The propagation of plane waves in nonlocal visco-thermoelastic porous medium based on nonlocal strain gradient theory

References

• Eringen AC. Theory of nonlocal thermoelasticity. Int J Eng Sci. 1974;12:1063–1077.
   Web of Science ®Google Scholar
• Eringen AC. Memory dependent nonlocal elastic solids. Lett Appl Eng Sci. 1974;2(3):145–149.
   Google Scholar
• Eringen AC. Edge dislocation in nonlocal elasticity. Int J Eng Sci. 1977;15:177–183.
   Web of Science ®Google Scholar
• Eringen AC. A mixture theory of electromagnetism and superconductivity. Int J Eng Sci. 1998;36(5/6):525–543.
   Web of Science ®Google Scholar
• Eringen AC. Nonlocal continuum theories. New York: Springer; 2002.
   Google Scholar
• Altan BS. Uniqueness in the linear theory of nonlocal elasticity. Bull Tech Univ Istanb. 1984;37:373–385.
   Google Scholar
• Eringen AC, Edelen DGB. On nonlocal elasticity. Int J Eng Sci. 1972;10:233–248.
   Web of Science ®Google Scholar
• Eringen AC. Nonlocal polar elastic continua. Int J Eng Sci. 1972;10:1–16.
   Web of Science ®Google Scholar
• Eringen AC. On Rayleigh surface waves with small wave lengths. Lett Appl Eng Sci. 1973;1:11–17.
   Google Scholar
• Eringen AC. Plane waves in nonlocal micropolar elasticity. Int J Eng Sci. 1984;22:1113–1121.
   Web of Science ®Google Scholar
• Acharya DP, Mondal A. Propagation of Rayleigh surface waves with small wavelengths in nonlocal visco-elastic solids. Sadhana. 2002;27:605–612.
   Web of Science ®Google Scholar
• Roy I, Acharya DP, Acharya S. Rayleigh wave in a rotating nonlocal magneto-elastic half-plane. J Theo Appl Mech. 2015;45:61–78.
   Web of Science ®Google Scholar
• Khurana A, Tomar SK. Wave propagation in nonlocal microstretch solid. Appl Math Model. 2016;40:5858–5875.
   Web of Science ®Google Scholar
• Yu YJ, Tian X-G, Liu X-R. Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity. Eur J Mech A/Sol. 2016;60:238–253.
   Web of Science ®Google Scholar
• Khurana A, Tomar SK. Rayleigh-type waves in nonlocal micropolar solid half-space. Ultrasonics. 2017;73:162–168.
   PubMed Web of Science ®Google Scholar
• Sing D, Kaur G, Tomar SK. Waves in nonlocal elastic solid with voids. J Elast. 2017;128:85–114.
   Web of Science ®Google Scholar
• Biot M. Thermoelasticity and irreversible thermodynamics. J Appl Phys. 1956;27:240–253.
   Web of Science ®Google Scholar
• Lord H, Shulman Y. A generalized dynamical theory of thermoelasticity. J Mech Phys Solid. 1967;15:299–309.
   Web of Science ®Google Scholar
• Green AE, Lindsay KA. Thermoelasticity. J Elasticity. 1972;2:1–7.
   Google Scholar
• Green AE, Naghdi PM. A re-examination of the basic properties of thermomechanics. Proc RSoc Lond Ser A. 1991;432:171–194.
   Web of Science ®Google Scholar
• Green AE, Naghdi PM. On damped heat waves in an elastic solid. J Therm Stresses. 1992;15:253–264.
   Web of Science ®Google Scholar
• Green AE, Naghdi PM. Thermoelasticity without energy dissipation. J Elast. 1993;31:189–208.
   Web of Science ®Google Scholar
• Chandrasekharaih DS. Thermoelasticity with second sound: a review. Appl Mech Rev. 1986;39(3):355–376.
   Google Scholar
• Chandrasekharaih DS. Hyperbolic thermoelasticity: a review of recent literature. Appl Mech Rev. 1998;51(12):705–729.
   Google Scholar
• Fliige W. Viscoelasticity. 2nd ed. Berlin: Springer-Verlag; 1975.
   Google Scholar
• Ferry JD. Viscoelastic properties of polymers. New York: Wiley; 1980.
   Google Scholar
• Christensen RM. Theory of viscoelasticity: an introduction. New York: Academic press; 1971.
   Google Scholar
• Ieasn D, Scalia A. Some theorems in the theory of thermoviscoelasticity. J Therm Stresses. 1989;12:225–239.
   Web of Science ®Google Scholar
• Bernoulli A, Patria MC. Discontinuity waves through a linear thermo-viscoelastic solid of integral type. Int J Non Linear Mech. 1991;26:141–150.
   Web of Science ®Google Scholar
• Figueiredo I, Trabucho L. A class of contact and friction dynamic problems in thermoelasticity and in thermoviscoelasticity. Int J Eng Sci. 1995;33(1):45–66.
   Web of Science ®Google Scholar
• Shen W, Zheng SM, Zhu PC. The existence and asymptotic behavior of weak solutions to non-linear thermoviscoelastic systems with clamped boundary conditions. Q Appl Mech. 1999;57:93–102.
   Google Scholar
• Ezzat MA, Othman MA, El-Karamany AS. State space approach to generalized thermo-viscoelastiocity with two relaxation times. Int J Eng Sci. 2002;33(1):45–66.
   Google Scholar
• Singh B. Wave propagation in a generalized thermoelastic material with voids. Appl Math Comput. 2007;189:698–709.
   Web of Science ®Google Scholar
• Nunziato JW, Cowin SC. A nonlinear theory of elastic materials with voids. Arch Rational Mech Anal. 1979;72:175–201.
   Web of Science ®Google Scholar
• Cowin SC, Nunziato JW. Linear elastic materials with voids. J Elasticity. 1983;13:125–147.
   Web of Science ®Google Scholar
• Puri P, Cowin SC. Plane waves in linear elastic materials with voids. J Elasticity. 1985;15:167–183.
   Web of Science ®Google Scholar
• Iesan D. A theory of thermoelastic materials with voids. Acta Mech. 1986;60:67–89.
   Web of Science ®Google Scholar
• Iesan D. Nonlinear plane strain of elastic materials with voids. Math Mech Solids. 2006;11(4):361–384.
   Web of Science ®Google Scholar
• Ciarletta M, Scalia A. On the nonlinear theory of nonsimple thermoelastic materials with voids. Z Angew Maths Mech. 1993;73:7–75.
   Web of Science ®Google Scholar
• Ciarletta M, Scarpetta E. Some results on thermoelasticity for dielectric materials with voids. Z Angew Maths Mech. 1995;75:707–714.
   Web of Science ®Google Scholar
• Dhaliwal RS, Wang J. A heat-flux dependent theory of thermoelasticity with voids. Acta Mech. 1995;110:33–39.
   Web of Science ®Google Scholar
• Hetnarski RB. The fundamental solution of the coupled thermoelastic problem for small times. Archwm Mech Stosow. 1964;16:23–31.
   Google Scholar
• Hetnarski RB. Solution of the coupled problem of thermoelasticity in form of a series of functions. Archwm Mech Stosow. 1964;16:919–941.
   Google Scholar
• Scarpetta E. On the fundamental solutions in micropolar elasticity with voids. Acta Mech. 1990;82:151–158.
   Web of Science ®Google Scholar
• Svanadze M. The fundamental matrix of the linearized equations of the theory of elastic mixtures, Proc. I. Vekue Institute of Applied mathematics, Tbilisi State University, Vol. 23, p 133–148, 1988.
   Google Scholar
• Svanadze M. The fundamental solution of the oscillation equations of thermoelasticity theory of mixtures of two solids. J Therm Stresses. 1996;19:633–648.
   Web of Science ®Google Scholar
• Svanadze M. Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures. J Therm Stresses. 2004;27:151–170.
   Web of Science ®Google Scholar
• Svanadze M, Tibullo V, Zampoli V. Fundmental solution in the theory of micropolar thermoelasticity without energy dissipation. J Therm Stresses. 2006;29:57–66.
   Web of Science ®Google Scholar
• Svanadze M, Ciarletta M, Scalia A. Fundamental solution in the theory of micropolar thermoelasticity for materials with voids. J Therm Stresses. 2007;30:213–229.
   Web of Science ®Google Scholar
• L. Hormander, Linear partial diferential operators, Springer Verlag: Berlin, 1963.
   Google Scholar
• L. Hormander, The analysis of linear partial differential operators II: differential operators with constant coefficients, Springer-Verlag: Berlin, 1983.
   Google Scholar
• Sharma K, Kumar P. Propagation of plane waves and fundamental solution in thermo-viscoelastic medium with voids. J Therm Stresses. 2013;36(2):94–111.
   Web of Science ®Google Scholar
• Kumar R, Devi S. Plane waves and fundamental solution in a modified couple stress generalized thermoelastic with three-phase-lag model. Multidiscipline Model Mater Struct. 2016;12(4):693–711.
   Web of Science ®Google Scholar
• Svanadze M. Fundamental solution in the theory of micropolar thermoelasticity for materials with voids. J Therm Stresses. 2007;30:219–238.
   Web of Science ®Google Scholar
• Biswas S, Abo-Dahab SM. Effect of phase-lags on Rayleigh wave propagation in initially stressed magneto-thermoelastic orthotropic medium. Appl Math Model. 2018;59:713–727.
   Web of Science ®Google Scholar
• Biswas S, Sarkar N. Fundamental solution of the steady oscillations equations in porous thermoelastic medium with dual-phase-lag model. Mech Mater. 2018;126:140–147.
   Web of Science ®Google Scholar
• Bachher M, Sarkar N. Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer. Waves Random Complex Media. 2019;29(4):595–613.
   Web of Science ®Google Scholar
• Mindlin R. Micro-structure in linear elasticity. Arch Ration Mech Anal. 1964;16:51–78.
   Web of Science ®Google Scholar
• Mindlin R. Second gradient of strain and surface-tension in linear elasticity. Int J Solids Struct. 1965;1:414–438.
   Google Scholar
• Lim CW, Zhang G, Reddy JN. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids. 2015;78:298–313.
   Web of Science ®Google Scholar