Thermo-electro-mechanical vibration and buckling analysis of quadrilateral and triangular nanoplates with the nonlocal finite strip method

Analooei, H. R.; Azhari, Mojtaba; Salehipour, Hamzeh

doi:10.1080/15397734.2021.1875331

Cited by 6 publications

(3 citation statements)

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“…Nonlocal buckling of triangular nanoplate embedded in Winkler-Pasternak foundation was investigated by Shahidi et al [38] In these two works [37,38] research is based on the weighted residual statement of the problem. Buckling study of triangular nanoplate was performed based on the nonlocal finite strip method by Analooei et al [39] In the presented research we continue the study of nanoplate of triangular shape, while the research aims to analyse vibrations and buckling of the graphene sheet in the nonlinear polymer. The latter leads to the necessity of analysing the influence of nonlinear effects as well as smallscale effects on the behaviour of nanocomposite.…”

Section: Introductionmentioning

confidence: 99%

“…Buckling study of triangular nanoplate was performed based on the nonlocal finite strip method by Analooei et al. [39] In the presented research we continue the study of nanoplate of triangular shape, while the research aims to analyse vibrations and buckling of the graphene sheet in the nonlinear polymer. The latter leads to the necessity of analysing the influence of nonlinear effects as well as small‐scale effects on the behaviour of nanocomposite.…”

Section: Introductionmentioning

confidence: 99%

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Vibrations and buckling of triangular graphene sheet in polymer matrix

Mazur,

Awrejcewicz

2023

Z Angew Math Mech

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The work is devoted to the study of vibrations and buckling of a graphene sheet (GS) with the shape of a right triangle, and embedded in a nonlinear polymer matrix. The research is based on the nonlocal elasticity theory and the application of the Bubnov‐Galerkin method. Due to the influence of the polymer surrounding, the study of vibrations is reduced to the analysis of a nonlinear cubic ordinary differential equation considering small‐scale effects. The nonlocal buckling problem for the triangular GS under in‐plane uniform compression is investigated including the finding of critical buckling load and the post‐buckling behaviour determined by the nonlinear medium effect.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibrations and buckling of triangular graphene sheet in polymer matrix

Mazur,

Awrejcewicz

2023

Z Angew Math Mech

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“…[30][31][32][33][34][35][36][37][38] In the Eringen's nonlocal theory, the internal size scale can be simply incorporated within the constitutive equations as a material parameter by assuming that the stress at a reference point is a function of the strain field at each point in the body. Based on the nonlocal finite strip method and the Kirchhoff plate theory, Analooei et al 39 studied the thermoelectro-mechanical vibration and buckling analysis of quadrilateral and triangular nanoplates. Assuming that the piezoelectric nanoplate is subjected to a biaxial force, with an external electric voltage and a uniform temperature rise, it was demonstrated that the small-scale effect plays a key role in buckling and vibration behavior of nanoplates.…”

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

Gholami

Ansari

Gholami

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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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.

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