Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect

Finite conductivity, surface energy and nonlocal effect can influence the electromechanical performance of micro/nano-electromechanical systems (MEMS/NEMS). However, these factors are yet ignored on stability analysis of MEMS/NEMS fabricated from functionally graded materials (FGM). In this paper, dynamic stability of double-sided NEMS fabricated from non-symmetric FGM is investigated incorporating finite conductivity, surface energy and nonlocal effect. The Gurtin-Murdoch model and Eringen's elasticity are employed to consider the surface energy and nonlocal effect, respectively. Effect of finite conductivity of FGM on electrostatic and Casimir attractions is incorporated via relative permittivity and plasma frequency of the material. The stability analysis of the nanostructure is conducted by plotting time history and phase portraits. Moreover, bifurcation analysis is conducted to investigate the stability of the fixed points of the nano-structure. The validity of the proposed model is examined by comparing the results of the present study with those reported in the literature. The impact of various parameters i.e. finite conductivity, nonlocal parameter, surface stresses and material characteristics on the dynamic instability of the NEMS are addressed. (C) 2015 Elsevier Ltd. All rights reserved

Modeling the instability of CNT tweezers using a continuum model

Carbon nanotube (CNT) tweezers are composed of two parallel cantilever CNTs with a distance in between. In this paper, the static response and instability of CNT-made nano-tweezers is theoretically investigated considering the effects of Coulomb electrostatic force and van der Waals molecular attraction. For this purpose, a nano-scale continuum model is employed to obtain the nonlinear constitutive equation of the nano-tweezers. The Euler-Bernoulli beam theory is applied to model the elastic response of the CNT. The van der Waals attraction is computed from the simplified Lennard-Jones potential. In order to solve the nonlinear constitutive equation of the system, three approaches, e.g. the hemotopy perturbation method (HPM), the Adomian decomposition (AD) and the finite difference method (FDM) are employed. The obtained results are in good agreement with the experimental measurements. As a case study, freestanding CNT tweezers has been investigated and the detachment length and minimum initial gap of the tweezers are determined. Moreover, the effective operation range of the van der Waals attraction that affects the instability behavior of the CNT tweezers is discussed

Microstructure-dependent dynamic behavior of torsional nano-varactor

Experiments depict that the physico-mechanical response of miniature devices is microstructure-dependent. However, the classic continuum theory cannot correctly predict the microstructure-dependency. In this paper, the strain gradient theory is employed to examine the dynamic behavior and instability characteristics of miniature varactor with trapezoidal geometry. The governing equation of the varactor is obtained incorporating the effects of Coulomb force, van der Waals (vdW) attraction, squeeze film damping and structural damping. The influences of microstructure on the dynamic instability of equilibrium points are studied by plotting the phase portrait and bifurcation diagrams. It is found that increase in the microstructure parameter enhances the torsional stability. In the presence of the applied voltage, the phase portrait shows the saddle-node bifurcation while for free-standing varactor a subcritical pitchfork bifurcation is observe

A new model for stability analysis of electromechanical nano-actuator based on Gurtin-Murdoch and consistent couple-stress theories

Herein, the pull-in instability of cantilever NEMS is studied considering the presence of dispersion forces and squeezed film damping. Recently developed consistent couple stress theory in combination with the Gurtin-Murdoch elasticity is employed to incorporate the coupled effects of size phenomena and surface energy. The governing equation was solved using Rayleigh-Ritz method. Effects of various parameters including surface layer, size dependency, dispersion forces and damping on the pull-in characteristics of the nano-actuator are discussed

Modeling the coupled effects of surface layer and size effect on the static and dynamic instability of narrow nano-bridge structure

For modeling the electromechanical behavior of nano-bridge structures with slender narrow-width beam elements, not only the simultaneous effects of surface layer and size dependency should be taken into account but also corrected force models should be considered. In this paper, the instability of a narrow-width nano-bridge is studied based on strain gradient theory and Gurtin–Murdoch surface elasticity. The mid-plane stretching is incorporated in the governing equation as well as corrected force distribution. Using Rayleigh–Ritz method, a parametric analysis is conducted to examine the impacts of surface layer, size dependence, dispersion forces and structural damping on static and dynamic instability voltage of the nano-bridge. © 2016, The Brazilian Society of Mechanical Sciences and Engineering

Electromechanical instability of nanobridge in ionic liquid electrolyte media: influence of electrical double layer, dispersion forces and size effect

In this paper, the electromechanical response and instability of the nanobridge immersed in ionic electrolyte media is investigated. The electrochemical force field is determined using double-layer theory and linearized Poisson–Boltzmann equation. The presence of dispersion forces, i.e., Casimir and van der Waals attractions are incorporated considering the correction due to the presence of liquid media between the interacting surfaces (three-layer model). The strain gradient elasticity is employed to model the size-dependent structural behavior of the nanobridge. To solve the nonlinear constitutive equation of the system, three approaches, e.g., the Rayleigh–Ritz method, Lumped parameter model and the numerical solution method are employed. Impacts of the dispersion forces and size effect on the instability characteristics as well as the effects of ion concentration and potential ratio are discussed. © 2015, Indian Association for the Cultivation of Science

A Nonlinear Model for Incorporating the Coupled Effects of Surface Energy and Microstructure on the Electromechanical Stability of NEMS

Surface energy and size phenomenon can play significant roles in physical performance of nano-electromechanical systems. Herein, the static and dynamic pull-in behavior of nano-tweezers and nano-switch fabricated from conductive cylindrical nano-wires is studied. The Gurtin–Murdoch surface elasticity in combination with the couple stress theory is employed to incorporate the coupled effects of surface energy and microstructure dependency (size phenomenon). Using Green–Lagrange strain, the higher-order surface stress components are incorporated in the nonlinear governing equation. The effect of gas damping is considered in the model as well as structural damping. The governing equation is solved using the reduced order method. The effects of various parameters on the static and dynamic pull-in parameters, phase plans and stability threshold of the nano-structures are demonstrated

A 2-DOF microstructure-dependent model for the coupled torsion/bending instability of rotational nanoscanner

It has been well established that the physical performance of nanodevices might be affected by the microstructure. Herein, a two-degree-of-freedom model base on the modified couple stress theory is developed to incorporate the impact of microstructure in the torsion/bending coupled instability of rotational nanoscanner. Effect of microstructure dependency on the instability parameters is determined as a function of the microstructure parameter, bending/torsion coupling ratio, van der Waals force parameter and geometrical dimensions. It is found that the bending/torsion coupling substantially affects the stable behavior of the scanners especially those with long rotational beam elements. Impact of microstructure on instability voltage of the nanoscanner depends on coupling ratio and the conquering bending mode over torsion mode. This effect is more highlighted for higher values of coupling ratio. Depending on the geometry and material characteristics, the presented model is able to simulate both hardening behavior (due to microstructure) and softening behavior (due to torsion/bending coupling) of the nanoscanners. © 2016, Springer-Verlag Berlin Heidelberg

Modeling the effect of microstructure on the coupled torsion/bending instability of rotational nano-mirror in Casimir regime

t has been well-established that the physical performance of nano-devices might be affected by the microstructure. Herein, a 2-degree-of-freedom model based on the modified couple stress elasticity is developed to incorporate the impact of microstructure in the torsion/bending coupled instability of rotational nano-electromechanical mirror. The governing equation of the mirror is derived incorporating the effects of electrostatic Coulomb and corrected Casimir forces with the consideration of the finite conductivity of interacting surfaces. Effect of microstructure-dependency on the instability parameters are determined as a function of the microstructure parameter, bending/torsion coupling ratio, vacuum fluctuation parameter and geometrical dimensions. It is found that the bending/torsion coupling substantially affects the stable behavior of the mirrors especially those with long rotational beam elements. Depending on the geometry and material characteristics, the presented model is able to simulate both hardening behavior (due to microstructure) and softening behavior (due to torsion/bending coupling) of the nano-mirror

The size-dependent electromechanical instability of double-sided and paddle-type actuators in centrifugal and Casimir force fields

The present research is devoted to theoretical study of the pull-in performance of double-sided and paddle-type NEMS actuators fabricated from cylindrical nanowire operating in the Casimir regime and in the presence of the centrifugal force. D'Alembert's principle was used to transform the angular velocity into an equivalent static, centrifugal force. Using the couple stress theory, the constitutive equations of the actuators were derived. The equivalent boundary condition technique was applied to obtain the governing equation of the paddle-type actuator. Three distinct approaches, the Duan-Adomian Method (DAM), Finite Difference Method (FDM), and Lumped Parameter Model (LPM), were applied to solve the equation of motion of these two actuators. This study demonstrates the influence of various parameters, i.e., the Casimir force, geometric characteristics, and the angular speed, on the pull-in performance. (C) 2017 Sharif University of Technology. All rights reserved