Free vibration and buckling behavior of functionally graded porous plates reinforced by graphene platelets using spectral Chebyshev approach

Anamagh, Mirmeysam Rafiei; Bediz, Bekir

doi:10.1016/j.compstruct.2020.112765

Cited by 80 publications

(12 citation statements)

References 35 publications

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“…According to the Equation ( 33), the element-stiffness matrix of the proposed beam element can be obtained. Equation (33) within the ith element can be rewritten as…”

Section: Finite-element Formulationmentioning

confidence: 99%

“…The graphene efficiency parameters [33] for different volume fractions are shown in Table 3. The assumptions G 23 = G 13 = 0.5G 12 are made for the numerical analysis [33]. The material constants for the MFC piezoelectric layer [50] are…”

Section: Verification Studymentioning

confidence: 99%

“…Liu et al [32] investigated the dynamic behaviors of porous FG-GRC plates that were resting on an elastic foundation. By using the spectral-Chebyshev approach, free vibration and buckling responses of porous FG-GRC plates were conducted by Anamagh and Bediz [33]. In a review of the aforementioned works, FSDT was used to analyze the FG-GRC structures.…”

Section: Introductionmentioning

confidence: 99%

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An Alternative Electro-Mechanical Finite Formulation for Functionally Graded Graphene-Reinforced Composite Beams with Macro-Fiber Composite Actuator

Fu¹,

Tang²,

Jin

et al. 2021

Materials

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With its extraordinary physical properties, graphene is regarded as one of the most attractive reinforcements to enhance the mechanical characteristics of composite materials. However, the existing models in the literature might meet severe challenges in the interlaminar-stress prediction of thick, functionally graded, graphene-reinforced-composite (FG-GRC)-laminated beams that have been integrated with piezoelectric macro-fiber-composite (MFC) actuators under electro-mechanical loadings. If the transverse shear deformations cannot be accurately described, then the mechanical performance of the FG-GRC-laminated beams with MFC actuators will be significantly impacted by the electro-mechanical coupling effect and the sudden change of the material characteristics at the interfaces. Therefore, a new electro-mechanical coupled-beam model with only four independent displacement variables is proposed in this paper. Employing the Hu–Washizu (HW) variational principle, the precision of the transverse shear stresses in regard to the electro-mechanical coupling effect can be improved. Moreover, the second-order derivatives of the in-plane displacement parameters have been removed from the transverse-shear-stress components, which can greatly simplify the finite-element implementation. Thus, based on the proposed electro-mechanical coupled model, a simple C0-type finite-element formulation is developed for the interlaminar shear-stress analysis of thick FG-GRC-laminated beams with MFC actuators. The 3D elasticity solutions and the results obtained from other models are used to assess the performance of the proposed finite-element formulation. Additionally, comprehensive parametric studies are performed on the influences of the graphene volume fraction, distribution pattern, electro-mechanical loading, boundary conditions, lamination scheme and geometrical parameters of the beams on the deformations and stresses of the FG-GRC-laminated beams with MFC actuators.

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“…According to the Equation ( 33), the element-stiffness matrix of the proposed beam element can be obtained. Equation (33) within the ith element can be rewritten as…”

Section: Finite-element Formulationmentioning

confidence: 99%

Section: Verification Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Alternative Electro-Mechanical Finite Formulation for Functionally Graded Graphene-Reinforced Composite Beams with Macro-Fiber Composite Actuator

Fu¹,

Tang²,

Jin

et al. 2021

Materials

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show abstract

“…Baghlani et al [30] studied uncertainty propagation in free vibration of an FG porous shell with GPL reinforcement. Anamagh et al [31] developed a spectral-Chebyshev approach to study vibrations of an FG porous plate reinforced with GPLs. Based on a trigonometric shear deformation theory, Anirudh et al [32] discussed the vibration behavior of a GPL reinforced FG porous beam.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Spinning Sandwich Annular Plates with Functionally Graded Graphene Nanoplatelet Reinforced Porous Core

Huang

Zhao

et al. 2022

Materials

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This paper conducted the free vibration analysis of a sandwich annular thin plate with whirl motion. The upper and lower faces of the annular plate are made of uniform solid metal, while its core is porous foamed metal reinforced by graphene nanoplatelets (GPLs). Both uniform and non-uniform distributions of GPLs and porosity along the direction of plate thickness which leads to a functionally graded (FG) core are taken into account. The effective material properties including Young’s modulus, Poisson’s ratio and mass density are calculated by employing the Halpin–Tsai model and the rule of mixture, respectively. Based on the Kirchhoff plate theory, the differential equations of motion are derived by applying the Lagrange’s equation. Then, the assumed mode method is utilized to obtain free vibration behaviors of the sandwich annular plate. The finite element method is adopted to verify the present model and vibration analysis. The effects of porosity coefficient, porosity distribution, graphene nanoplatelet (GPL) distribution, graphene nanoplatelet (GPL) weight fraction, graphene nanoplatelet length-to-thickness ratio (GPL-LTR), graphene nanoplatelet length-to-width ratio (GPL-LWR), spinning speed, outer radius-to-thickness ratio and inner radius-to-thickness ratio of the plate, are examined in detail.

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“…In such a context, several theories and computational models have been developed in the last decades in the field of GPL-reinforced media. Anamagh and Bediz [13], for example, studied the buckling and vibration response of GPL-reinforced rectangular plates with different boundary conditions, based on a spectral-Tchebychev model. Reddy et al [14] surveyed the vibrational frequencies of the composite plates reinforced by GPLs, and investigated the effect of various parameters, primarily, boundary conditions, distribution patterns, geometry and weight fractions of GPLs, on the natural frequencies of the system.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and Numerical Solution for the Bending and Frequency Response of Graphene Reinforced Nanocomposite Rectangular Plates

et al. 2021

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In this work, we study the vibration and bending response of functionally graded graphene platelets reinforced composite (FG-GPLRC) rectangular plates embedded on different substrates and thermal conditions. The governing equations of the problem along with boundary conditions are determined by employing the minimum total potential energy and Hamilton’s principle, within a higher-order shear deformation theoretical setting. The problem is solved both theoretically and numerically by means of a Navier-type exact solution and a generalized differential quadrature (GDQ) method, respectively, whose results are successfully validated against the finite element predictions performed in the commercial COMSOL code, and similar outcomes available in the literature. A large parametric study is developed to check for the sensitivity of the response to different foundation properties, graphene platelets (GPL) distribution patterns, volume fractions of the reinforcing phase, as well as the surrounding environment and boundary conditions, with very interesting insights from a scientific and design standpoint.

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Free vibration and buckling behavior of functionally graded porous plates reinforced by graphene platelets using spectral Chebyshev approach

Cited by 80 publications

References 35 publications

An Alternative Electro-Mechanical Finite Formulation for Functionally Graded Graphene-Reinforced Composite Beams with Macro-Fiber Composite Actuator

An Alternative Electro-Mechanical Finite Formulation for Functionally Graded Graphene-Reinforced Composite Beams with Macro-Fiber Composite Actuator

Free Vibration Analysis of Spinning Sandwich Annular Plates with Functionally Graded Graphene Nanoplatelet Reinforced Porous Core

Theoretical and Numerical Solution for the Bending and Frequency Response of Graphene Reinforced Nanocomposite Rectangular Plates

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