Purpose In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium. Design/methodology/approach The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis. Findings The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed. Originality/value To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.

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In the present paper, the theory of multi-phase-lags with fractional derivative heat transfer thermoelasticity was used to study the wave propagation on a nonlocal fiber-reinforced thermoelastic medium. The exact expressions for the displacement components, temperature, and stress components are obtained by using the Fourier and Laplace transforms. The comparisons are shown graphically to explore the effects of rotation, initial stress and fractional order parameters as well as a nonlocal parameter on different physical quantities. Numerical computations are carried out with the help of Matlab software.