scholarly journals Functionally Graded Piezoelectric Medium Exposed to a Movable Heat Flow Based on a Heat Equation with a Memory-Dependent Derivative

Materials ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 3953 ◽  
Author(s):  
Ahmed E. Abouelregal ◽  
Hijaz Ahmad ◽  
Shao-Wen Yao
Keyword(s):  
Axial Direction ◽  
Functionally Graded ◽  
Piezoelectric Medium ◽  
Piezoelectric Response ◽  
Modified Model ◽  
The Laplace Transform ◽  
Graded Material ◽  
Limited Length ◽  
Functionally Graded Piezoelectric ◽  
Generalized Heat Conduction

The current work deals with the study of a thermo-piezoelectric modified model in the context of generalized heat conduction with a memory-dependent derivative. The investigations of the limited-length piezoelectric functionally graded (FGPM) rod have been considered based on the presented model. It is assumed that the specific heat and density are constant for simplicity while the other physical properties of the FGPM rod are assumed to vary exponentially through the length. The FGPM rod is subject to a moving heat source along the axial direction and is fixed to zero voltage at both ends. Using the Laplace transform, the governing partial differential equations have been converted to the space-domain, and then solved analytically to obtain the distributions of the field quantities. Numerical computations are shown graphically to verify the effect of memory presence, graded material properties, time-delay, Kernel function, and the thermo-piezoelectric response on the physical fields.

THERMOPIEZOELECTRIC ANALYSIS OF A FUNCTIONALLY GRADED PIEZOELECTRIC MEDIUM

2011 ◽  
Vol 03 (01) ◽  
pp. 47-68 ◽  
Author(s):  
A. H. AKBARZADEH ◽  
M. H. BABAEI ◽  
Z. T. CHEN
Keyword(s):  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
Functionally Graded ◽  
Piezoelectric Medium ◽  
Inversion Method ◽  
Laplace Domain ◽  
Decoupling Method ◽  
The Laplace Transform ◽  
Functionally Graded Piezoelectric ◽  
The Time Domain

The thermopiezoelectrical behavior of a functionally graded piezoelectric medium (FGPM) is investigated in the present work. For the special case, the dynamic response of an FGPM rod excited by a moving heat source is studied. The material properties of the FGPM rod are assumed to vary exponentially through the length, except for specific heat and thermal relaxation time which are held constant for simplicity. The governing differential equations in terms of displacement, temperature, and electric potential are obtained in a general form that includes coupled and uncoupled thermoelasticity. The coupled formulation considers classical thermoelasticity as well as generalized thermoelasticity. Employing the Laplace transform and successive decoupling method, unknowns are given in the Laplace domain. Employing a numerical Laplace inversion method, the solutions are gained in the time domain. Numerical examples for the transient response of the FGPM rod are displayed to clarify the differences among the results of the generalized, coupled, and uncoupled theories for various nonhomogeneity indices. The results are verified with those reported in the literature.

Response analysis of hybrid functionally graded material plate subjected to thermo-electro-mechanical loading

2020 ◽  
pp. 146442072098003
Author(s):  
Pawan Kumar ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Piezoelectric Material ◽  
Functionally Graded Material ◽  
Axial Stress ◽  
Functionally Graded ◽  
Response Analysis ◽  
Functionally Graded Piezoelectric Material ◽  
Graded Material ◽  
Functionally Graded Piezoelectric

Static and free vibration response analysis of a functionally graded piezoelectric material plate under thermal, electric, and mechanical loads is done in this study. The displacement field is acquired using the first-order shear deformation theory, and the Hamilton principle is applied to deduce the motion equations. Temperature-dependent material properties of the functionally graded material plate are used, and these properties follow the power-law distributions along the thickness direction. However, the properties of piezoelectric material layers are assumed to be independent of the electric field and temperature. Finite element formulation for the functionally graded piezoelectric material plate is done using the combined effect of mechanical and electrical loads. The effects of parameters like electrical loading, volume fraction exponent N, and temperature distribution on the static and free vibration characteristics of the functionally graded piezoelectric material square plate are analyzed and presented. Responses are obtained in terms of the centerline deflection, axial stress and the nondimensional natural frequency with various boundary conditions. It is observed that the centerline deflection and nondimensional natural frequency increases as exponent N increases. At the same time, the axial stress decreases with an increase in exponent N. The findings of the static and the free vibration analysis suggest the potential application of the functionally graded piezoelectric material plate in the piezoelectric actuator as well as for sensing deflection in bimorph.

Dynamic Response for a Functionally Graded Rectangular Plate Subjected to Thermal Shock Based on LS Theory

2013 ◽  
Vol 332 ◽  
pp. 381-395 ◽  
Author(s):  
Seyed Mohsen Nowruzpour Mehrian ◽  
Mohammad Hasan Naei ◽  
Shahla Zamani Mehrian
Keyword(s):  
Thermal Shock ◽  
Rectangular Plate ◽  
Time Domain ◽  
Sudden Change ◽  
Functionally Graded ◽  
State Equations ◽  
The Laplace Transform ◽  
Graded Material ◽  
Thermoelastic Response ◽  
The Time Domain

Thermal shock describes the way that a material exposed to a sudden change in temperature. These conditions usually take place in aerospace industry, when aircraft encounter the atmosphere layers. It also happens in combustion chamber of engines when mixture of fuel and air ignite in cylinder. Classical thermoelasticity is not capable to analyze such a problem. Therefore, generalized coupled thermoelasticity theories arose. In this article, the dynamic coupled thermoelastic response of a rectangular plate made of functionally graded material subjected to a thermal shock based on Lord-Shulman theory is studied. Using state space approach, the state equations of the problem are obtained. The plate’s boundary condition is simply support on the edges and the variation of mechanical properties is assumed to change along the thickness of the plate. The Laplace transform is applied to transform governing equations from time domain to the Laplace domain. Then by using a numerical method, the equations are solved and the results are inversed to the time domain displacement and temperature field are acquired. Results are presented for different power law indices and they are validated by previous reported literature.

Circumferential waves in pre-stressed functionally graded cylindrical curved plates

2014 ◽  
Vol 21 (1) ◽  
pp. 87-97 ◽  
Author(s):  
Jiangong Yu ◽  
Chuanzeng Zhang ◽  
Xiaoming Zhang
Keyword(s):  
Initial Stress ◽  
Wave Equations ◽  
Axial Direction ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Initial Stresses ◽  
Polynomial Method ◽  
Coupled Wave Equations ◽  
Graded Material ◽  
Polynomial Series

AbstractInitial stress (pre-stress) in functionally graded material (FGM) structures is often inevitable because of the limitation of available manufacturing technology. On the basis of the “mechanics of incremental deformations”, the circumferential wave characteristics in FGM cylindrical curved plates under uniform initial stresses in the radial and axial directions are investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. Through numerical examples, the convergence of the polynomial method is discussed. The influences of the initial stresses on the circumferential Lamb-like and the circumferential SH waves are investigated, respectively. Numerical results show that they are quite distinct. Moreover, the influences of the initial stress in the axial direction are very different from those in the radial direction, both on the dispersion curves and on the displacement and stress distributions.

Effects of piezoelectric rings on electro-elasto-dynamic behaviour of functionally graded cylindrical shell

2016 ◽  
Vol 28 (2) ◽  
pp. 272-289 ◽  
Author(s):  
Mohammadreza Saviz
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Virtual Work ◽  
Electrical Potential ◽  
Axial Direction ◽  
Functionally Graded ◽  
Radial Coordinate ◽  
Graded Material

A layer-wise finite element approach is adopted to analyse the hollow cylindrical shell made of functionally graded material with piezoelectric rings as sensor/actuator, under dynamic load. The mechanical properties of the substrate are regulated by volume fraction as a function of radial coordinate. The thickness of functionally graded material shell and piezo-rings is divided into mathematical sub-layers and then the general layer-wise laminate theory is formulated through introducing piecewise continuous approximations across the thickness, accounting for any discontinuity in derivatives of the displacement at the interface between the ring and cylinder. The virtual work statement including structural and electrical potential energies yields the three-dimensional governing equations which are reduced to two-dimensional differential equations, using layer-wise method. For axisymmetric case, the resulted equations are solved with one-dimensional finite element method in the axial direction. By assembling stiffness and mass matrices, the required stress and displacement continuities at each interface and between the two adjacent elements are forced. The results for free vibration and static loading are applied to study the convergence and verified by comparing them to solutions of similar existing problems. The induced deformation by piezoelectric actuators as well as the effect of rings on functionally graded material shell is investigated.

On modal analysis of axially functionally graded material beam under hygrothermal effect

2019 ◽  
Vol 234 (5) ◽  
pp. 1085-1101 ◽  
Author(s):  
Pankaj Sharma ◽  
Rahul Singh ◽  
Muzamal Hussain
Keyword(s):  
Modal Analysis ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Axial Direction ◽  
Functionally Graded ◽  
Element Analysis ◽  
Hygrothermal Effect ◽  
Graded Material ◽  
Eigen Frequencies ◽  
Axially Functionally Graded Material

This investigation focuses on the modal analysis of an axially functionally graded material beam under hygrothermal effect. The material constants of the beam are supposed to be graded smoothly along the axial direction under both power law and sigmoid law distribution. A finite element analysis with COMSOL Multiphysics® (version 5.2) package is used to find the Eigen frequencies of the beam. The accuracy of the technique is authenticated by relating the results with the prior investigation for reduced case. The effects of moisture changes, temperature, and volume fraction index, length-to-thickness ratio on the Eigen frequencies are investigated in detail. It is believed that the present investigation may be useful in the design of highly efficient environmental sensors for structural health monitoring perspective.

Dynamic Crack Analysis in Functionally Graded Piezoelectric Solids by Meshless Local Petrov-Galerkin Method

2007 ◽  
Vol 348-349 ◽  
pp. 149-152 ◽  
Author(s):  
Jan Sladek ◽  
Vladimir Sladek ◽  
Chuan Zeng Zhang
Keyword(s):  
Weak Form ◽  
Functionally Graded ◽  
Dynamic Crack ◽  
Laplace Transform Technique ◽  
Mlpg Method ◽  
The Laplace Transform ◽  
Meshless Approximation ◽  
Piezoelectric Solids ◽  
Functionally Graded Piezoelectric ◽  
Dynamic Loading Conditions

In the present paper, the meshless local Petrov-Galerkin (MLPG) method is extended to two-dimensional (2-D) continuously nonhomogeneous piezoelectric solids with cracks under dynamic loading conditions. To eliminate the time-dependence, the Laplace-transform technique is applied to the governing partial differential equations which are satisfied in the Laplace-transformed domain in a weak-form on small fictitious subdomains. A meshless approximation is used for spatial variations of the displacements and the electric potential.

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