Modeling of memory-dependent derivative in a fiber-reinforced plate under gravitational effect

References

• A. Sur and M. Kanoria, “Fibre-reinforced magneto-thermoelastic rotating medium with fractional heat conduction,” Procedia Eng., vol. 127, pp. 605–612, 2015.
   Google Scholar
• A. Sur and M. Kanoria, “Modeling of fibre-reinforced Magneto-thermoelastic plate with heat sources,” Procedia Eng., vol. 173, pp. 875–882, 2017.
   Google Scholar
• A. Sur and M. Kanoria, “Thermoelastic interaction in a viscoelastic functionally graded half-space under three phase lag model,” Eur. J. Comput. Mech., vol. 23, pp. 179–198, 2014.
   Google Scholar
• P. Das and M. Kanoria, “Study of finite thermal wavs in a magneto-thermo-elastic roatating medium,” J. Therm. Stresses, vol. 37, pp. 405–428, 2014.
   Web of Science ®Google Scholar
• P. Das, A. Kar, and M. Kanoria, “Analysis of magneto-thermoelastic response in a transversely isotropic hollow cylinder under thermal shock with three-phase-lag effect,” J. Therm. Stresses, vol. 36, pp. 239–258, 2013.
   Web of Science ®Google Scholar
• S. K. Roy Choudhuri, “On a thermoelastic three-phase-lag model,” J. Therm. Stresses, vol. 30, pp. 231–238, 2007.
   Web of Science ®Google Scholar
• S. Chakravorty, S. Ghosh, and A. Sur, “Thermo-viscoelastic interaction in a three-dimensional problem subjected to fractional heat conduction,” Procedia Eng., vol. 173, pp. 851–858, 2017.
   Google Scholar
• A. Sur and M. Kanoria, “Fractional order generalized thermoelastic functionally graded solid with variable material properties,” J. Solid Mech., vol. 6, pp. 54–69, 2014.
   Google Scholar
• A. Sur and M. Kanoria, “Three dimensional thermoelastic problem under two-temperature theory,” Int. J. Comput. Methods, vol. 14, no. 2, pp. 1750030– (1–17), 2016. DOI:10.1142/S021987621750030X.
   Web of Science ®Google Scholar
• T. J. I’A. Bromwich, “On the influence of gravity on elastic waves and in particular on the vibrations of an elastic globe,” Proc. Lond. Math. Soc., vol. 30, pp. 98–120, 1898.
   Google Scholar
• M. I. A. Othman and K. Lotfy, “The influence of gravity on 2-D problem of two temperature generalized thermoelastic medium with thermal relaxation,” J. Comput. Theor. Nanosci., vol. 12, pp. 2587–2600, 2015.
   Google Scholar
• S. N. De and P. R. Sengupta, “Surface waves under the influence of gravity,” Garlands Beitr. Geophys., vol. 85, pp. 311–318, 1976.
   Google Scholar
• S. M. Said, “Influence of gravity on generalized magneto-thermoelastic medium for three-phase-lag model,“ J. Comput. Appl. Math., vol. 291, pp. 142–157, 2016.
   Web of Science ®Google Scholar
• M. I. A. Othman, S. Y. Atwa, A. Jahangir, and A. Khan, “Gravitational effect on plane waves in generalized thermo-microstretch elastic solid under Green-Naghdi theory,” Appl. Math. Inf. Sci. Lett., vol. 1, pp. 25–38, 2013.
   Google Scholar
• S. Kumar and P. C. Pal, “Wave propagation in an inhomogeneous anisotropic generalized thermoelastic solid under the effect of gravity,” Comput. Therm. Sci. Int. J., vol. 6, pp. 241–250, 2014.
   Google Scholar
• F. S. Bayones and N. S. Hussein, “Fibre-reinforced generalized thermoelastic medium subjected to gravity field,” J. Modern Phys., vol. 6, pp. 1113–1134, 2015.
   Google Scholar
• P. Pal and M. Kanoria, “Thermoelastic wave propagation in a transversely isotropic thick plate under Green-Naghdi theory due to gravitational field,” J. Therm. Stresses, vol. 40, pp. 470–485, 2017.
   Web of Science ®Google Scholar
• K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Berlin, Heidelberg: Springer-Verlag, 2010.
   Google Scholar
• M. Caputo, “Linear models of dissipation whose Q is almost frequency independent II,” Geophys. J. Roy Astron. Soc., vol. 3, pp. 529–539, 1967.
   Web of Science ®Google Scholar
• M. Caputo and F. Mainardi, “Linear model of dissipation in anelastic solids,” La Rivista del Nuovo Cimento, vol. 1, pp. 161–198, 1971.
   Google Scholar
• A. Sur and M. Kanoria, “Fractional order two-temperature thermoelasticity with finite wave speed,” Acta Mech., vol. 223, pp. 2685–2701, 2012.
   Web of Science ®Google Scholar
• P. Purkait, A. Sur, and M. Kanoria, “Thermoelastic interaction in a two dimensional infinite space due to memory dependent heat transfer,” Int. J. Adv. Appl. Math. Mech., vol. 5, no. 1, pp. 28–39, 2017.
   Google Scholar
• Y. J. Yu, W. Hu, and X. G. Tian, “A novel generalized thermoelasticity model based on memory-dependent derivative,” Int. J. Eng. Sci., vol. 81, pp. 123–134, 2014.
   Web of Science ®Google Scholar
• M. A. Ezzat, A. S. El-Karamany, and A. A. El-Bary, “Electro-thermoelasticity theory with memory-dependent derivative heat transfer,” Int. J. Eng. Sci., vol. 99, pp. 22–38, 2016.
   Web of Science ®Google Scholar
• M. A. Ezzat and A. A. El-Bary, “Memory-dependent derivatives theory of thermo-viscoelasticity involving two-temperature,” J. Mech. Sci. Tech., vol. 29, pp. 4273–4279, 2015.
   Web of Science ®Google Scholar
• M. A. Ezzat, A. S. El-Karamany, and A. A. El-Bary, “Generalized thermoelasticity with memory-dependent derivatives involving two temperatures,” Mech. Adv. Mater. Struct., vol. 23, pp. 545–553, 2016.
   Web of Science ®Google Scholar
• M. A. Ezzat, A. S. El-Karamany, and A. A. El-Bary, “Modeling of memory-dependent derivative in generalized thermoelasticity,” Eur. Phys. J. Plus, vol. 131, Article 372, 2016.
   Web of Science ®Google Scholar
• K. Lotfy and N. Sarkar, “Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature,” Mech. Time-Depend. Mater., 2017. DOI:10.1007/s11043-017-9340-5.
   Web of Science ®Google Scholar
• J. L. Wang and H. F. Li, “Surpassing the fractional derivative: Concept of the memory-dependent derivative,” Comput. Math. Appl., vol. 62, pp. 1562–1567, 2011.
   Web of Science ®Google Scholar
• A. S. El-Karamany and M. A. Ezzat, “Thermoelastic diffusion with memory-dependent derivative,” J. Therm. Stresses, vol. 39, pp. 1035–1050, 2016.
   Web of Science ®Google Scholar
• A. Sur and M. Kanoria, “Modeling of memory-dependent derivative in a fibre-reinforced plate,” Thin Walled Struct., 2017. DOI:10.1016/j.tws.2017.05.005.
   Web of Science ®Google Scholar
• S. Chiriţǎ, C. D’Apice, and V. Zampoli, “The time differential three-phase-lag heat conduction model: Thermodynamic compatibility and continuous dependence,” Int. J. Heat Mass Transfer, vol. 102, pp. 226–232, 2016.
   Web of Science ®Google Scholar
• V. Zampoli and A. Landi, “A domain of influence result about the time differential three-phase-lag thermoelastic model,” J. Therm. Stress, 2016. DOI:10.1080/01495739.2016.1195242.
   Web of Science ®Google Scholar
• A. E. Green and P. M. Nagdhi, “A unified procedure for construction of theories of deformable media. II. Generalized Continua,” Proc. R. Soc. A, vol. 448, pp. 357–377, 1995.
   Google Scholar
• G. Honig and U. Hirdes, “A method for the numerical inversion of the Laplace transform,” J. Comput. Appl. Math., vol. 10, pp. 113–132, 1984.
   Web of Science ®Google Scholar
• A. J. M. Spencer, Continuum Theory of the Mechanics of Fibre-Reinforced Composites. Springer, 1984. ISBN:978–3-7091–4336-0.
   Google Scholar
• S. H. Mallik and M. Kanoria, “A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source,” Eur. J. Mech. A Solids, vol. 27, pp. 607–621, 2008.
   Web of Science ®Google Scholar
• M. F. Markham, “Measurement of the elastic constants of fibre composites by ultrasonics,” Composites, vol. 1, no. 2, pp. 145–149, 1970.
   Google Scholar
• A. Sur and M. Kanoria, “Propagation of thermal waves in a functionally graded thick plate,” Math. Mech. Solids, vol. 22, pp. 718–736, 2015.
   Web of Science ®Google Scholar
• R. Quintanilla and R. Racke, “A note on stability in three-phase-lag heat conduction,” J. Heat Mass Transfer, vol. 51, pp. 24–29, 2008.
   Web of Science ®Google Scholar