A unified higher order plate theory for functionally graded microplates based on the modified couple stress theory

Lou, Jia; He, Liwen; Du, Jianke

doi:10.1016/j.compstruct.2015.08.009

Cited by 37 publications

(11 citation statements)

References 40 publications

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“…They considered static response of beam under transverse loading. Lou et al [28] analyzed the effect of the material length scale parameter to thickness ratio on the bending, buckling and free vibration behavior of functionally graded microplate using a unified higher order plate theory. According to MCST, Wang et al [29] analyzed the nonlinear bending behavior of circular microbeam subjected to the uniformly distributed transverse loads.…”

Section: Ghorbanpour Arani and Shokravimentioning

confidence: 99%

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Free transverse vibration analysis of orthotropic multi-viscoelastic microplate system embedded in visco-Pasternak medium via modified strain gradient theory

Jamalpoor

Bahreman

Hosseini

2017

Jnl of Sandwich Structures & Materials

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In this paper, an analytical process is proposed to investigate the size-dependent free vibration of orthotropic multi-viscoelastic microplate systems (OMVMPS) embedded in Kelvin–Voigt visco-Pasternak medium according to the modified strain gradient theory. Governing equations of motion in the partial form and the related boundary conditions are derived by utilizing the Kirchhoff plate theory and Hamilton’s variational principle. The two different sorts of “chain” boundary conditions like “clamped Chain” and “free chain” systems are considered for the ends of microplate system. Navier’s method, which convinces that the simply supported boundary conditions and trigonometric methods are applied to analytically investigate the size effect of the natural frequencies of OMVMPS. The numerical outcomes are offered to report the variation of OMVMPS natural frequencies with the numerous amounts of the microplate numbers, the length scale parameter, aspect ratio, visco-Pasternak foundation parameters, the thickness of microplate, and higher modes number. Several numerical outcomes of this research depict that when the number of microplates is low, there is a significant distinction between natural frequencies achieved for “clamped chain” and “free chain” systems. Also, it is demonstrated that by increasing the number of microplates, the effect of the visco-Pasternak substrate on the natural frequency of system vibration decreases.

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Section: Ghorbanpour Arani and Shokravimentioning

confidence: 99%

“…Lou et al. [28] analyzed the effect of the material length scale parameter to thickness ratio on the bending, buckling and free vibration behavior of functionally graded microplate using a unified higher order plate theory. According to MCST, Wang et al.…”

Section: Introductionmentioning

confidence: 99%

Free transverse vibration analysis of orthotropic multi-viscoelastic microplate system embedded in visco-Pasternak medium via modified strain gradient theory

Jamalpoor

Bahreman

Hosseini

2017

Jnl of Sandwich Structures & Materials

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“…The MCST sinusoidal shear deformation model was also developed by Thai and Vo [47] for deflections and natural frequencies of simply supported microplates. Some other refined plate models [48,49] and quasi-3D [50][51][52] were also employed the MCST for FG microplates. In addition, the thermal effects are examined for the FG microplates in many publications.…”

Section: Introductionmentioning

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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“…He et al [26] presented a MCST four-variable refined plate model using analytical solution for the FG microplates. Lou et al [27] then developed this model for a unified framework including the von Karman's geometric nonlinearity. It should be noted that above studies [26][27][28][29][30], the normal strain or normal deformation, which becomes significant for thick plates, is not included.…”

Section: Introductionmentioning

confidence: 99%

“…Lou et al [27] then developed this model for a unified framework including the von Karman's geometric nonlinearity. It should be noted that above studies [26][27][28][29][30], the normal strain or normal deformation, which becomes significant for thick plates, is not included. In order to take into account both shear and normal deformation effects, Nguyen et al [28] presented four-variable quasi-3D model to analyse the bending, vibration and buckling behaviours of FG microplates using the isogeometric solutions.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent behaviour of functionally graded sandwich microplates under mechanical and thermal loads

Trinh

Thai

et al. 2017

Composites Part B: Engineering

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This paper presents the static bending, free vibration and buckling behaviours of functionally graded sandwich microplates under mechanical and thermal loads. Governing equations of both higher-order shear deformation and quasi-3D theories are derived based on the variational principle and modified couple stress theory. Apart from mechanical load, the temperature profiles considered are either uniform or linear distribution through the thickness, which results in changes of material properties and stress resultants. Numerical results are obtained using Navier solutions. The difference between quasi-3D and 2D models in dealing with mechanical and thermal load is discussed. Temperature-dependent and temperature-independent material properties are examined. The effects of geometry and power-law index together with mechanical loads and various temperature distributions on the size-dependent behaviours of functionally graded sandwich plates are also investigated.

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A unified higher order plate theory for functionally graded microplates based on the modified couple stress theory

Cited by 37 publications

References 40 publications

Free transverse vibration analysis of orthotropic multi-viscoelastic microplate system embedded in visco-Pasternak medium via modified strain gradient theory

Free transverse vibration analysis of orthotropic multi-viscoelastic microplate system embedded in visco-Pasternak medium via modified strain gradient theory

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

Size-dependent behaviour of functionally graded sandwich microplates under mechanical and thermal loads

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