Generalized Lagging Response of Thermoelastic Beams

The vibrations of Euler-Bernoulli metal beam are accommodated in the present study by taking into account the possibility of activating the microstructural effects, captured by the temperature gradient phase lag, in the fast transient process captured by the heat flux phase lag. The thermal moment is approximated as the difference between the top and the bottom surface temperatures (Massalas and Kalpakidis 1983). Three generalizations of the Biot model of thermomechanics are considered: Lord-Shulman, dual-phase-lag (Tzou 1997), and modified dual-phase-lag (Awad 2012). It is found that when the response time is shortened, the material dimensions are small, or when the method of heating is changed, the dual-phase-lag model records a significant decrease in the lattice variables. The spurious serrations of the classical thermoelastic wave are smoothed in the dual-phase-lag wave. The dual-phase-lag thermoelasticity is the closest macroscopic approach to the ultrafast model (Chen et al. 2002).