Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories

Kolahchi, Reza; Hosseini, Hadi; Esmailpour, Masoud

doi:10.1016/j.compstruct.2016.08.032

Cited by 79 publications

(23 citation statements)

References 48 publications

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“…Given the fact that the vibration response is harmonic, the deflection owing to the vibrations of thin nanoplates are mentioned by (11) where i 2 = −1 and ω is the natural frequency. By using (2), (9), and (11), the equations of motion for the piezoelectric nanoplates are written in terms of displacements W b and W s as follows:…”

Section: Formulationmentioning

confidence: 99%

“…There are many theories to derive structural equation of piezoelectric and graphene nanoplate. Therefore, the piezoelectric nanostructures and graphene sheets have been investigated via classical plate hypothesis [4][5][6][7][8], first-order shear deformation hypothesis [9][10][11]. While few efforts were also conducted to examine both the influences of non-local elasticity and the surface layer on the piezoelectric nanosize structures via refined plate hypothesis.…”

Section: Introductionmentioning

confidence: 99%

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Fundamental frequency analysis of rectangular piezoelectric nanoplate under in‐plane forces based on surface layer, non‐local elasticity, and two variable refined plate hypotheses

Jamali

Ghassemi

2018

Micro & Nano Letters

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Fundamental frequency analysis of rectangular piezoelectric nanoplates via the surface layer and non-local small-scale hypotheses is investigated in the present work. The piezoelectric nanoplate is under in-plane forces. The equilibrium governing of piezoelectric nanoplates is attained via the two variable refined plate hypothesis, and then the equations of motion are achieved utilising Hamilton's principle. To solve these equations, the finite difference method is employed. To verify the exactness of the finite difference method, the governing equations are tested by the Navier's solution. Numerical results show a good accuracy among the outcomes of the present work and some accessible cases in the literature. The numerical results show that for negative residual surface stress, as the boundary condition becomes stiffer the effect of surface layer increases, while for positive one that phenomenon is inverse.

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Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fundamental frequency analysis of rectangular piezoelectric nanoplate under in‐plane forces based on surface layer, non‐local elasticity, and two variable refined plate hypotheses

Jamali

Ghassemi

2018

Micro & Nano Letters

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“…DQM has several benefits that are listed as below [22–26]: DQM is a powerful method which can be used to solve numerical problems in the analysis of structural and dynamical systems. The accuracy and convergence of the DQM is higher than FEM. DQM is an accurate method for solution of nonlinear differential equations in approximation of the derivatives. This method can easily and exactly satisfy a variety of boundary conditions and require much less formulation and programming effort. Recently, DQM has been extended to handle irregular shaped. …”

Section: Dqmmentioning

confidence: 99%

Vibration and buckling analysis of laminated sandwich conical shells using higher order shear deformation theory and differential quadrature method

Nasihatgozar

Khalili

2017

Jnl of Sandwich Structures & Materials

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Vibration and buckling analysis of laminated sandwich truncated conical shells with compressible or incompressible core are presented in this work considering curvature effects. The formulation uses the quadratic and cubic functions for transverse and in-plane displacements of the core and the first-order shear deformation theory for the face sheets. The motion equations of each individual layer are derived according to the principle of minimum total potential energy considering the continuity of the displacements and the internal stress fields at the interfaces. Differential quadrature method is applied in order to obtain the frequency and buckling load of the sandwich structure. The effects of different parameters such as core to face sheet stiffness ratio, number of layers of the face sheets, boundary condition, geometrical parameters of the core and the face sheets, semi vertex angle of the cone, trapezoidal shape, and in-plane stresses of the core are examined on the vibration and buckling response of sandwich truncated conical shells. Comparison of the present results with those reported in the literature confirms the accuracy of the proposed theory. Numerical results indicate that the effects of in-plane stresses of the core significantly affect the frequency with increasing the core to face sheet stiffness ratio.

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“…Kolahchi and his co-workers have studied the nonlinear buckling, bending, nonlinear dynamic stability, and nonlinear transverse vibration of nano-FG plate, nano-composite plate, nano-sandwich plates, and piezoelectric plate reinforced with single walled carbon nanotubes, respectively [37–44].…”

Section: Introductionmentioning

confidence: 99%

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

Mahmoudi¹,

Benyoucef²,

Tounsi³

et al. 2017

Jnl of Sandwich Structures & Materials

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In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

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Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories

Cited by 79 publications

References 48 publications

Fundamental frequency analysis of rectangular piezoelectric nanoplate under in‐plane forces based on surface layer, non‐local elasticity, and two variable refined plate hypotheses

Fundamental frequency analysis of rectangular piezoelectric nanoplate under in‐plane forces based on surface layer, non‐local elasticity, and two variable refined plate hypotheses

Vibration and buckling analysis of laminated sandwich conical shells using higher order shear deformation theory and differential quadrature method

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

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