Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory

Żur, Krzysztof Kamil; Arefi, Mohammad; Kim, Jinseok; Reddy, J. N.

doi:10.1016/j.compositesb.2019.107601

Cited by 186 publications

(34 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The goal is to find the analytical solutions of Eqs. (27) to (30) under various boundary conditions imposed on the lateral edges, as shown in Table 2. The edges of the plate are either embedded or simply supported.…”

Section: Analytical Solutionmentioning

confidence: 99%

“…Embedded plate (C) The Navier method is used under the specified boundary conditions to find the analytical solution to Eqs. (27)- (29) and (30). The displacement functions, which satisfy the boundary conditions, are expressed as the following Fourier series:…”

Section: Analytical Solutionmentioning

confidence: 99%

“…Note that both Eringen's nonlocal elasticity theory and the classical plate theory are used for the determination of the equilibrium equations. The refined higher-order shear deformation theory was used by Żur et al [30] for the analysis of the vibrations and buckling of FGM structures in terms of the nonlocal parameter, volume fraction index, power law index, mechanical, electrical and magnetic loads, mechanical, electrical, and magnetic loadings, as well as the geometric ratio of the section.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Vibration Analysis of Viscoelastic FGM Nanoscale Plate Resting on Viscoelastic Medium Using Higher-order Theory

Hamzi

Mechab

Abbad

et al. 2020

Period. Polytech. Civil Eng.

View full text Add to dashboard Cite

The present article aims essentially to present an analytical and numerical method which makes it possible to study the damped vibrations of viscoelastic FGM nanoplates resting on viscoelastic foundations. A new model for the higher-order shear deformation plate theory is coupled with the internal Kelvin - Voigt viscoelastic model and the three-parameter viscoelastic foundation model for the purpose of reducing and minimizing the vibration response of the system. It is widely admitted that the mechanical properties of these new functionally gradient materials (FGMs) vary according to the thickness of the plate and depend on its volume fraction. The use of FGM plates seems to be an ideal solution for the study of free vibrations because of their multifunctionality that is fully integrated with the nonlocal Eringen effect. The dynamic response of such a complex system has been investigated by varying the aspect ratio of the plate, the mechanical characteristics of the material used, the internal and external damping and the foundation rigidity. The results obtained, with and without the nonlocal effect, were compared with those of different models of higher-order theories and under various boundary conditions; they were found to be in good agreement with those reported in the literature.

show abstract

Section: Analytical Solutionmentioning

confidence: 99%

Section: Analytical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vibration Analysis of Viscoelastic FGM Nanoscale Plate Resting on Viscoelastic Medium Using Higher-order Theory

Hamzi

Mechab

Abbad

et al. 2020

Period. Polytech. Civil Eng.

View full text Add to dashboard Cite

show abstract

“…Such theories are the theory of micropolar elasticity by the Cosserat brothers [13], the couple stress theory by Mindlin and Tiersten, Toupin, Koiter [14–16]. The nonlocal elasticity theory by Eringen [17], which is based on the fact that the stress at a given point is a function of strains at all other points in the body, was applied in various nano/microstructure problems [18–29]. The strain gradient theory by Lam et al.…”

Section: Introductionmentioning

confidence: 99%

Vibrations and buckling of orthotropic small‐scale plates with complex shape based on modified couple stress theory

2020

View full text Add to dashboard Cite

Free vibrations of microplates with non‐classical shape are considered in the paper. Governing equations are based on the modified couple stress theory and Kirchhoff–Love plate theory. It is assumed that the plate is isotropic or orthotropic and satisfy various boundary conditions. An analysis is performed by the variational‐structural method which is based on R‐functions theory and Ritz method. The testing of the proposed method is carried out by comparison with known in literature results and analytical solutions. The developed method is applied to the study of the influence of the material length scale parameter, boundary conditions, shape parameters, material characteristics on vibration frequencies. Also, size‐dependent analysis for buckling of the isotropic and orthotropic microplate subjected to uniaxial load is performed by the proposed approach. Critical loads for a plate with complex shape, different types of boundary conditions and material are calculated in order to study their effect on buckling.

show abstract

“…In addition, functionally graded structures have attracted considerable attention in models of nano/micro mechanics. The studies on functionally graded nano/micro structures such as FG nanoplate [3][4][5][6][7], FG nanobeam [8][9][10][11][12][13][14], FG nanorod [14][15][16][17][18] have been presented by researchers in recent years.…”

Section: Introductionmentioning

confidence: 99%

A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods

Uzun

Yaylı

2020

International Journal of Engineering and Applied Sciences

View full text Add to dashboard Cite

In the present study, a nonlocal finite element formulation of free longitudinal vibration is derived for functionally graded nano-sized rods. Size dependency is considered via Eringen's nonlocal elasticity theory. Material properties, Young's modulus and mass density, of the nano-sized rod change in the thickness direction according to the power-law. For the examined FG nanorod finite element, the axial displacement is specified with a linear function. The stiffness and mass matrices of functionally graded nano-sized rod are found by means of interpolation functions. Functionally graded nanorod is considered with clamped-free boundary condition and its longitudinal vibration analysis is performed.

show abstract

Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory

Cited by 186 publications

References 49 publications

Vibration Analysis of Viscoelastic FGM Nanoscale Plate Resting on Viscoelastic Medium Using Higher-order Theory

Vibration Analysis of Viscoelastic FGM Nanoscale Plate Resting on Viscoelastic Medium Using Higher-order Theory

Vibrations and buckling of orthotropic small‐scale plates with complex shape based on modified couple stress theory

A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods

Contact Info

Product

Resources

About