Analysis of Thermal Deformations of FGM Thin Plates

2013 ◽  
Vol 681 ◽  
pp. 333-336
Author(s):  
Ming Lu Wang
Keyword(s):  
Thermal Stress ◽  
Rectangular Plate ◽  
Thin Plate ◽  
Functionally Graded Materials ◽  
Governing Equation ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Navier Solution ◽  
Simply Supported

The governing equation of thermoelastic FGM thin plates was obtained by degenerating the governing equation of thermoviscoelastic FGM thin plates. A Navier solution of a simply supported FGM rectangular plate under thermal loads was get. Based on the Navier solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the maximal deflection and thermal stress of the functionally graded materials thin plate is investigated.

Thermoelastic Deformations of Functionally Graded Materials Plates

2013 ◽  
Vol 740 ◽  
pp. 570-573
Author(s):  
Ming Lu Wang
Keyword(s):  
Thermal Stress ◽  
Rectangular Plate ◽  
Thin Plate ◽  
Functionally Graded Materials ◽  
Governing Equation ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Navier Solution ◽  
Simply Supported

The governing equation of thermoelastic FGM thin plates was obtained by degenerating the governing equation of thermoviscoelastic FGM thin plates. A Navier solution of a simply supported FGM rectangular plate under thermal loads was get. Based on the Navier solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the maximal deflection and thermal stress of the functionally graded materials thin plate is investigated.

A Mathematical Model of Functionally Graded Materials Thin Plates and Levy Solutions

2013 ◽  
Vol 740 ◽  
pp. 574-577
Author(s):  
Ming Lu Wang
Keyword(s):  
Mathematical Model ◽  
Rectangular Plate ◽  
Thin Plate ◽  
Functionally Graded Materials ◽  
Governing Equation ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Simply Supported ◽  
Static Responses

The governing equation of elastic FGM thin plates was obtained by degenerating the governing equation of viscoelastic FGM thin plates. A Levy solution of a simply supported FGM rectangular plate was gotten. Based on the Levy solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the static responses of the functionally graded materials thin plate is investigated.

The Levy Solution of Functionally Graded Materials Elastic Thin Plates

2013 ◽  
Vol 681 ◽  
pp. 329-332
Author(s):  
Feng Zheng ◽  
Ming Lu Wang
Keyword(s):  
Rectangular Plate ◽  
Thin Plate ◽  
Functionally Graded Materials ◽  
Governing Equation ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Simply Supported ◽  
Static Responses

The governing equation of elastic FGM thin plates was obtained by degenerating the governing equation of viscoelastic FGM thin plates. A Levy solution of a simply supported FGM rectangular plate was gotten. Based on the Levy solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the static responses of the functionally graded materials thin plate is investigated.

Nonlinear Oscillations of Functionally Graded Materials Rectangular Thin Plates with Parametrical and External Excitations

2013 ◽  
Vol 302 ◽  
pp. 200-203
Author(s):  
Xiao Li Bian ◽  
Shuang Bao Li
Keyword(s):  
Thin Plate ◽  
Functionally Graded Materials ◽  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Functionally Graded ◽  
Thin Plates ◽  
Rectangular Thin Plate ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Averaged Equations

Nonlinear oscillations of a simply supported functionally graded materials (FGM) rectangular plate under one-to-one internal resonance are investigated in this paper. The FGM rectangular thin plate is subjected to the transversal and in-plane excitations. Material properties are assumed to be temperature-dependent. Based on the Galerkin’s method, a two-degree-of-freedom nonlinear system with quadratic and cubic nonlinearities governing equations of motions for the FGM rectangular thin plate is derived. The averaged equations are obtained by the method of multiple scales. Numerical simulations illustrate that there exist nonlinear oscillations for the FGM rectangular thin plate.

Shilnikov Type Multi-Pulse Orbits of Functionally Graded Materials Rectangular Plate

2010 ◽  
Author(s):  
Wei Zhang ◽  
Ming-Hui Yao ◽  
Dong-Xing Cao
Keyword(s):  
Normal Form ◽  
Rectangular Plate ◽  
Functionally Graded Materials ◽  
Chaotic Dynamics ◽  
Functionally Graded ◽  
Phase Method ◽  
Global Dynamics ◽  
Graded Materials ◽  
Chaotic Motions ◽  
Simply Supported

Multi-pulse chaotic dynamics of a simply supported functionally graded materials (FGMs) rectangular plate is investigated in this paper. The FGMs rectangular plate is subjected to the transversal and in-plane excitations. The properties of material are graded in the direction of thickness. Based on Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the FGMs plate are derived by using the Hamilton’s principle. The four-dimensional averaged equation under the case of 1:2 internal resonance, primary parametric resonance and 1/2-subharmonic resonance is obtained by directly using the asymptotic perturbation method and Galerkin approach to the partial differential governing equation of motion for the FGMs rectangular plate. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the FGMs rectangular plate. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the FGMs rectangular plate are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the simply supported FGMs rectangular plate.

Analysis of Bifurcations for a Functionally Graded Materials Plate

2013 ◽  
Vol 300-301 ◽  
pp. 988-991 ◽  
Author(s):  
Wei Qin Yu
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Periodic Motions ◽  
Graded Materials ◽  
Normal Form Theory ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Form Theory ◽  
Bifurcation And Stability ◽  
Numerical Approaches

Using the analytical and numerical approaches, the nonlinear dynamic behaviors in the vicinity of a compound critical point are studied for a simply supported functionally graded materials (FGMs) rectangular plate. Normal form theory, bifurcation and stability theory are used to find closed form solutions for equilibria and periodic motions. Stability conditions of these solutions are obtained explicitly and critical boundaries are also derived. Finally, numerical results are presented to confirm the analytical predictions

Chaotic Motion of a Functionally Graded Materials Square Thin Plate

2012 ◽  
Vol 531 ◽  
pp. 593-596
Author(s):  
Shuang Bao Li ◽  
Yu Xin Hao
Keyword(s):  
Thin Plate ◽  
Functionally Graded Materials ◽  
Chaotic Motion ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Steady State Heat ◽  
Steady State Heat Transfer

Chaotic motion of a simply supported functionally graded materials (FGM) square thin plate under one-to-two internal resonance is studied in this paper. The FGM plate is subjected to the transversal and in-plane excitations. Material properties are assumed to be temperature-dependent and change continuously throughout the thickness of the plate. The temperature variation is assumed to occur in the thickness direction only and satisfy the steady-state heat transfer equation. Based on the Reddy’s third-order plate theory and Hamilton’s principle, the nonlinear governing equations of motion for the FGM plate are derived by using the Galerkin’s method to describe the transverse oscillation in the first two modes Numerical simulations illustrate that there exist chaotic motion for the FGM rectangular plate.

Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory

2017 ◽  
Vol 29 (5) ◽  
pp. 741-763 ◽  
Author(s):  
Ali Kiani ◽  
Moslem Sheikhkhoshkar ◽  
Ali Jamalpoor ◽  
Mostafa Khanzadi
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Simply Supported

In the present article, according to the nonlocal elasticity theory within the framework of the third-order shear deformable plate assumption, the theoretical analysis of thermomechanical vibration response of magneto-electro-thermo-elastic nanoplate made of functionally graded materials resting on the visco-Pasternak medium is carried out. The simply supported magneto-electro-thermo-elastic nanoplate is supposed to subject to initial external electric, magnetic potentials, and temperature environment. The material characteristics of magneto-electro-thermo-elastic nanoplate are assumed to be variable continuously across the thickness direction based upon power law distribution. Hamilton’s principle is utilized to achieve the partial differential equations and corresponding boundary conditions. The equilibrium equations are solved analytically to determine the complex eigenfrequency using Navier’s approach which satisfies the simply supported boundary conditions. Numerical studies are performed to illustrate the dependency of the natural frequency of the system on the damping coefficient of the visco-Pasternak medium, nonlocal parameter, aspect ratio, temperature change, volume fraction index of functionally graded material, initial external electric voltage, initial external magnetic potential, and plate thickness. It is clearly indicated that these factors have highly significant impacts on the dynamic behavior of the proposed system.

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