Three-dimensional analysis for transient coupled thermoelastic response of a functionally graded rectangular plate

2011 ◽  
Vol 330 (16) ◽  
pp. 3990-4001 ◽  
Author(s):  
Feng-xi Zhou ◽  
Shi-rong Li ◽  
Yuan-ming Lai
Keyword(s):  
Rectangular Plate ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Thermoelastic Response

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.

Three-Dimensional Elastic Solution of a Transversely Isotropic Functionally Graded Rectangular Plate

2012 ◽  
Vol 591-593 ◽  
pp. 2655-2660 ◽  
Author(s):  
Guo Jun Nie ◽  
Zhao Yang Feng ◽  
Jun Tao Shi ◽  
Ying Ya Lu ◽  
Zheng Zhong
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Rectangular Plate ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Functionally Graded ◽  
Elastic Solution ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Present Solution

Three-dimensional elastic solution of a simply supported, transversely isotropic functionally graded rectangular plate is presented in this paper. Suppose that all elastic coefficients of the material have the same power-law dependence on the thickness coordinate. By introducing two new displacement functions, three equations of equilibrium in terms of displacements are reduced to two uncoupled partial differential equations. Exact solution for a second-order partial differential equation expressed by one of displacement functions is obtained and analytical solution for another fourth-order partial differential equation expressed by another displacement function is found by employing the Frobenius method. The validity of the present solution is first investigated. And the effect of the gradation of material properties on the mechanical behavior of the plate is studied through numerical examples.

scholarly journals Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method

Materials ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3401 ◽  
Author(s):  
Cui ◽  
Zhou ◽  
Ye ◽  
Gaidai ◽  
Li ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Power Law ◽  
Analytical Method ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Sandwich Plates

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented.

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