Modeling and Vibration Characteristics of Cracked Nano-Beams Made of Nanocrystalline Materials

Shaat, Mohamed; Khorshidi, Majid Akbarzadeh; Abdelkefi, Abdessattar; Shariati, Mahmoud

doi:10.1016/j.ijmecsci.2016.07.037

Cited by 58 publications

(10 citation statements)

References 71 publications

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“…The postbuckling loads obtained in Eqs. (22), (24), (25) and (26) can lead to the critical buckling loads N cr when the postbuckling amplitude is set to zero W = 0.…”

Section: Solutionmentioning

confidence: 99%

“…In the literature, a wide range of studies have been done on the vibration, buckling and postbuckling analyses of beams especially micro-or nano-beams [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], but there are few studies on the postbuckling analysis of porous micro-or nanostructures [34][35][36][37]. She et al [34] presented the thermal buckling and postbuckling of FG nanotubes with porosities.…”

Section: Introductionmentioning

confidence: 99%

“…(25)] and in symmetric distribution, I 1 is equal to zero so M 1,symmetric > M 1,asymmetric , while the buckling load depends on M 1 , M 2 and M 3 for the linear and exponential non-uniformities.The static postbuckling responses of non-uniform porous microbeams are shown in Figs. 4 and 5.…”

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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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“…The postbuckling loads obtained in Eqs. (22), (24), (25) and (26) can lead to the critical buckling loads N cr when the postbuckling amplitude is set to zero W = 0.…”

Section: Solutionmentioning

confidence: 99%

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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“…Size‐dependent beam and plate models are established on the basis of these non‐classical elasticity theories. For micro‐beam, Shaat et al . used the couple stress theory to establish a size‐dependent micro‐beam model to investigate the vibration response of cracked beams.…”

Section: Introductionmentioning

confidence: 99%

A size‐dependent Bernoulli‐Euler beam model based on strain gradient elasticity theory incorporating surface effects

2019

Z Angew Math Mech

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In this paper, a size-dependent model for Bernoulli-Euler beam is developed by using a general strain gradient theory and a surface elasticity theory. The general strain gradient theory is used to capture the strain gradient effects while the surface elasticity theory is applied to explain the surface effects. As comparison, the approximate theories including the couple stress theory and the simplified strain gradient theory are also used to describe the strain gradient effects. The Hamilton's principle is used to derive the governing equations, boundary conditions and initial conditions. The static bending and free vibration behaviour of nanobeams with different boundary conditions are analysed. Compared with the results predicted by the couple stress theory with surface effects and the simplified strain gradient theory with surface effects, because the general strain gradient theory contains the influences of all strain gradients, the deflection predicted by the general strain gradient theory with surface effects is smallest while the natural frequency is highest. The general strain gradient theory reflects size effects more accurately. K E Y W O R D SBernoulli-Euler beam, Hamilton's principle, size-dependent, strain gradient effects, surface effects

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“…In majority of recent studies on static and dynamic behavior of micro/nanobeams in the presence of a micro or nano-scale crack, the flexibility constant which introduces the crack severity is considered as a hypothetical input. However, there are studies which formulate the severity of the crack as a function of the crack depth, the material length scale parameter and other mechanical characteristics of the beam (Shaat et al, 2016;Akbarzadeh Khorshidi et al, 2017). These papers use energy stored in the spring and compare it with the strain energy release rate at the crack surfaces.…”

Section: Introductionmentioning

confidence: 99%

Investigation of flexibility constants for a multi-spring model: a solution for buckling of cracked micro/nanobeams

Khorshidi¹,

Shariati²

2019

Journal of Theoretical and Applied Mechanics

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In this paper, a multi-spring model is used for modelling of the crack in a micro/nanobeam under axial compressive load based on a modified couple stress theory. This model includes an equivalent rotational spring to transmit the bending moment and an equivalent longitudinal spring to transmit the axial force through the cracked section, which leads to promotion of the modelling of discontinuities due to the presence of the crack. Moreover, this study considers coupled effects between the bending moment and axial force on the discontinuities at the cracked section. Therefore, four flexibility constants appear in the continuity conditions. In this paper, these four constants are obtained as a function of crack depth, separately. This modelling is employed to solve the buckling problem of cracked micro/nanobeams using a close-form method, Euler-Bernoulli theory and simply supported boundary conditions. Finally, the effects of flexibility constants, crack depth and crack location on the critical buckling load are studied.

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Modeling and Vibration Characteristics of Cracked Nano-Beams Made of Nanocrystalline Materials

Cited by 58 publications

References 71 publications

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

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

A size‐dependent Bernoulli‐Euler beam model based on strain gradient elasticity theory incorporating surface effects

Investigation of flexibility constants for a multi-spring model: a solution for buckling of cracked micro/nanobeams

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