Journal of Theoretical
and Applied Mechanics

56, 1, pp. 15-30, Warsaw 2018
DOI: 10.15632/jtam-pl.56.1.15

A generalized thermoelastic dual-phase-lagging response of thick beams subjected to harmonically varying heat and pressure

Ashraf M. Zenkour
The generalized thermoelastic problem of a thermo-mechanically loaded beam is studied.
The upper surface of the beam is thermally isolated and subjected to a mechanical load while
the bottom surface is traction free and subjected to a heating source. Based on the heat
conduction equation containing the thermoelastic coupling term and the two-dimensional
elasticity theory, thermoelastic coupling differential equations of motion are established.
The generalized thermoelasticity theory with the dual-phase-laggings (DPLs) model is used
to solve this problem. A closed-form analytical technique is used to calculate vibration of
displacements and temperature. The effects of the phase-laggings (PLs), the intensity of the
applied load and heat parameters on the field quantities of the beam are discussed. The
variation along the axial direction and through-the-thickness distributions of all fields are
investigated. Some comparisons have been also shown graphically to estimate the effects of
the time on all the studied fields.
Keywords: thermoelasticity, dual-phase-lag model, two-dimensional elasticity solution