Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories

Mechab, Ismail; Mechab, Boubaker; Benaissa, Samir; Sérier, B.; Bouiadjra, B. Bachir

doi:10.1007/s40430-015-0482-6

Cited by 74 publications

(30 citation statements)

References 39 publications

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“…where the resultants forces and the moments can be obtained using Equations (7) and (8), and can be presented in the following form:…”

Section: Coupled Equations Of Motionmentioning

confidence: 99%

“…Barati et al [7] studied buckling of functionally graded piezoelectric rectangular plates with porosities based on the four-variable plate theory. Mechab et al [8] studied free vibration of the FGM nanoplate with porosities resting on Winkler and Pasternak elastic foundation based on the two-variable plate theory. Mojahedin et al [9] analyzed buckling of radially loaded clamped saturated porous circular plates based on higher order shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

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Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Żur

Jankowski

2019

Symmetry

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Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

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“…where the resultants forces and the moments can be obtained using Equations (7) and (8), and can be presented in the following form:…”

Section: Coupled Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Żur

Jankowski

2019

Symmetry

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“…Based on a non-local, four-variable refined plate theory, Belkorissat et al [15] analyzed free vibration behavior of functionally graded nanoplates. Mechab et al [32] examined the free vibration properties of porous functionally graded nanoplates resting on elastic foundations by using the two-variable refined plate theory. Based on the two-variable refined plate theory, Nami and Janghorban [33] investigated the free vibration problems of rectangular nanoplates via the strain gradient elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Wang

Zhang

2018

Coatings

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In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

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“…Wave propagation phenomena of a FG-MEE nanorod is investigated via nonlocal continuum mechanics by Narendar (2016). Furthermore, there are a number of literatures regarding the effects of FGMs on the nanostructures (Natarajan et al 2012;Ansari et al 2015a;Barretta et al 2016;Thang et al 2017;Mechab et al 2016;Jamalpoor and Kiani 2017;Hosseini et al 2017).…”

Section: Introductionmentioning

confidence: 99%

Nanoscale mass nanosensor based on the vibration analysis of embedded magneto-electro-elastic nanoplate made of FGMs via nonlocal Mindlin plate theory

et al. 2017

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In the current paper, the sensitivity performance of functionally graded magneto-electro-elastic (FG-MEE) nanoplate with attached nanoparticles as a nanosensor is analyzed based on nonlocal Mindlin plate assumption. Power law distribution model is employed to display how the material properties of FG-MEE nanoplate vary across the thickness direction. It is supposed that FG-MEE nanoplate is under initial external electric and magnetic potentials. Boundary condition of each edge of FG-MEE nanoplate is assumed to be simply supported. Furthermore, a Pasternak substrate is applied for modelling the total reaction pressure between nanoplate and foundation. Partial differential equations and corresponding boundary conditions are first achieved using Hamilton's variational principle and then analytically solved to determine the frequency shift utilizing Navier's approach. Numerical examples are performed to elucidate the dependency of the sensitivity performance of FG-MEE nanosensor on the volume fraction exponent, nonlocal parameter, total attached mass and location of the nanoparticle, aspect ratio, mode number, initial external electric voltage, initial external magnetic potential, and Pasternak medium coefficients. It is clearly indicated that these factors have highly significant impacts on the variations of frequency shift.

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Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories

Cited by 74 publications

References 39 publications

Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Nanoscale mass nanosensor based on the vibration analysis of embedded magneto-electro-elastic nanoplate made of FGMs via nonlocal Mindlin plate theory

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