Size effect on pull-in behavior of electrostatically actuated microbeams based on a modified couple stress theory

Kong, Shengli

doi:10.1016/j.apm.2013.02.024

Cited by 58 publications

(13 citation statements)

References 39 publications

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“…In this regards, the non-classical theories such as non-local elasticity (Eringen and Edelen 1972), couple stress theory (Kong, 2013;Ejike, 1969), strain gradient theory (Lam et al, 2003), modified couple stress theory (Yang et al, 2002) etc. have been developed to consider the size effect in theoretical continuum models.…”

Section: Using Various Approachesmentioning

confidence: 99%

“…The most comprehensive work was done by Mindlin[14] which contained five additional material parameters and encompassed other non-local theories as special cases Non-local elasticity has been used to study buckling, bending vibration dislocation mechanics, fracture mechanics, surface tension fluids, etc. (Reddy, 2007;Mohammadi et al, 2012;2013;Moosavi et al, 2011;Danesh et al, 2012;Farajpour et al, 2012) Lam et al (2003, introduced a modified strain gradient theory with three material length scale parameters relevant to dilatation gradient, deviatoric gradient, and symmetric rotation gradient tensors. While some simple size dependent models based on modified couple stress theory have been applied to analyze the pull-in instability of MEMS/NEMS (Tadi HRokni, et al, 2013;Noghrehabadi et al, 2013;Zhang and Fu, 2012;Mindlin and Tiersten, 1962;Yin et al, 2011), only rare works have utilized strain gradient theory for analyzing.…”

Section: Using Various Approachesmentioning

confidence: 99%

See 1 more Smart Citation

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Koochi

Sedighi

Abadyan

2014

Lat. Am. j. solids struct.

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It is well recognized that size dependency of materials characteristics, i.e. size-effect, often plays a significant role in the performance of nano-structures. Herein, strain gradient continuum theory is employed to investigate the size dependent pull-in instability of beam-type nano-electromechanical systems (NEMS). Two most common types of NEMS i.e. nano-bridge and nano-cantilever are considered. Effects of electrostatic field and dispersion forces i.e. Casimir and van der Waals (vdW) attractions have been considered in the nonlinear governing equations of the systems. Two different solution methods including numerical and Rayleigh-Ritz have been employed to solve the constitutive differential equations of the system. Effect of dispersion forces, the size dependency and the importance of coupling between them on the instability performance are discussed.

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Section: Using Various Approachesmentioning

confidence: 99%

Section: Using Various Approachesmentioning

confidence: 99%

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Koochi

Sedighi

Abadyan

2014

Lat. Am. j. solids struct.

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“…They introduced a non-classical model for the electrostatically actuated microbeam by using MCST with the Rayleigh-Ritz method. S. Kong [16] also showed that normalized pull-in voltage of the microbeam by the MCST is 3.1 times greater than that predicted by the CT when the microbeam thickness equals to the material length scale parameter. Askari et al [17] studied the size-dependent dynamic pull-in analysis of clamped-clamped microbeams under mechanical shock based on MCST.…”

Section: Introductionmentioning

confidence: 93%

A theoretical study for the vibration of a cantilever microbeam as a free boundary problem

Abdollahi

Ahdiaghdam

Ivaz

et al. 2016

Applied Mathematical Modelling

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Vibration of a beam has extensive applications in engineering and industry.The objective of this article is to provide a novel analytical model by free boundary approach to derive a more exact model for the small oscillations of a cantilever microbeam in contact with an incompressible bounded fluid in a cavity.First, a system of integral equations is proposed to solve and interpret the problem. Then, the existence of the solution is proved by the use of the Banach fixed point theorem At the end, an example is presented for verifying the proposed method and comparing the results with the fixed boundary approach.

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“…A modified couple stress model first proposed by Yang et al [17] is adopted to capture micro-scale effects, using a symmetric couple stress tensor, and one material length scale parameter. These features make the modified couple stress model preferable for variational formulation of beam and plate theories [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Static and eigenvalue problems of Sigmoid Functionally Graded Materials (S-FGM) micro-scale plates using the modified couple stress theory

Jung

Han

2015

Applied Mathematical Modelling

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Bending, Vibration and Buckling analysis of Sigmoid Functionally Graded Materials (S-FGM)micro-scale plates using the modified couple stress theory is presented in this paper. The microscale effects of S-FGM micro-scale plates are captured using the single material length scale parameter of a modified couple stress theory. The material properties are assumed to vary only through the thickness of the S-FGM micro-scale plate, by mixing two different materials. The shear deformation effects are included, using the third-order shear deformation theory. The present theory does not require a shear correction factor, because of the parabolic distribution of the transverse shear strains through the thickness. The third-order theory that accounts for the functionally graded material, and the micro-scale effects have been derived using the principle of virtual displacements. In the present theory, the variation of two materials through thickness is embedded into the plate constitutive relation. The static and eigenvalue problems are solved by the Navier method. Numerical examples of bending, vibration and buckling problems are presented, to illustrate the effects of the sigmoid power-law distribution of the two materials, and the dimensionless material length scale parameter. In particular, in the case of biaxial compression and tension, the magnitude and direction of the buckling load should be considered simultaneously.

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Size effect on pull-in behavior of electrostatically actuated microbeams based on a modified couple stress theory

Cited by 58 publications

References 39 publications

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

Modeling the size dependent pull-in instability of beam-type NEMS using strain gradient theory

A theoretical study for the vibration of a cantilever microbeam as a free boundary problem

Static and eigenvalue problems of Sigmoid Functionally Graded Materials (S-FGM) micro-scale plates using the modified couple stress theory

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