Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory

Şi̇mşek, Mesut; Aydın, Mustafa

doi:10.1016/j.compstruct.2016.10.034

Cited by 74 publications

(22 citation statements)

References 72 publications

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“…34, (35) and Eq. (38) into Eq. (32) and eliminating the virtual displacement vector d  , the matrix form of the global equilibrium equations for size-dependent thermal buckling of FGM micro-plate having porosities can be established in the following matrix form:…”

Section: Nurbs-based Formulation Of Functionally Graded Micro-plate Wmentioning

confidence: 99%

“…Shafiei and Kazemi [37] investigated the effect of porosities, small scale effect, nonlinear, FG index, etc., on nonlinear buckling behavior of micro-/nano-beam using porous material under clamped boundary conditions. Based on Mindlin plate theory and MSCT, Şimşek and Aydin [38] studied static bending and forced vibration of porous FG micro-plate under moving load. Moreover, the MSCT also was employed for free vibration analysis of magneto elastic porous FG circular nanoplate by Hosseini et al [39].…”

Section: Introductionmentioning

confidence: 99%

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Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates

Cuong-Le

Tran

Bui

et al. 2019

Composite Structures

111

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In this article, we present for the first time a research analysis for the size-dependent effects on thermal buckling and post-buckling behaviors of functionally graded material micro-plates with porosities (imperfect FGM) using isogeometric analysis. A seventh-order shear deformation plate theory associated with the modified couple stress theory (MCST) is particularly imposed to capture the size-dependent phenomenon within imperfect FGM micro-plates. The material properties of imperfect FGM micro-plates with three different distributions of porosities including even, uneven and logarithmic-uneven varying across the plate thickness are derived from the modified rule-of-mixture assumption. The nonlinear governing equation for sizedependent imperfect FGM micro-plate under uniform, linear and nonlinear temperature rise is derived using the Von-Kármán assumption and Hamilton's principle. Through numerical example, the effect of temperature rise, boundary conditions, power index, porosity volume fraction, porosity distribution pattern and material length scale parameter on thermal buckling and post-buckling behaviors of FGP micro-plates are investigated.

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Section: Nurbs-based Formulation Of Functionally Graded Micro-plate Wmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates

Cuong-Le

Tran

Bui

et al. 2019

Composite Structures

111

View full text Add to dashboard Cite

show abstract

“…To obtain the governing equations, the Hamilton's principle is applied. The Π is total potential energy of sandwich microbeam consists of strain energy ( U ) that is a combination of macro strain energy ( U s ) and micro strain energy ( U m ), kinetic energy ( T ) and the external work ( W E ) as follow:

δ \prod = δ \int_{0}^{t} false(T - U - W_{E} false) d t = 0,

U = U_{s} + U_{m}

where:

U_{s} = \frac{1}{2} \int_{V}^{} σ_{i j} ε_{i j} d V,

U_{m} = \frac{1}{2} \int_{V}^{} m_{i j} χ_{i j} d V

where

σ_{i j}

and

ε_{i j}

are the stress and strain tensors, respectively,

χ_{i j}

is symmetric curvature tensor and

m_{i j}

is deviator the couple stress tensor that may be stated as:

m_{i j} = 2 {(l_{m})}^{2} μ false(z false) χ_{i j}

MCST presents a length scale parameter that is additional material constant. This parameter which is shown by l m can be used to illustrate the size effect in microstructures.…”

Section: Governing Equationsmentioning

confidence: 99%

“…where and are the stress and strain tensors, respectively, is symmetric curvature tensor and is deviator the couple stress tensor that may be stated as [61] :…”

Section: Hamilton's Principlementioning

confidence: 99%

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

2019

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In this study, free vibration of the sandwich microbeam with porous core and FG carbon nanotubes reinforced composite face sheets which is rested on Winkler‐Pasternak substrate is investigated. It is assumed the beam is in thermal environment and is subjected to thermal load and the displacement components are described based on sinusoidal shear deformation beam theory. The small scale effects are taken into account according to the modified couple stress theory. The core and face sheets properties are diffused through the thickness. The motion equations are derived and solved using Hamilton's principle and Navier's method, respectively. Effect of different parameters such as porosity coefficient and distributions, different types of CNTs distribution, small scale and geometrical size of the beam is considered. The results show by enhancing the porosity, the frequency decreased. The findings of the current study can be used to design prominent role in modern engineering applications.

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“…This means that the analytical and numerical studies on FGMs cannot disregard the effect of porosity. Moreover, it is well known that the variation of porosity within the thickness yields a considerable variation in the mechanical properties [42,47,48]. On the other hand, the experimental evaluation of the porosity effect at a micro/nanoscale represents a difficult and expensive task.…”

Section: Introductionmentioning

confidence: 99%

Wave Propagation of Porous Nanoshells

et al. 2018

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This study aims at investigating the wave propagation of porous nanoshells. The Bi-Helmholtz non-local strain gradient theory is employed in conjunction with a higher-order shear deformation shell theory, in order to include the size-dependent effects. The nanoshells are made of a porous functionally graded material (P-FGM), whose properties vary continuously along the thickness direction. A variational approach is here applied to handle the governing equations of the problem, which are solved analytically to compute the wave frequencies and phase velocities as function of the wave numbers. The sensitivity of the wave response is analyzed for a varying porosity volume fraction, material properties, non-local parameters, strain gradient length scales, temperature, humidity, and wave numbers. Based on the results, it is verified that the size-dependence of the response is almost the same to the one of plates, beams and tubes.

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Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory

Cited by 74 publications

References 72 publications

Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates

Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates

Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT

Wave Propagation of Porous Nanoshells

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