An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions

Mahi, A.; Bedia, E.A. Adda; Tounsi, Abdelouahed; Mechab, Ismail

doi:10.1016/j.compstruct.2010.01.010

Cited by 138 publications

(61 citation statements)

References 8 publications

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“…Chakraborty et al [3] discuss thermo-elastic beam problems based on the first order shear theory. Mahi et al [4] consider free vibrations of symmetric FGM beams subjected to an initial thermal stress. In case of combined variations of material properties in transverse and longitudinal directions, many achievements are due to Murin et al [5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Thermo-Elasticity in Shell Structures Made of Functionally Graded Materials

Kugler¹,

Fotiu²,

Muŕın³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. An efficient low order finite shell element is derived for the thermo-elastic analysis of shell structures made of functionally graded materials or multilayer composites. It is based on a one-way coupling between the thermal and the mechanical analysis. The thermal quantities are evaluated using a new iterative scheme that properly accounts for convection boundary conditions and large gradients of the thermal conductivity. The resulting non-constant temperature field with respect to the thickness direction gives nodal forces and couples, which are applied on a shear weak six parameter shell formulation. Here, drill rotations are included, supplemented with a proper method for calculating effective elastic properties. Numerical results indicate efficiency and accuracy of the proposed approach.4838

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Section: Introductionmentioning

confidence: 99%

Thermo-Elasticity in Shell Structures Made of Functionally Graded Materials

Kugler¹,

Fotiu²,

Muŕın³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…FGM structures in general and FGM beams in particular are increasingly used as structural components in aircraft and space vehicles. The static and vibration analyses of FGM beams by using different analytical and numerical methods are extensively reported in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13]; contributions based on the finite element method are briefly discussed below.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Nguyen¹,

Bui

2017

Mathematical Problems in Engineering

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A higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the element. The effect of environmental temperature is taken into account in the element derivation by considering that the material properties are temperature-dependent and the temperature is nonlinear distribution in the beam thickness. The accuracy of the derived formulation is confirmed by comparing the results obtained in the present work with the published data. Numerical investigations show that the formulated element is efficient, and it is capable of giving accurate vibration characteristics by a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity, temperature rise, and loading parameter on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic behaviour of the beam is also examined and highlighted.

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“…Several references [5][6][7] analysed the dynamic responses of the steel beams under high temperatures and different loads. Mahi et al [8] derived the governing equations of motion by Hamilton's principle and proposed an exact solution to investigate the free vibration of the beams with different boundary conditions in the temperature field.…”

Section: Introductionmentioning

confidence: 99%

Modal Analysis of a Simply Supported Steel Beam with Cracks under Temperature Load

Yan¹,

Chen²,

Yang³

2017

Shock and Vibration

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Based on the transfer matrix method, an analytical method is proposed to conduct the modal analysis of the simply supported steel beam with multiple transverse open cracks under different temperatures. The open cracks are replaced with torsion springs without mass, and local flexibility caused by each crack can be derived; the temperature module is introduced by the mechanical properties variation of the structural material, and the temperature load is caused by the temperature variation, which can be transformed to the axial force on the cross-section. The transfer matrix of the whole beam with the temperature and geometric parameters of cracks can be obtained. According to boundary conditions of the simply supported beam, natural frequencies of the beam can be calculated, which are compared with the finite element results. Results indicate that the analytical method proposed has a high accuracy; the natural frequencies of the simply supported steel beam are mostly affected by the temperature load, which cannot be ignored.

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An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions

Cited by 138 publications

References 8 publications

Thermo-Elasticity in Shell Structures Made of Functionally Graded Materials

Thermo-Elasticity in Shell Structures Made of Functionally Graded Materials

Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Modal Analysis of a Simply Supported Steel Beam with Cracks under Temperature Load

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