Free Vibration Analysis of Functionally Graded Nanobeams Based on Different Order Beam Theories Using Ritz Method

Elmeiche, Abbes; Megueni, A.; Lousdad, Abdelkader

doi:10.3311/ppme.8707

Cited by 13 publications

(9 citation statements)

References 25 publications

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“…Ec=380GPa, ρ=3960 Kg/m 3 , =0.3, and those of Aluminum (Al) are: Em=70 Gpa, ρ=2702 Kg/m 3 , =0.3. The indices of the Rayleigh-Ritz test function which must satisfy the boundary conditions are given in Table 1 [7].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Since the applications of these new materials (FGM) continue to develop. Due to the wide application of FGM, Several studies have been conducted on the mechanical and thermal behavior of FGM [2][3][4][5][6][7][8][9]; they studied the thermal effects on the vibration behavior of the Euler Bernoulli beam with an FGM operating gradient with temperature-dependent porosity.…”

Section: Introductionmentioning

confidence: 99%

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Forced Vibration Analysis of Functionally Graded Beams Carrying Moving Harmonic Loads under Random Boundary Conditions

Elmeiche¹,

Bouamama²,

Elhannani³

2020

MMEP

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This paper introduces forced vibration analysis of functionally graded materials (FGMs) beams subjected to moving harmonic loads in different physical and geometric states, under random boundary conditions. A mathematical model was developed based on a new refined logarithmic shear deformation theory (LSBT), used the Hamilton principle combined with the introduction of weak forms into the dynamic analysis, while including rotational inertia. The raster force is designed by the Dirac-delta function expressing moving harmonic loads. The Rayleigh-Ritz solution is used to separate system variables from equations with general boundary conditions. The fundamental frequencies of free vibration analysis are determined by solving the system of equations governing the eigenvalue problems and the modal responses of forced vibration behavior are also solved numerically using Newmark's temporal integration method. The numerical results presented make it possible to clearly appreciate the contribution of this theoretical development by examining in detail the influence of several parameters on the Dynamic Amplification Factor (DAF) of the FGMs beams.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Forced Vibration Analysis of Functionally Graded Beams Carrying Moving Harmonic Loads under Random Boundary Conditions

Elmeiche¹,

Bouamama²,

Elhannani³

2020

MMEP

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“…In the late 1980s, scientific researchers found the means for combining the particles of a structure according to a special method that led to a material with very specific properties, which vary according to a known function. The new material was named as Functionally Graded Material (FGM), and as the name indicates, this material is generally associated with composite particles where the volume fraction of the particles varies in one or more directions [1].…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of functionally graded tapered rotor shaft system

Elhannani¹,

Refassi²,

Elmeiche³

et al. 2019

Mechanics and Mechanical Engineering

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This investigation deals with the vibration analysis of a rotating tapered shaft in Functionally Graded Material (FGM). The dynamic system is modeled using the Timoshenko beam theory (FSDBT) with consideration of gyroscopic effect and rotary inertia. The equations of motion are expressed by the hierarchical finite element method based on bi-articulated boundary conditions. The material properties are continuously varied in the thickness direction of a hollow shaft according to the exponential law function (E-FGM). The presented model is validated by comparing the numerical results found with the available literature. Various analyses are carried out to determine the influence of taper angle and material distribution of the two extreme materials on the dynamic behavior of FGM conical rotors system.

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“…Several studies have been conducted on the mechanical and thermal behavior of FGM [7][8][9][10][11]. The simplest of the FGM, two different materials gradually change from one to the other Aydogdu and Taskin [12] studied the free vibration of functional graded beams with a simply supported boundary condition, Bouamama et al [13] studied the frequency response of the FGM sandwich beam with different boundary conditions and volume fractions, Alshorbagy et al [14] studied the characteristics of Euler-Bernoulli beams for the free vibration of FGM beams both axially and transversely across the beam thickness.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Stability Analysis of Functionally Graded Timoshenko Beams with Internal Viscous Damping Distribution

Bouamama¹,

Elmeiche²,

Elhennani³

et al. 2019

JESA

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This paper investigates the dynamic stability of functionally graded material (FGM) beams, using the Timoshenko model with internal viscous damping distribution (DIVD). It is assumed that the material properties change continuously across the thickness direction of the beam, according to the power law function for the FGM (P-FGM). The governing equations of motion were developed by the Lagrange principle. Then, the finite element method was adopted to describe unamortized natural frequencies and the damped eigenfrequencies of the dynamic system. The numerical results were compared with those available in the literature. Illustrative examples were given to show the influence of internal damping distribution, material distribution and slenderness ratio on the dynamic stability margin of FGM Timoshenko beams. The research findings provide new insights into the dynamic stability of the FGM.

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Free Vibration Analysis of Functionally Graded Nanobeams Based on Different Order Beam Theories Using Ritz Method

Abstract: Abstract

Cited by 13 publications

References 25 publications

Forced Vibration Analysis of Functionally Graded Beams Carrying Moving Harmonic Loads under Random Boundary Conditions

Forced Vibration Analysis of Functionally Graded Beams Carrying Moving Harmonic Loads under Random Boundary Conditions

Vibration analysis of functionally graded tapered rotor shaft system

Dynamic Stability Analysis of Functionally Graded Timoshenko Beams with Internal Viscous Damping Distribution

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