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

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.

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Thermoelastic Deformations of Functionally Graded Materials Plates

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.740.570 ◽

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.

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The Levy Solution of Functionally Graded Materials Elastic Thin Plates

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.681.329 ◽

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.

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Analysis of Thermal Deformations of FGM Thin Plates

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.681.333 ◽

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.

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Chaotic Motion of a Functionally Graded Materials Square Thin Plate

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.531.593 ◽

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.

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Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

Journal of Applied Mechanics ◽

10.1115/1.2712231 ◽

2006 ◽

Vol 74 (5) ◽

pp. 861-874 ◽

Cited By ~ 17

Author(s):

Florin Bobaru

Keyword(s):

Functionally Graded Materials ◽

Material Properties ◽

Volume Fraction ◽

Effective Properties ◽

Functionally Graded ◽

Dominant Factor ◽

Temperature Dependent ◽

Graded Materials ◽

Critical Stresses ◽

Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

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Dynamic Response of Cantilever FGM Cylindrical Shell

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.130-134.3986 ◽

2011 ◽

Vol 130-134 ◽

pp. 3986-3993 ◽

Cited By ~ 4

Author(s):

Yu Xin Hao ◽

Wei Zhang ◽

L. Yang ◽

J.H. Wang

Keyword(s):

Cylindrical Shell ◽

Volume Fraction ◽

Nonlinear Oscillations ◽

Equations Of Motion ◽

Functionally Graded ◽

Governing Equations ◽

Temperature Dependent ◽

Graded Materials ◽

First Order ◽

Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

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