The effect of dual-phase-lag model on reflection of thermoelastic waves in a solid half space with variable material properties

2018

jtam

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.

Section: Introductionmentioning

confidence: 99%

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

2018

jtam

“…The heat equation associated with LS theory is of hyperbolic type and consequently eliminates the paradox of infinite velocity of propagation inherent in both coupled (CTE) and uncoupled theories of thermoelasticity. Tzou (1995Tzou ( , 1997) presented another alteration with Fourier's law to investigate two time lags (see also Abbas and Zenkour, 2014; Abouelregal, 2011; Abouelregal and Abo-Dahab, 2012; Zenkur, 2016b; Zenkour et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic response of nanobeam resonators subjected to exponential decaying time varying load

Abouelregal

2017

jtam

This work investigates the vibrational response of thermoelastic nanobeam resonators induced by ramp-type heating and subjected to exponential decaying time varying load via Euler-Bernoulli beam theory. Governing equations are derived in the context of nonlocal generalized thermoelasticity theory with dual phase lags. The nonlocal nanobeam theory incorporates a nonlocal parameter to capture the small scale effect. Using the Laplace transform technique, an analytical solution has been attained. and inversions of the transformed solutions have been carried out by means of calculus of residues. The effects of nonlocal, point load and ramping-time parameters on all studied fields of the nanobeam are investigated and discussed.

“…To the author's best knowledge, only a few authors have presented the exact two-dimensional solution of the generalized thermoelastic beam problem up to present time. Downloaded by [RMIT University Library] at 23: 12 29 June 2016 Many investigators have used different forms of the normal mode analysis to obtain the exact analytical solutions of various thermoelastic problems [1,8,9,10,11,19,21,22,23,28]. Most of these publications have used the Laplace transformation to eliminate the time parameter.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Coupled Solution for Thermoelastic Beams via Generalized Dual-Phase-Lags Model

Mathematical Modelling and Analysis

2016

The generalized thermoelastic problem of a thick-walled simply-supported beam subjected to different applied heat source and mechanical loads at its surfaces is studied. The thermoelastic coupling differential equations of motion of the beam are established. The generalized thermoelasticity based on the dual-phase-lags (DPLs) theory is considered to treat this problem. An exact 2-D coupled solution is presented to deduce analytical expressions for the temperature, displacements and stresses. The time-harmonic motion behavior as well as the thermal and mechanical conditions at the bounded faces of the beam is used for this purpose. The effect of the DPLs on the field quantities against the axial and normal directions of the beam under thermomechanical loads is discussed. Final investigations to various thermoelastic models are made.