The size-dependent natural frequency of Bernoulli–Euler micro-beams

Kong, Shengli; Zhou, Shenjie; Nie, Zhifeng; Wang, Kai

doi:10.1016/j.ijengsci.2007.10.002

Cited by 543 publications

(205 citation statements)

References 18 publications

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“…Micro/nano-scale mechanical elements are also used in micro-pumps, accelerometers, micro-mirrors and microswitches. A large number of engineering applications utilize the mechanical properties of thin films materials for tar- geted performance specifications such as those vibration shock sensor, atomic force microscopes and resonant testing method (Kong et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

“…MEMS/NEMS systems' responses have been the subject of several analytical studies in two past decades. Based on the modified couple-stress theory introduced by Yang et al (2002), Kong et al (2008) analytically calculated the size-dependent natural frequencies of Euler-Bernoulli beams. Shahba et al (2011) studied the free vibration and stability analysis of axially FG tapered Timoshenko beams using a finite element approach.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

Baghani

Mohammadsalehi

Dabaghian

2016

Lat. Am. j. solids struct.

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In this paper, analytical couple-stress solution for size-dependent large-amplitude vibrations of FG (functionally-graded) taperednanobeams is presented. Using the modified couple-stress theory, the small scale effects are accounted for. Employing the Homotopy-Pade Analysis Method, efficient and accurate analytical expressions for the deflection and non-linear frequencies of the both single and double tapered nanobeam are presented. Very good agreement is observed between the present work results and some available results reported in the literature. This study may be helpful to investigate the size-dependent mechanical properties of MEMS\NEMS. Therefore, the proposed analytical solution can be used as an efficient tool for the material or geometrical parametric studies of small scale devices consisting of beams for their design and optimization which involves a large number of simulations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

Baghani

Mohammadsalehi

Dabaghian

2016

Lat. Am. j. solids struct.

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“…For instance, non-local EB beam models have been built by Kong et al [22] based on a modified couple stress theory, by Zhang et al [23] based on a so-called hybrid approach, which involves a strain energy functional depending on local and nonlocal curvatures. A non-local TM beam model has been built by Wang et al [24] in conjunction with the gradient elasticity theory presented by Lam et al [12], and by Ma et al [25] based on a modified couple stress theory.…”

Section: Introductionmentioning

confidence: 99%

A new displacement-based framework for non-local Timoshenko beams

2015

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In this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of nonadjacent beam segments, and separately accounting for pure axial, pure bending and pure shear deformation modes. The variational consistency of the proposed non-local beam model is demonstrated by minimization of an appropriate total potential energy functional. Numerical results concerning the static behavior for different boundary and loading conditions are presented. It is shown that the proposed nonlocal beam model is able to capture experimental data on the static deflection of micro-beams, available in the literature.

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“…On the other hand, many researches showed that in micro and nano scales the materials have strong size dependence in deformation behavior (Papargyri-Beskou et al, 2003;Lazopoulos and Lazopoulos, 2010;Asghari et al, 2010;Park and Gao, 2006;Fu and Zhang, 2011;Kong et al, 2008Kong et al, , 2009Fathalilou et al, 2011). Size-dependent behavior is an inherent property of materials, which appears for a beam when the characteristic size such as thickness or diameter is close to the internal length-scale parameter of materials .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, some researchers have applied the non-classic theories of elasticity to study the mechanical behavior of electrostatically actuated micro and nano beams Asghari et al, 2010;Fu and Zhang, 2011;Kong et al, 2008Kong et al, , 2009Fathalilou et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Gap Dependent Bifurcation Behavior of a Nano-Beam Subjected to a Nonlinear Electrostatic Pressure

Fathalilou

Sadeghi

Rezazadeh

2014

Lat. Am. j. solids struct.

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This paper presents a study on the gap dependent bifurcation behavior of an electro statically-actuated nano-beam. The sizedependent behavior of the beam was taken into account by applying the couple stress theory. Two small and large gap distance regimes have been considered in which the intermolecular vdW and Casimir forces are dominant, respectively. It has been shown that changing the gap size can affect the fundamental frequency of the beam. The bifurcation diagrams for small gap distance revealed that by changing the gap size, the number and type of the fixed points can change. However, for large gap regime, where the Casimir force is the dominant intermolecular force, changing the gap size does not affect the quality of the bifurcation behavior.

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The size-dependent natural frequency of Bernoulli–Euler micro-beams

Cited by 543 publications

References 18 publications

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

A new displacement-based framework for non-local Timoshenko beams

Gap Dependent Bifurcation Behavior of a Nano-Beam Subjected to a Nonlinear Electrostatic Pressure

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