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

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.

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Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2021064 ◽

2021 ◽

Author(s):

Changkun Wei ◽

Jiaqing Yang ◽

Bo Zhang

Keyword(s):

Time Domain ◽

Electromagnetic Scattering ◽

Scattering Problem ◽

Three Dimensional ◽

Scattering Problems ◽

Laplace Transform Technique ◽

The Laplace Transform ◽

Time Domain Electromagnetic ◽

Numer Anal ◽

The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

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The Effect of Thermal Shock on the Thermal Conductivity of a Functionally Graded Material**Contribution of the National Institute of Standards and Technology and therefore not subject to copyright in the USA.

Functionally Graded Materials 1996 ◽

10.1016/b978-044482548-3/50070-6 ◽

1997 ◽

pp. 425-432

Author(s):

A.J. Slifka ◽

A. Kumakawa ◽

B.J. Filla ◽

J.M. Phelps ◽

N. Shimoda

Keyword(s):

Thermal Conductivity ◽

Thermal Shock ◽

Functionally Graded Material ◽

Functionally Graded ◽

The Usa ◽

Graded Material

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

Materials ◽

10.3390/ma13183953 ◽

2020 ◽

Vol 13 (18) ◽

pp. 3953 ◽

Cited By ~ 5

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.

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