The influence of dispersion forces on the size-dependent pull-in instability of general cantilever nano-beams containing geometrical non-linearity

SoltanRezaee, Masoud; Farrokhabadi, Amin; Ghazavi, Mohammad Reza

doi:10.1016/j.ijmecsci.2016.10.010

Cited by 28 publications

(14 citation statements)

References 65 publications

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“…By use of a weighted-residual method, a reduction procedure was used to get a reduced-order model which was solved by use of a continuation technique. SoltanRezaee et al [44] investigated the static and dynamic pull-in instability of general cantilever nanobeams containing geometrical nonlinearity in the presence of quantum vacuum fluctuation and piecewise electrostatic attractions. The pull-in voltages and fundamental natural frequencies were obtained numerically using the step-bystep linearization method.…”

Section: A Literature Reviewmentioning

confidence: 99%

“…Moreover, most of the studies on the dynamic pull-in behavior of electrostatically actuated structures limit to the numerical solution methods. [39][40][41]43,44] In this study, a semi-analytical solution is developed to study the dynamic pull-in instability of electrostatically actuated multilayer nanoresonators using the nonlocal elasticity theory and Euler-Bernoulli beam model. Resonators are modeled as symmetric multilayered beams with fixed-fixed and fixed-free end conditions which are embedded in an elastic medium containing the Winkler and Pasternak elastic foundations.…”

Section: Present Studymentioning

confidence: 99%

“…Also, it is evident from the literature review that the effects of small scale and intermolecular forces should be taken account in the mechanical analysis of nanoscale structures. Moreover, most of the studies on the dynamic pull‐in behavior of electrostatically actuated structures limit to the numerical solution methods . In this study, a semi‐analytical solution is developed to study the dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators using the nonlocal elasticity theory and Euler–Bernoulli beam model.…”

Section: Introductionmentioning

confidence: 99%

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On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

Taati

2019

Z Angew Math Mech

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Based on the nonlocal Euler–Bernoulli beam theory, a theoretical approach is developed to investigate the effects of small scale and intermolecular force on the dynamic pull‐in behavior of electrostatically actuated nanoresonators. To this purpose, nanoresonators are modeled as multilayer beams with rectangular cross‐sections and fixed‐fixed and fixed‐free end conditions which are embedded in an elastic medium containing Winkler and Pasternak elastic foundations. Also, the effects of nonlocal parameter, fringing field due to the finite width of beams, Casimir or van der Waals intermolecular forces, nonlinear term induced by mid‐plane stretching and Winkler and Pasternak elastic foundations are considered in the mathematical modeling of pull‐in behavior. Finally, a hybrid semi‐analytical method is proposed to solve the nonlinear partial differential equation in two steps using the separation of variable technique. First, the Galerkin method is used to reduce a nonlinear ordinary differential equation with respect to time variable. Next, the parameter expansion method is applied to solve ensuing equation and obtain the time history response of transverse deflection. As case studies, the numerical results including curves of voltage‐normalized frequency, time history of normalized maximum deflection and phase portrait of two six‐layer cantilever and fully fixed beams are presented and discussed in detail. Findings indicate that the effect of small scale on the pull‐in voltages is more significant for both boundary conditions, in comparison with the intermolecular force. Also, it is seen that the pull‐in voltages of cantilever beams become larger by considering the nonlocal effect, contrary to the case of fully fixed beams.

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Section: A Literature Reviewmentioning

confidence: 99%

Section: Present Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

Taati

2019

Z Angew Math Mech

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“…An area of sensor design with a lot of potential is the microelectromechanical systems (MEMSs) 4 and, more recently, nano-electromechanical systems. [5][6][7] Originally, the term MEMS represented systems which integrate mechanical and electrical components at the micron scale. However, many physical domains have been explored, including fluidic, thermal, optical, and magnetic.…”

Section: Introductionmentioning

confidence: 99%

“…If St < < 1 a quasi-static approach applies. For the class of structures at hand, this generally happens for f < 10 6 Hz. In these conditions compressibility can be neglected.…”

Section: Introductionmentioning

confidence: 99%

The oscillating and electrostatic characteristics of microelectromechanical system cantilever structure analyzed based on the air gap domain

Jian

Zhang

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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Extensive modeling and simulation of the damping phenomenon, electrostatic actuation, and structural vibration analysis are performed. The governing partial differential equations of cantilever plate are obtained, and the resonant frequencies are calculated from the equilibrium equations. The damping forces of squeeze film are analyzed by obtaining the damping ratio and spring constant. Electrostatic actuation is applied to oscillate the cantilever to ensure that the displacement of the plate is above the thermal noise floor. Electrostatic actuating forces, displacement, and capacitance are calculated both numerically and analytically from the Poisson's equations. Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Squeeze film effects are simulated by the finite element method. The accuracy of the compact model is studied by comparing its response to the numerical results calculated with the finite element method. The agreement is very good in a wide frequency band. The numerical study and the compact model are directly applicable in predicting the damping force and damping factors of squeeze film.

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Study of Electrostatic and Dispersion Forces in Nanoelectromechanical Systems ( NEMS )

SoltanRezaee¹,

Farrokhabadi²

2022

Nanotechnology in Electronics

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The influence of dispersion forces on the size-dependent pull-in instability of general cantilever nano-beams containing geometrical non-linearity

Cited by 28 publications

References 65 publications

On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

The oscillating and electrostatic characteristics of microelectromechanical system cantilever structure analyzed based on the air gap domain

Study of Electrostatic and Dispersion Forces in Nanoelectromechanical Systems ( NEMS )

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