Vibrational behavior of beams made of functionally graded materials by using a mixed formulation

Zghal, Souhir; Dammak, Fakhreddine

doi:10.1177/0954406220916533

Cited by 34 publications

(13 citation statements)

References 29 publications

(31 reference statements)

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“…It can be seen that there are no stretching-bending couplings in equation ( 9), and the nonlinear governing equations have simple forms as shown in equation (14).…”

Section: Boundary Conditionsmentioning

confidence: 99%

Exact solution for nonlinear static behaviors of functionally graded beams with porosities resting on elastic foundation using neutral surface concept

Long

Nguyen

Tú

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, an exact solution for nonlinear static behaviors of functionally graded (FG) beams with porosities resting on the elastic foundation is presented. The FG material properties with porosities are assumed to vary along the thickness of the beam, and two types of porosity distributions are considered. Actually, the geometrical middle surface of the FG beam selected in computations is very popular in the literature. By contrast, in this study, the physical neutral surface of the beam is utilized. Based on the Timoshenko beam theory, von Kármán nonlinear assumption, together with neutral surface concept, the nonlinear governing equations of the FG beam resting on the elastic foundation are derived. By using the physical neutral surface, the nonlinear governing equations have simple forms and can be solved directly. The exact solution for the problem with all immovable and moveable boundary conditions is conducted in detail. Some numerical investigations to show the effects of boundary conditions, material properties, length-to-thickness ratio, elastic foundation coefficients and several types of applied load on nonlinear static bending behaviors of the beam are given.

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“…It can be seen that there are no stretching-bending couplings in equation ( 9), and the nonlinear governing equations have simple forms as shown in equation (14).…”

Section: Boundary Conditionsmentioning

confidence: 99%

Exact solution for nonlinear static behaviors of functionally graded beams with porosities resting on elastic foundation using neutral surface concept

Long

Nguyen

Tú

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Further details about the construction of the stiffness matrix K can be found in Zghal et al 8,24 Numerical applications and discussion…”

Section: Numerical Model Of the Beammentioning

confidence: 99%

“…23 In particular, the effects of the power-law index and porosity factors are investigated and examined in detail. As well as, Zghal and Dammak 24 conducted various analysis on FGM beams, plates, and shells covering vibrational behavior of FGM beams, mechanical, thermal, and thermoelastic responses 25–27 of FGM plates and shells. In these works, various finite element models and numerical strategies have been exploited to perform different aspects of FGM structures.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of porous beams with gradually varying mechanical properties

Zghal

Ataoui

Dammak

2021

Proceedings of the Institution of Mechanical Engineers, Part M:

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This work is aimed to present analysis on free vibration behavior of porous beams with gradually varying mechanical properties based on a robust finite beam element. The governing equations are developed using a mixed variational formulation considering high-order displacement distribution. A new parabolic distribution of the transverse shear strains is introduced and the zero condition of the shear stresses at the upper and bottom surfaces of the beam is satisfied. The porosity can be spread into the beam with evenly and unevenly distributions. According to a modified power function, the material properties are varying along the thickness direction of the FGM porous beam. The presented results show the effect of gradient index, porosity coefficient and forms, boundary conditions, and geometrical parameters on the vibration of FGM beams. It is found that porous beams can be useful as a passive method for control of vibration for structural components.

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“…A refined mixed finite element beam model was proposed by Zghal et al [24] to know the influence of porosity on static bending analysis of beams made of functionally graded porous materials. A mixed formulation was used by Zghal and Dammak [25] to investigate the vibrational behavior of beams made of functionally graded materials. The authors conducted numerical simulations to know the efficiency and applicability of the proposed model.…”

Section: Introductionmentioning

confidence: 99%

Linear Transient Dynamic Analysis of Plates With and Without Cutout

Nayak

Khante

2021

Arab J Sci Eng

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The present work exhibits the analysis of a plate with and without cutout considering the dynamic analysis in a transient zone with its application in the civil, structural, and aerospace industry. For this, first-order shear deformable C 0 continuous Finite Element (FE) is implemented to examine transient response of plate. The governing ODE of motion's is integrated using central difference explicit time integration scheme. A lumped mass matrix is obtained by a special diagonlization scheme and the total mass of the element is conserved by inducing effective rotary inertia terms. A FE program is developed based on derived FE formulation to investigate the effect of dynamic loading on such plates. The analysis exhibits the results in terms of displacement, forces, and bending moment of the plate for various aspect ratios and different parameters. The results are shown in terms of tables and graphs for smaller to larger cutout in plates with its different aspect ratio considering transient analysis. The results reveal that transient dynamics analysis shows a considerable difference in the behavior of plates with and without cutout in terms of time period, amplitude, and bending moment than that obtained from static analysis.

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Vibrational behavior of beams made of functionally graded materials by using a mixed formulation

Cited by 34 publications

References 29 publications

Exact solution for nonlinear static behaviors of functionally graded beams with porosities resting on elastic foundation using neutral surface concept

Exact solution for nonlinear static behaviors of functionally graded beams with porosities resting on elastic foundation using neutral surface concept

Free vibration analysis of porous beams with gradually varying mechanical properties

Linear Transient Dynamic Analysis of Plates With and Without Cutout

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