Vibration analysis of functionally graded microbeam under initial stress via a generalized thermoelastic model with dual-phase lags

2021 ◽  
Author(s):  
A. E. Abouelregal ◽  
W. W. Mohammed ◽  
Hamid Mohammad-Sedighi
Keyword(s):  
Initial Stress ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Dual Phase ◽  
Thermoelastic Model ◽  
Phase Lags ◽  
Generalized Thermoelastic

Vibration analysis of functionally graded thermoelastic nonlocal sphere with dual-phase-lag effect

2020 ◽  
Vol 231 (5) ◽  
pp. 1765-1781 ◽  
Author(s):  
Dinesh Kumar Sharma ◽  
Mitali Bachher ◽  
Santanu Manna ◽  
Nantu Sarkar
Keyword(s):  
Vibration Analysis ◽  
Functionally Graded ◽  
Phase Lag ◽  
Dual Phase ◽  
Lag Effect

DUAL PHASE LAG HEAT CONDUCTION IN FUNCTIONALLY GRADED HOLLOW SPHERES

2014 ◽  
Vol 06 (01) ◽  
pp. 1450002 ◽  
Author(s):  
A. H. AKBARZADEH ◽  
Z. T. CHEN
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Hollow Spheres ◽  
Functionally Graded ◽  
Inversion Method ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Spherically Symmetric ◽  
Dual Phase ◽  
Phase Lags

In the present work, the dual phase lag heat conduction in functionally graded hollow spheres is investigated under spherically symmetric and axisymmetric thermal loading. The heat conduction equation is given based on the dual phase lag theory to consider the details of energy transport in the material in comparison with the non-Fourier hyperbolic heat conduction. All the material properties of the sphere are taken to vary continuously along the radial direction following a power-law with arbitrary non-homogeneity indices except the phase lags which are assumed to be constant for simplicity. The specified spherically symmetric and axisymmetric boundary conditions of the sphere lead to a 1D and 2D heat conduction problem, respectively. Employing the Laplace transform to eliminate the time dependency of the problem, analytical solutions are obtained for the temperature and heat flux. The final results in the time domain are obtained by a numerical Laplace inversion method. The speed of thermal wave in the functionally graded sphere based on the dual phase lag is compared with that of the hyperbolic heat conduction. Furthermore, the numerical results are shown to clarify the effects of phase lags and non-homogeneity indices on the thermal response. The current results are verified with those reported in the literature.

scholarly journals Solution of Lord-Shulmans and dual-phase-lag theories problem on a photothermal rotational semiconductor medium with voids and initial stress

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 59-68
Author(s):  
Hammad Alotaibi
Keyword(s):  
Boundary Conditions ◽  
Initial Stress ◽  
Carrier Density ◽  
Equations Of Motion ◽  
Phase Lag ◽  
Dual Phase ◽  
Stress Components ◽  
Differential Equa ◽  
Generalized Thermoelastic ◽  
Thermoelastic Theory

This paper discusses a photo-thermal rotational semiconductor medium with ini?tial stress, and voids by considering two thermoelastic theories: Lord-Shulman and Dual-Phase-Lag models. The equations of motion, temperature, voids, and photothermal have been investigated under two generalized thermoelastic theory. The technique of normal mode has been applied to solve the differential equa?tions system with appropriate boundary conditions. Quantities of physical interest such as displacement, stress components, concentration, temperature, and carrier density are calculated and displayed graphically to demonstrate the effect of the external parameters. The obtained results, by using the two theories, show that the dual-phase-lag theory gives an origin results comparing with obtained results by Lord-Shulman theory. By neglecting the initial stress and voids, and considering the only dual-phase-lag theory, then the results obtained in this paper are deduced to the results of Abbas et al. [1].

Heat conduction in one-dimensional functionally graded media based on the dual-phase-lag theory

2012 ◽  
Vol 227 (4) ◽  
pp. 744-759 ◽  
Author(s):  
AH Akbarzadeh ◽  
ZT Chen
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Spherical Coordinates ◽  
One Dimensional ◽  
Phase Lags ◽  
Functionally Graded Media

In this article, heat conduction in one-dimensional functionally graded media is investigated based on the dual-phase-lag theory to consider the microstructural interactions in the fast transient process of heat conduction. All material properties of the media are assumed to vary continuously according to a power-law formulation with arbitrary non-homogeneity indices except the phase lags which are taken constant for simplicity. The one-dimensional heat conduction equations based on the dual-phase-lag theory are derived in a unified form which can be used for Cartesian, cylindrical, and spherical coordinates. A semi-analytical solution for temperature and heat flux is presented using the Laplace transform to eliminate the time dependency of the problem. The results in the time domain are then given by employing a numerical Laplace inversion technique. The semi-analytical solution procedure leads to exact expressions for the thermal wave speed in one-dimensional functionally graded media with different geometries based on the dual-phase-lag and hyperbolic heat conduction theories. The transient temperature distributions have been found for various types of dynamic thermal loading. The numerical results are shown to reveal the effects of phase lags, non-homogeneity indices, and thermal boundary conditions on the thermal responses for different temporal disturbances. The results are verified with those reported in the literature for hyperbolic heat conduction in cylindrical and spherical coordinates.

scholarly journals Solution of Lord-Shulmans and dual-phase-lag theories problem on a photothermal rotational semiconductor medium with voids and initial stress

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 59-68
Author(s):  
Hammad Alotaibi
Keyword(s):  
Boundary Conditions ◽  
Initial Stress ◽  
Carrier Density ◽  
Equations Of Motion ◽  
Phase Lag ◽  
Dual Phase ◽  
Stress Components ◽  
Differential Equa ◽  
Generalized Thermoelastic ◽  
Thermoelastic Theory

This paper discusses a photo-thermal rotational semiconductor medium with ini?tial stress, and voids by considering two thermoelastic theories: Lord-Shulman and Dual-Phase-Lag models. The equations of motion, temperature, voids, and photothermal have been investigated under two generalized thermoelastic theory. The technique of normal mode has been applied to solve the differential equa?tions system with appropriate boundary conditions. Quantities of physical interest such as displacement, stress components, concentration, temperature, and carrier density are calculated and displayed graphically to demonstrate the effect of the external parameters. The obtained results, by using the two theories, show that the dual-phase-lag theory gives an origin results comparing with obtained results by Lord-Shulman theory. By neglecting the initial stress and voids, and considering the only dual-phase-lag theory, then the results obtained in this paper are deduced to the results of Abbas et al. [1].

Sign in / Sign up

Export Citation Format

Share Document