A discussion on incorporating the Poisson effect in microbeam models based on modified couple stress theory

Dehrouyeh-Semnani, Amir Mehdi; Nikkhah‐Bahrami, Mansour

doi:10.1016/j.ijengsci.2014.10.003

Cited by 64 publications

(19 citation statements)

References 50 publications

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“…Since incorporating the Poisson's ratio causes underestimation of de ection due to the overestimation of bending rigidity of microbeam [10,11], the Poisson's ratio is assumed here to be zero. For all considered examples, unless mentioned otherwise, the beam's dimensions are L = 20h 1 and b = 2h 1 .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…They also investigated the Poisson's e ect on the static bending and free vibration of a simply supported beam. However, later, it was shown that considering Poisson's e ect can lead to erroneous results, and the results obtained by omitting Poisson's e ect are much closer to the experimental data [10,11]. Kahrobaiyan et al [12] used modi ed couple stress theory to obtain the dynamic characteristics of atomic force microscopes cantilevers.…”

Section: Introductionmentioning

confidence: 98%

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Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

et al. 2017

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KEYWORDSAbstract. In this paper, we study static bending and free vibration behaviors of Bernoulli-Euler microbeams with a single delamination using the modi ed couple stress theory. The delaminated beam is modeled by four interconnected sub-beams using the delamination zone as their boundaries. The free and constrained mode theories are utilized to model the interaction of delamination surfaces in the damaged area. The continuity as well as compatibility conditions are satis ed between the neighboring sub-beams. After veri cation of the results for some case studies with available solutions, the e ects of various parameters, such as spanwise and thicknesswise locations of the delamination, material length-scale parameter, and boundary conditions, on the static bending and free vibration characteristics of the size-dependent microbeam, have been investigated in detail.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

et al. 2017

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“…47,48 The MCST o®ers a direct framework to deal with the inclusion of internal material length scale of one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) micron-scale structures, 32,49,50 and is the theory adopted in the current study. Useful discussions on some aspect of the MCST and other nonclassical models of micro-scale beams are presented in the recent studies by Dehrouyeh-Semnani et al 51,52 By complementing the theoretical basis of the MCST with an appropriate homogenization scheme, a number of representative studies have been reported in the literature on the frequency analyses of FG micro-scale beams. Thē rst known model of FG microbeams, premised on the MCST and the classical rule of mixture, is reported in Asghari et al 53 The authors presented solution for the model of the FG microbeam with pinned ends in the absence of the e®ect of the axial coupling.…”

Section: Introductionmentioning

confidence: 99%

Eigenanalyses of Functionally Graded Micro-Scale Beams Entrapped in an Axially-Directed Magnetic Field with Elastic Restraints

Mustapha

Hawwa

2016

Int. J. Str. Stab. Dyn.

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Approximate numerical solutions are obtained for the vibration response of a functionally graded (FG) micro-scale beam entrapped within an axially-directed magnetic¯eld using the di®erential transformation method (DTM). Idealized as a one-dimensional (1D) continuum with a noticeable microstructural e®ect and a thickness-directed material gradient, the microbeam's behavior is studied under a range of nonclassical boundary conditions. The immanent microstructural e®ect of the micro-scale beam is accounted for through the modi¯ed couple stress theory (MCST), while the microscopic inhomogeneity is smoothened with the classical rule of mixture. The study demonstrates the robustness and°exibility of the DTM in providing benchmark results pertaining to the free vibration behavior of the FG microbeams under the following boundary conditions: (a) Clamped-tip mass; (b) clamped-elastic support (transverse spring); (c) pinned-elastic support (transverse spring); (d) clamped-tip mass-elastic support (transverse spring); (e) clamped-elastically supported (rotational and transverse springs); and (f) fully elastically restrained (transverse and rotational springs on both boundaries). The analyses revealed the possibility of using functional gradation to adjust the shrinking of the resonant frequency to zero (rigid-body motion) as the mass ratio tends to in¯nity. The magnetic¯eld is noted to have a negligibly minimal in°uence when the gradient index is lower, but a notably dominant e®ect when it is higher.

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“…Askari and Tahani [23] investigated size-dependent dynamic pull-in analysis of beam-type MEMS under mechanical shock based on the modified couple stress theory. Dehrouyeh-Semnani and Nikkhah-Bahrami [24] presented a discussion on incorporating the Poisson effect in microbeam models based on the modified couple stress theory. Farokhi and Ghayesh [25] investigated nonlinear dynamical behaviour of geometrically imperfect microplates based on the modified couple stress theory.…”

Section: Introductionmentioning

confidence: 99%

Reflection and transmission at the boundary surface of modified couple stress thermoelastic media

Kumar

Kumar²

2016

International Journal of Applied Mechanics and Engineering

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In this paper the reflection and transmission at a plane interface in modified couple stress generalized thermoelastic solid half spaces in the context of Loard-Shulman (LS) and Green-Lindsay (GL) theories in welded contact are investigated. Amplitude ratios of various reflected and transmitted waves are obtained due to incidence of a set of coupled longitudinal waves and coupled transverse waves. It is found that the amplitude ratios of various reflected and transmitted waves are functions of the angle of incidence, frequency and are affected by the couple stress properties of the media. Some special cases are deduced from the present formulation.

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A discussion on incorporating the Poisson effect in microbeam models based on modified couple stress theory

Cited by 64 publications

References 50 publications

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

Eigenanalyses of Functionally Graded Micro-Scale Beams Entrapped in an Axially-Directed Magnetic Field with Elastic Restraints

Reflection and transmission at the boundary surface of modified couple stress thermoelastic media

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