Thermo-electro-mechanical bending of FG piezoelectric microplates on Pasternak foundation based on a four-variable plate model and the modified couple stress theory

Abazid, Mohammad Alakel; Sobhy, Mohammed

doi:10.1007/s00542-017-3492-8

Cited by 42 publications

(15 citation statements)

References 93 publications

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“…This paper also 21 generates the benchmark results for FG and FG-sandwich micro-plates with various configurations, which can be useful in the future reference. a/h l/h p = 0 p = 1 p = 10 FSDT [34] RFVPT [64] Present HSDT FSDT [34] RFVPT [64] Present HSDT Table 5: Size effect in the first two natural frequencies of simply supported plates.…”

Section: Discussionmentioning

confidence: 99%

State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

Trinh

Thai

et al. 2018

Composites Part B: Engineering

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The size-dependent static, free vibration and buckling behaviours of functionally graded (FG) sandwich plates are analysed in this study. Utilising the modified couple stress theory and variational principle, governing equations of motion are developed with a refined shear deformation theory. The rectangular plates embedded on two opposite simply-supported edges with the arbitrary combinations of the other two. Based on the state-space Levy solution, the deflections, stresses, natural frequencies and critical buckling loads are analytically solved for the closed-form formulations. The effects of material distribution and graded schemes, geometric parameters and boundary conditions are also investigated to examine the size-dependent behaviours of FG sandwich microplates.

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Section: Discussionmentioning

confidence: 99%

State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

Trinh

Thai

et al. 2018

Composites Part B: Engineering

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“…Sobhy 12 discussed depending on a four variable shell theory the magneto-electro thermal bending of composite doubly-curved shallow shells consisting of two piezoelectromagnetic face sheets considering a variety of boundary conditions. Moreover, Abazid and Sobhy 13 investigated the thermal and electro-mechanical size-dependent bending of simply supported functionally graded piezoelectric (FGP) microplates depending on a refined four-variable shear deformation plate theory together with the modified couple stress theory. Furthermore, Abazid 14 explored the thermomechanical buckling, free vibration, and wave dispersion in smart piezo-electromagnetic nanoplates under humid conditions by using both the nonlocal strain gradient theory (NSGT) and the sinusoidal shear deformation plate theory.…”

Section: Introductionmentioning

confidence: 99%

Electro-thermal buckling of FG graphene platelets-strengthened piezoelectric beams under humid conditions

Sobhy

Abazid

Mukahal

2022

Advances in Mechanical Engineering

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In this article, thermal buckling analysis of multilayer functionally graded graphene platelets (FGGPL) strengthened piezoelectric beam subjected to external electric voltage as well as humid conditions is illustrated. The effective Young’s modulus of the nanocomposite beam is estimated within the framework of Halpin-Tsai model. While, Poisson’s ratio, mass density, and piezoelectric properties are calculated by the rule of the mixture. Four FGGPL distribution types are considered in this study. A refined two-unknown beam theory considering shear deformation as well as thickness stretching effect is employed to describe the displacement components. The principle of virtual work including thermal, moisture, and electric loads is used to derive the stability differential equations. To check the accuracy of the obtained buckling temperature, some comparison examples are performed. The impacts of the GPLs volume fraction, distribution type, length-to-depth ratio, humid conditions, external electric voltage, and piezoelectric properties on the critical buckling temperature are studied.

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“…The influence of a pulsatile flow on the large-amplitude bifurcation behavior of viscoelastic microtubes subject to longitudinal pretention using modified couple stress theory was studied by Ghayesh et al 22 The size-dependent bending response of functionally graded piezoelectric (FGP) micro-plates resting on two-parameter elastic foundations and subjected to an external mechanical load, electric voltage, and elevated temperature presented by Abazid and Sobhy. 23 Trinh et al 24 utilized the modified couple stress theory and state-space Levy solution for size-dependent static, free vibration, and buckling behaviors of functionally graded sandwich plates. Thanh et al 25 based on New modified couple stress theory and iso-geometric analysis, explored the size-dependent thermal bending and buckling analyses of composite laminate micro-plate.…”

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

Proceedings of the Institution of Mechanical Engineers, Part C:

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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.

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Thermo-electro-mechanical bending of FG piezoelectric microplates on Pasternak foundation based on a four-variable plate model and the modified couple stress theory

Cited by 42 publications

References 93 publications

State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

Electro-thermal buckling of FG graphene platelets-strengthened piezoelectric beams under humid conditions

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

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