Eigen analysis of functionally graded beams with variable cross-section resting on elastic supports and elastic foundation

Hien, Ta Duy; Van, Thuan Nguyen; Noh, Hyuk Chun

doi:10.12989/sem.2014.52.5.1033

Cited by 16 publications

(3 citation statements)

References 25 publications

(17 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The articles for AFG beams can be given as follow; the free vibration of an FGM beam on an elastic foundation and spring supports was investigated by Duy et al 13 The material properties and thickness of the beam were assumed to range in width and length directions obeying the exponential law. An analytical formulation and finite element formulation were used to obtain the natural frequencies of the FGM beams.…”

Section: Introductionmentioning

confidence: 99%

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

Demir¹

2023

The International Journal of Acoustics and Vibration

View full text Add to dashboard Cite

The frequency parameters of an Axially Functionally Graded (AFG) bar for viscoelastic and point mass boundary conditions are studied in this paper. The structures with functionally graded materials under axial loads can be modelled as AFG bars. Those may be considered as support elements with spring and dashpot in the vibration isolation. Keeping the ratio of force frequency and natural frequency at a certain level is ensured to control the natural frequency therefore dynamic amplification factor with different material combinations. Various boundary conditions are attained by changing the spring and damping coefficients of viscoelastic support elements and the ratio of rod mass to tip mass. Researchers assume that the beam material properties in directions of length and thickness change exponentially, individually, or both in their studies. There are a few studies on the AFG rods in the existing studies. Analysis is carried out via the finite element method for the non-dimensional frequency parameters of the bar in MATLAB. The energy equations of the motion are obtained in the frame of axial bar theory considering the material properties of the bar vary longitudinally according to the power-law distribution. The effects of material distribution, spring, damping and tip mass values on the bar's frequency parameters and structural behaviour have been extensively investigated.

show abstract

Section: Introductionmentioning

confidence: 99%

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

Demir¹

2023

The International Journal of Acoustics and Vibration

View full text Add to dashboard Cite

show abstract

“…Xu et al 21 investigated 2D elasticity solution for bending of FGB with variable thickness. Duy et al 22 presented the Eigen analysis of FGB with variable cross section on elastic support and elastic foundations. Recently, Calim 23 presented transient analysis of axially functionally graded Timoshenko beam with variable cross section.…”

Section: Introductionmentioning

confidence: 99%

Accurate solution for functionally graded beams with arbitrarily varying thicknesses resting on a two-parameter elastic foundation

Huang

2020

The Journal of Strain Analysis for Engineering Design

View full text Add to dashboard Cite

This work presents analytical solutions for bending deformation and stress distributions in functionally graded beams with arbitrarily and continuously variable thicknesses and resting on a two-parameter Pasternak elastic foundation. Based on two-dimensional elasticity theory directly, the general solutions of displacements and stresses which completely satisfy the differential equations governing the equilibrium for arbitrarily varying thickness functionally graded beams are derived for the first time. The undetermined coefficients in the general solution are obtained using Fourier series expansion along the upper and lower surfaces. The accuracy and efficiency of the proposed method are verified through several typical examples. The effects of mechanical and geometry parameters on the stress and displacement distributions of varying thickness functionally graded beams resting on a two-parameter Pasternak elastic foundation are discussed further.

show abstract

“…[5][6][7][8][9] for mechanical analysis of axially functionally graded beam, Refs. [10][11][12][13][14][15][16][17][18][19] for functionally material variation through the thickness of the beam and Refs. [20][21][22][23][24][25][26][27] for two-directional functionally graded beams.…”

Section: Introductionmentioning

confidence: 99%

Bending, buckling and vibration analysis of functionally graded non-uniform nanobeams via finite element method

Rajasekaran

Khaniki

2018

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

In the current study, bending, buckling and vibration behaviours of functionally graded in depth direction non-uniform nanobeams are investigated in the framework of nonlocal strain gradient theory. Material variation is assumed through the thickness and modelled using exponential, sigmoid and power-law functions. Moreover, cross-sectional variation is also considered using exponential and power-law functions. Using these general non-uniformity and non-homogeneity in conjunction with nonlocal strain gradient theory, a general beam is modelled. For this general model, equations of motion are derived using Hamilton's principle and solved by using a novel technique in combining finite element method with Lagrangian interpolation technique, Gaussian quadrature method and Wilson's Lagrangian multiplier method. Mechanical behaviour of such structures is fully explained with parametric study for all three cases of bending, buckling and vibration response. It is shown that combination of material variation, non-uniformity and scale effects has a significant effect in changing the mechanical behaviour of such structures in both static and dynamic cases.

show abstract

Eigen analysis of functionally graded beams with variable cross-section resting on elastic supports and elastic foundation

Cited by 16 publications

References 25 publications

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

Accurate solution for functionally graded beams with arbitrarily varying thicknesses resting on a two-parameter elastic foundation

Bending, buckling and vibration analysis of functionally graded non-uniform nanobeams via finite element method

Contact Info

Product

Resources

About