A Porous Microbeam Model for Bending and Vibration Analysis Based on the Sinusoidal Beam Theory and Modified Strain Gradient Theory

Wang, Yan Qing; Zhao, Haoxiang; Ye, Chao; Zu, Jean W.

doi:10.1142/s175882511850059x

Cited by 46 publications

(13 citation statements)

References 32 publications

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“…Therefore, the boundary conditions for the axial displacement are assumed as u = 0 at x = 0, L. So, we have Substituting Eqs. (12) and (13) into Eq. (9b), the governing equation can be rewritten as…”

Section: Governing Equationsmentioning

confidence: 99%

“…Even and uneven porosity distributions have been employed to study the different behaviors of porous structures [6][7][8][9][10] as two porosity patterns. Symmetric, asymmetric and uniform porosity distributions along the thickness are other types of the porosity distributions which have been taken into account to model the metal foams [11][12][13][14]. Also, the effects of pore size and pore shape were studied in tissue engineering and biomechanics [15,16].…”

Section: Introductionmentioning

confidence: 99%

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Effect of nano-porosity on postbuckling of non-uniform microbeams

Khorshidi

2019

SN Appl. Sci.

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This study is accomplished to investigate the effect of different types of porosity distribution on the static postbuckling response of non-uniform microbeams under the simply supported boundary conditions. The modified couple stress theory is used to capture the size effect in microscales, and the von-Karman strain-displacement relation is employed to describe the nonlinearity effect. The relative elasticity characteristics, e.g., Young's modulus and the material length scale parameter, are considered as a function of relative mass density. The nonlinear governing equations for Euler-Bernoulli porous microbeams with non-uniform cross section are derived by a variational energy method and solved using a closed-form solution. The critical buckling load and the static postbuckling response of porous non-uniform microbeams, non-porous non-uniform microbeams and porous uniform microbeams are compared with together. Therefore, effects of nano-porosity and non-uniformity on the postbuckling behavior of the microbeam are investigated.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of nano-porosity on postbuckling of non-uniform microbeams

Khorshidi

2019

SN Appl. Sci.

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“…Also, the MCST has used to express the size effect. Wang et al . analyzed vibration and bending of the porous microbeam using SSDT.…”

Section: Introductionmentioning

confidence: 99%

“…Also, the MCST has used to express the size effect. Wang et al [35] analyzed vibration and bending of the porous microbeam using SSDT. They used Hamilton's principle in order to derive the governing equation and natural frequency has been obtained employing Navier's solution method.…”

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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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“…Barati and Zenkour [35] examined the post-buckling behavior of nanoporous metal foam nanobeams based on a non-local, non-linear refined shear deformation beam model. By using the sinusoidal beam theory and modified strain gradient theory, Wang et al [36] investigated bending and vibration of nanoporous metal foam microbeams.…”

Section: Introductionmentioning

confidence: 99%

Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Wang

Zhang

2018

Coatings

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In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

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A Porous Microbeam Model for Bending and Vibration Analysis Based on the Sinusoidal Beam Theory and Modified Strain Gradient Theory

Cited by 46 publications

References 32 publications

Effect of nano-porosity on postbuckling of non-uniform microbeams

Effect of nano-porosity on postbuckling of non-uniform microbeams

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

Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

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