123
  • Aouadi, M. (2007). Uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion. Journal of Thermal Stresses, 30, 665–678.10.1080/01495730701212815
  • Arai, T., Ayusawa, K., Sato, H., Miyata, T., Kawamura, K., & Kobayashi, K. (1991). Properties of hydrophone with porous piezoelectric ceramics. Japanese Journal of Applied Physics, 30, 2253–2255.10.1143/JJAP.30.2253
  • 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, 4214–4217.10.1143/JJAP.32.4214
  • Biot, M. A. (1956). Thermoelasticity and Irreversible Thermodynamics. Journal of Applied Physics, 27, 240–253.10.1063/1.1722351
  • Biot, M. A. (1962a). Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 33, 1482–1498.10.1063/1.1728759
  • Biot, M. A. (1962b). Generalized theory of acoustic propagation in porous dissipative media. The Journal of the Acoustical Society of America, 34, 1254–1264.10.1121/1.1918315
  • Chandrasekharaiah, D. S. (1984). A generalised linear thermoelasticity theory of piezoelectric media. Acta Mechanica, 71, 293–349.
  • Chen, W. Q. (2000). On the general solution for piezothermoelasticity for transverse isotropy with application. Journal of Applied Mechanics, 67, 705–711.10.1115/1.1328349
  • Ezzat, M. A., & El Karamany, A. S. (2002). The uniqueness and reciprocity theorems for generalized thermoviscoelasticity for anisotropic media. Journal of Thermal Stresses, 25, 507–522.10.1080/01495730290074261
  • Gómez Alvarez-Arenas, T. E., & Montero de Espinosa, F. (1996). Highly coupled dielectric behavior of porous ceramics embedding a polymer. Applied Physics Letters, 68, 263–265.10.1063/1.115657
  • Hashimoto, K. V., & Yamaguchi, M. (1986). Piezoelectric and dielectric properties of composite materials. Proceedings of the IEEE Ultrasonics Symposium, 2, 697–702.
  • Hayashi, T., et al. (1991). Processing of porous 3-3 PZT ceramics using capsule-free O 2 -HIP. Japanese Journal of Applied Physics, 30, 2243–2246.10.1143/JJAP.30.2243
  • Ieşan, D. (1990). Reciprocity, uniqueness and minimum principles in the linear theory of piezoelectricity. International Journal of Engineering Science, 28, 1139–1149.10.1016/0020-7225(90)90113-W
  • Ignaczak, J. (1979). Uniqueness in generalized thermoelasticity. Journal of Thermal Stresses, 2, 171–175.10.1080/01495737908962399
  • Kuang, Z. B. (2010). Variational principles for generalized thermodiffusion theory in pyroelectricity. Acta Mechanica, 214, 275.10.1007/s00707-010-0285-x
  • Kumar, R., & Gupta, V. (2013). Uniqueness and reciprocity theorem and plane waves in thermoelastic diffusion with a fractional order derivative. Chinese Physics B, 22, 074601.10.1088/1674-1056/22/7/074601
  • Kumar, R., & Kansal, T. (2013). Variational principle, uniqueness and reciprocity theorems in the theory of generalized thermoelastic diffusion material. Qscience Connect, 27.
  • Li, J. Y. (2003). Uniqueness and reciprocity theorems for linear thermo-electro-magneto-elasticity. The Quarterly Journal of Mechanics and Applied Mathematics, 56, 35–43.10.1093/qjmam/56.1.35
  • Li, J. Y., & Dunn, M. L. (1998). Micromechanics of magnetoelectroelastic composite materials: Average fields and effective behavior. Journal of Intelligent Material Systems and Structures, 9, 404–416.10.1177/1045389X9800900602
  • 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, 2312–2326.10.1016/j.jsv.2013.12.005
  • Majhi, M. C. (1995). Discontinuities in generalized thermo elastic wave propagation in a semi-infinite piezoelectric rod. Journal of Technical Physics, 36, 269–278.
  • Mindlin, R. D. (1974). Equations of high frequency vibrations of thermopiezoelectric crystal plates. International Journal of Solids and Structures, 10, 625–637.10.1016/0020-7683(74)90047-X
  • Nowacki, W. (1974). Dynamical problem of thermodiffusion in solid-1. Bull. Of polish Academy of Science Series. Science and Technology, 22, 56–64.
  • Nowacki, W. (1978). Some general theorems of thermopiezoelectricity. Journal of Thermal Stresses, 1, 171–182.10.1080/01495737808926940
  • Nowacki, W. (1979). Foundation of linear piezoelectricity. In H. Parkus (Ed.), Interactions in elastic solids (Chapter 1). Wein: Springer.
  • 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, 48–59.
  • Othman, M. I. A. (2004). The uniqueness and reciprocity theorems for generalised thermoviscoelasticity with thermal relaxation times. Mechanics and Mechanical Engineering, 7, 77–87.
  • 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 (SPAWDA), 226–230. doi:10.1109/SPAWDA.2014.6998567
  • Rao, S. S., & Sunar, M. (1993). Analysis of thermopiezoelectric sensors and acutators in advanced intelligent structures. American Institute of Aeronautics and Astronautics Journal, 31, 1280–1286.
  • Sharma, M. D. (2004a). Three-dimensional wave propagation in a general anisotropic poroelastic medium: Phase velocity, group velocity and polarization. Geophysical Journal International, 156, 329–344.10.1111/gji.2004.156.issue-2
  • Sharma, M. D. (2004b). 3-D wave propagation in a general anisotropic poroelastic medium: Reflection and refraction at an interface with fluid. Geophysical Journal International, 157, 947–958.10.1111/gji.2004.157.issue-2
  • Sharma, M. D. (2005). Polarisations of quasi-waves in a general anisotropic porous solid saturated with viscous fluid. Journal of Earth System Science, 114, 411–419.10.1007/BF02702141
  • Sharma, M. D. (2008). Wave propagation in thermoelastic saturated porous medium. Journal of Earth System Science, 117, 951–958.10.1007/s12040-008-0080-4
  • Sharma, M. D. (2009). Boundary conditions for porous solids saturated with viscous fluid. Applied Mathematics and Mechanics, 30, 821–832.10.1007/s10483-009-0702-6
  • Sharma, M. D. (2010). Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media. Acta Mechanica, 215, 307–318.10.1007/s00707-010-0336-3
  • Sharma, M. D., & Gogna, M. L. (1991). Wave propagation in anisotropic liquid-saturated porous solids. The Journal of the Acoustical Society of America, 90, 1068–1073.10.1121/1.402295
  • Sharma, J. N., & Kumar, M. (2000). Plane harmonic waves in piezothermoealstic materials. Indian Journal of Engineering and Materials Sciences, 7, 434–442.
  • Sharma, J. N., & Walia, V. (2007). Further investigations on Rayleigh waves in piezothermoelastic materials. Journal of Sound and Vibration, 301, 189–206.10.1016/j.jsv.2006.09.018
  • Sharma, J. N., Pal, M., & Chand, D. (2005). Propagation characteristics of Rayleigh waves in transversely isotropic piezothermoelastic materials. Journal of Sound and Vibration, 284, 227–248.10.1016/j.jsv.2004.06.036
  • Sherie, H. H., & Dhaliwa, R. S. (1980). A uniqueness theorem and a variational principle for generalized thermoelasticity. Journal of Thermal Stresses, 3, 223–230.10.1080/01495738008926964
  • 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, 1710–1714.10.1007/BF00540771
  • Vashishth, A. K., & Gupta, V. (2009). Vibrations of porous piezoelectric ceramic plates. Journal of Sound and Vibration, 325, 781–797.10.1016/j.jsv.2009.03.034
  • Vashishth, A. K., & Gupta, V. (2011). Uniqueness theorem, theorem of reciprocity, and eigenvalue problems in linear theory of porous piezoelectricity. Applied Mathematics and Mechanics, 32, 479–494.10.1007/s10483-011-1432-8
  • Xia, Z., Ma, S., 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, 57–69.10.1016/S0304-3886(03)00089-5