Influence of Variable Nonlocal Parameter and Porosity on the Free Vibration Behavior of Functionally Graded Nanoplates

Ansari

Proceedings of the Institution of Mechanical Engineers, Part C:

et al. 2022

In this paper, a size-dependent nanoplate model is developed to describe the free vibration and buckling behaviors of magneto-electro-thermo-elastic (METE) rectangular nanoplates. It is assumed that the METE nanoplate is subjected to external electric voltage, external magnetic potential, and uniform temperature rise. The nonlocal elasticity theory along with the third-order shear deformation plate theory is employed for the size-dependent mathematical modeling of nanoplates. The presented model has two advantages over available models: (1) the need for the correction factor is bypassed and (2) it can be successfully applied to thick nanoplates. The governing equations and the corresponding boundary conditions are derived using the Hamilton’s principle which are then discretized on the space domain based on the generalized differential quadrature (GDQ) method. Afterward, an efficient numerical Galerkin procedure is adopted to reduce the discretized equations into Duffing-type ordinary differential equations. Numerical results are presented to examine the influences of nonlocal parameter, length-to-thickness ratio, temperature rise, external electric potential, external magnetic potential and type of boundary condition on the free vibration, and buckling behaviors of METE nanoplates. It is revealed that frequency and critical buckling load of nanoplates are dependent on magneto-electro-mechanical loadings, whereas they are less dependent on thermal loading.

Section: Introductionmentioning

confidence: 99%

Size-dependent free vibration and buckling analysis of magneto-electro-thermo-elastic nanoplates based on the third-order shear deformable nonlocal plate model

Ansari

Proceedings of the Institution of Mechanical Engineers, Part C:

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

“…Computational optimization for porosity-dependent iso-geometric analysis of functionally graded (FG) sandwich nano-plates were proposed by Phung-Van et al 46 Ghabussi et al 47 implemented a numerical-based generalized differential quadrature method for frequency analysis of a viscoelastic graphene nanoplatelet-reinforced composite circular microplate. Vinh and Huy 48 examined the Influence of variable nonlocal parameter and porosity on the free vibration behavior of functionally graded nano-plates using modified classical Eringen’s elasticity theory. Tsiatas 49 developed the first model of size-dependent to statically analyze micro-plates based on the theory of classical plate (CPT).…”

Section: Introductionmentioning

confidence: 99%

Accurate solution for size-dependent free vibration analysis of functionally graded micro-plates with Levy boundary conditions

Saber

Saidi

Bahaadini

2022

This paper has developed the Levy solution of a size-dependent model for free vibration analysis functionally graded thin rectangular plate according to the theories of first-order shear deformation as well as modified couple stress. The couple stress theory is used to calculate the effects of small-scale parameter, while the first-order shear deformation theory is employed to calculate the effects of shear deformation. By taking the displacement field according to the Mindlin plate theory, application of the Hamilton principle aims at obtaining five governing equations of motion and desired six boundary conditions. The governing equations of motion have been solved based on Levy boundary conditions by using four auxiliary functions. Numerical findings have been used to determine the impacts of various parameters including small-scale parameter changes, power-law index changes, as well as aspect ratios changes with different boundary conditions. As the results show, an increase in the size effects makes that plate tougher and consequently the natural frequency is increased. Also, it can be seen that in little thicknesses of plate, the effects of small-scale parameter are noticeable, but as the plate becomes thicker, the effects will be insignificant.

The role of nonlocality on low and high frequency behaviors of functionally graded sandwich nanoplates

Ghazwani,

Alnujaie,

Eltaher

et al. 2024

Z Angew Math Mech

The role of nonlocality on low and high frequency behaviors and modes of the functionally graded (FG) sandwich nanoplates is investigated in this study for the first time using simple nonlocal higher‐order shear deformation theory (HSDT). The simple HSDT consists of only four unknowns in its equation of the displacement field. The nonlocal elasticity theory is used to consider the small‐scale effects on the behaviors of the nanoplates. The governing equations of motion are established by applying Hamilton's principle, then Navier's solution technique is employed to solve these equations to achieve the free vibration behaviors of the FG sandwich nanoplates. The vibrations of the nanoplates under both low and high frequency conditions are investigated, but the high frequency vibration of the nanoplates is discussed extensively. The influences of the geometrical dimensions, material gradient index, and nonlocal parameter on the high frequency vibration of the FG nanoplates are also considered and discussed comprehensively.