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Research Papers

Vibration of a Temperature-Dependent Thermally Pre/Postbuckled FGM Beam Over a Nonlinear Hardening Elastic Foundation

[+] Author and Article Information
S. E. Esfahani

Mechanical Engineering Department,
Islamic Azad University,
South Tehran Branch,
Tehran, Iran

M. R. Eslami

Professor and Fellow of the Academy of Sciences
ASME Fellow
e-mail: eslami@aut.ac.ir
Mechanical Engineering Department,
Amirkabir University of Technology,
Tehran, Iran

1Corresponding author.

Manuscript received October 7, 2012; final manuscript received February 26, 2013; published online August 22, 2013. Assoc. Editor: Glaucio H. Paulino.

J. Appl. Mech 81(1), 011004 (Aug 22, 2013) (13 pages) Paper No: JAM-12-1467; doi: 10.1115/1.4023975 History: Received October 07, 2012; Revised February 26, 2013; Accepted August 22, 2013

Small amplitude vibrations of a functionally graded material beam under in-plane thermal loading in the prebuckling and postbuckling regimes is studied in this paper. The material properties of the FGM media are considered as function of both position and temperature. A three parameters elastic foundation including the linear and nonlinear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The solution is sought in two regimes. The first one, a static phase with large amplitude response, and the second one, a dynamic regime near the static one with small amplitude. In both regimes, nonlinear governing equations are discretized using the generalized differential quadrature (GDQ) method and solved iteratively via the Newton–Raphson method. It is concluded that depending on the type of boundary condition and loading type, free vibration of a beam under in-plane thermal loading may reach zero at a certain temperature which indicates the existence of bifurcation type of instability.

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Figures

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Fig. 1

Coordinate system and geometry of a FGM beam resting over a three-parameters elastic foundation

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Fig. 2

A comparison between the results of this study and those reported by Li et al. [3] for fundamental frequency of S–S isotropic homogeneous Euler–Bernoulli beams. Temperature parameter is defined as τ = (12/δ2)αΔT.

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Fig. 3

A comparison between the results of this study and those reported by Li et al. [3] for fundamental frequency of C–S isotropic homogeneous Euler–Bernoulli beams. Temperature parameter is defined as τ = (12/δ2)αΔT.

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Fig. 4

Effect of temperature dependency and various power law indices on the first mode frequency of S–S FGM beams with δ = 0.04 subjected to UTR loading

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Fig. 5

Effect of temperature dependency and various power law indices on the first mode frequency of C–C FGM beams with δ = 0.04 subjected to UTR loading

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Fig. 6

Influences of three-parameters nonlinear elastic foundation (Kw*,Kg*,KNL*) on the first mode frequency of linearly graded C–C FGM beam with δ = 0.04 subjected to UTR loading

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Fig. 7

Influences of three-parameters nonlinear elastic foundation (Kw*,Kg*,KNL*) on the first mode frequency of linearly graded S–S FGM beam with δ = 0.04 subjected to UTR loading

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Fig. 8

Effect of various boundary conditions of linearly graded FGM beam on the dimensionless frequency and deflection with δ = 0.04 subjected to UTR loading

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Fig. 9

Influences of various power law indices and temperature dependency on the first frequency of C–C FGM beam with δ = 0.04 subjected to HC loading

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Fig. 10

Effect of various power law indices and temperature dependency on S–S FGM beams with δ = 0.04 subjected to HC loading

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