Effect of hyperbolic heat conduction on the linear and nonlinear vibration of CNT reinforced size-dependent functionally graded microbeams

2019 ◽  
Vol 137 ◽  
pp. 57-72 ◽  
Author(s):  
A. Pourasghar ◽  
Z. Chen
Keyword(s):  
Heat Conduction ◽  
Nonlinear Vibration ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Size Dependent ◽  
Linear And Nonlinear

Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Conduction Theory ◽  
Hollow Cylinders ◽  
Fourier Heat Conduction ◽  
Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

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.

Analysis of One-Dimensional Hyperbolic Heat Conduction in a Functionally Graded Thin Plate

2011 ◽  
Author(s):  
Mohammad Reza Raveshi ◽  
Shayan Amiri ◽  
Ali Keshavarz
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Functionally Graded ◽  
Dimensionless Temperature ◽  
Hyperbolic Heat Conduction ◽  
Temperature Peak ◽  
Trial Solution ◽  
One Dimensional ◽  
Graded Material ◽  
The Time Domain

This paper presents the analytical solution of one-dimensional non-Fourier heat conduction problem for a finite plate made of functionally graded material. To investigate the influence of material properties variation, exponential space-dependant functions of thermal conductivity and specific heat capacity are considered. The problem is solved analytically in the Laplace domain, and the final results in the time domain are obtained using numerical inversion of the Laplace transform. The trial solution method with collocation optimizing criterion has been applied to solve the hyperbolic heat conduction equation based on polynomial shape function approximation. Due to the reflection and interaction of the thermal waves, the temperature peak happens on the insulated wall of the FGM plate, so the major aim of this paper is to find the amount of temperature peak and the time at which it happens. It has been shown that the dimensionless temperature peak and its happening time increase along with an increase in the dimensionless relaxation time. The results are validated by comparison with the results from an exact available solution solved at special case which shows a close agreement.

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.

Nonlinear Vibration of PZT4/PZT-5H Monomorph and Bimorph Beams with Graded Microstructures

2015 ◽  
Vol 15 (07) ◽  
pp. 1540015 ◽  
Author(s):  
Jie Yang ◽  
Sritawat Kitipornchai ◽  
Chuang Feng
Keyword(s):  
Nonlinear Vibration ◽  
Smart Materials ◽  
Structural Control ◽  
Volume Fraction ◽  
Piezoelectric Materials ◽  
Slenderness Ratio ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Functionally Graded Piezoelectric Materials ◽  
Linear And Nonlinear

Monomorph and bimorph actuators made of piezoelectric materials are widely used in smart materials and structural control. Recent studies show that their performances can be remarkably improved by the use of functionally graded piezoelectric materials (FGPMs) whose compositional profile and effective material properties are graded along the thickness direction. This paper investigates the linear and nonlinear vibration behaviors of monomorph and bimorph made from a mixture of PZT4 and PZT-5H with material composition following a power law distribution. Theoretical formulations are based on von Kármán kinematic relationships and Timoshenko beam theory to account for the effect of transverse shear deformation. The differential quadrature method (DQM) and the second-order backward difference scheme are employed to obtain the linear and nonlinear vibration frequencies. A parametric study is conducted to investigate the influences of volume fraction index, slenderness ratio, nonlinear deformation and different loading conditions.

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