MODELING THE INFLUENCE OF SURFACE EFFECT ON INSTABILITY OF NANO-CANTILEVER IN PRESENCE OF VAN DER WAALS FORCE

Surface effect often plays a significant role in the pull-in performance of nano-electromechanical systems (NEMS) but limited works have been conducted for taking this effect into account. Herein, the influence of surface effect has been investigated on instability behavior of cantilever nano-actuator in the presence of van der Waals force (vdW). Three different methods, i.e. an analytical modified Adomian decomposition (MAD), Lumped parameter model (LPM) and numerical solution have been applied to solve the governing equation of the system. The results demonstrate that surface effect reduces the pull-in voltage of the system. Moreover, surface energy causes the cantilever nano-actuator with the assigned parameter to deflect as a softer structure. It is found that while surface effect becomes important for low values of the cantilever nano-actuator thickness, vdW attraction is significant for low initial gap values. Surprisingly, the increase in the initial gap, enhances the contribution of surface effect in pull-in instability of the system while reduces the contribution of vdW attraction. Furthermore, the minimum initial gap and the detachment length of the cantilever nano-actuator that does not stick to the substrate due to vdW force and surface effect has been approximated. A good agreement has been observed between the values of instability parameters predicted via these three methods. Whilst compared to the instability voltage predicted by numerical solution, the pull-in voltage obtained by MAD series and LPM method is overestimated and underestimated, respectively.

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APPROXIMATING THE EFFECT OF VAN DER WAALS FORCE ON THE INSTABILITY OF ELECTROSTATIC NANO-CANTILEVERS

International Journal of Modern Physics B ◽

10.1142/s0217979211102083 ◽

2011 ◽

Vol 25 (29) ◽

pp. 3965-3976 ◽

Cited By ~ 20

Author(s):

ALI KOOCHI ◽

AMINREZA NOGHREHABADI ◽

MOHAMADREZA ABADYAN

Keyword(s):

Van Der Waals ◽

Convergent Series ◽

Lumped Parameter Model ◽

Distributed Parameter ◽

Analytical Results ◽

Lumped Parameter ◽

Fringing Field ◽

Beam Type ◽

Nano Electromechanical System ◽

Good Agreement

Beam-type nano-electromechanical system (NEMS) is one of the most components in constructing nano-devices. Herein, a distributed parameter model is used to study the influence of van der Waals (vdW) attraction on the pull-in performance of the cantilever NEMS. Homotopy perturbation method (HPM) is applied to solve the nonlinear governing equation of the actuators in the form of convergent series. Moreover, analytical results are compared with those of numerical method as well as a lumped parameter model. The pull-in voltage and critical cantilever tip deflection of NEMS are determined. Results depict that vdW attraction decreases the pull-in deflection and voltage of the NEMS. On the other hand, the fringing field increases the pull-in deflection while decreases the pull-in voltage of the system. The analytical results have good agreement with numerical results and those available in the literature.

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Closed Form Solutions for the Problem of Statical Behavior of Nano/Micromirrors Under the Effect of Capillary Force and Van Der Waals Force

Volume 11: Nano and Micro Materials, Devices and Systems; Microsystems Integration ◽

10.1115/imece2011-63112 ◽

2011 ◽

Author(s):

Ali Darvishian ◽

Hamid Moeenfard ◽

Hasan Zohoor ◽

Mohammad Taghi Ahmadian

Keyword(s):

Capillary Force ◽

Rotation Angle ◽

Van Der Waals ◽

Van Der Waals Force ◽

Combined Effect ◽

Geometrical Parameters ◽

Closed Form Solutions ◽

The Stability ◽

Vdw Force ◽

Stability Limits

The current paper deals with the problem of static instability of Micro/Nano mirrors under the combined effect of capillary force and van der Waals force. First the governing equations of the statical behavior of Micro/Nano mirrors under the combined effect of capillary force and casimir force is obtained using the newtons first law of motion. The dependence of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that existence of vdW torque can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the vdW toque applied to the mirror. Finally analytical tool Homotopy Perturbation Mehtod (HPM) is utilized for prediction of the nano/micromirror behaviour under combined capillary and vdW force. It is observed that a sixth order perturbation approximation accurately predicts the rotation angle and stability limits of the mirror. Results of this paper can be used for successful fabrication of nano/micromirrors using wet etching process where capillary force plays a major role in the system.

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Optimization of Lumped Parameter Models to Mitigate Numerical Oscillations in the Transient Responses of Short Transmission Lines

Energies ◽

10.3390/en14206534 ◽

2021 ◽

Vol 14 (20) ◽

pp. 6534

Author(s):

Jaimis S. L. Colqui ◽

Anderson R. J. de Araújo ◽

Sérgio Kurokawa ◽

José Pissolato Filho

Keyword(s):

Power Systems ◽

Transmission Lines ◽

Lumped Parameter Model ◽

Transient Responses ◽

Lumped Parameter ◽

Lumped Parameter Models ◽

Spurious Oscillations ◽

The Time Domain ◽

Time Transformations ◽

Good Agreement

The Lumped Parameter Model (LPM) is a known approach to represent overhead transmission lines (TLs), especially when these elements comprehend a few tens of kilometers. LPMs employ a large number of cascaded π-circuits to compute accurately the transient responses. These responses contain numerical spurious oscillations (NSO) characterized by erroneous peaks which distort the transient responses, mainly their peak values. Two modified LPM topologies composed of damping resistances inserted along the longitudinal or transversal branches of the cascaded π-circuits offer significant mitigations in the NSO. In this paper, in an effort to have the maximum mitigation of the NSO and low distortion in the transient responses, two modified topologies with optimized damping resistances are proposed to represent short TLs. Results demonstrate expressive attenuation in the peaks of NSO which reflect good agreement in comparison with the responses computed by the Bergeron’s line model. The mitigation of the NSO is carried out directly in the time domain and it does not require either analog or digital filters.Furthermore, no frequency-to-time transformations are necessary in this procedure. These alternative topologies can be incorporated into any electromagnetic transient program to study switching operations in power systems.

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Dynamic Model for a Dome-Loaded Pressure Regulator

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.482464 ◽

1997 ◽

Vol 122 (2) ◽

pp. 290-297 ◽

Cited By ~ 9

Author(s):

A. Nabi ◽

E. Wacholder ◽

J. Dayan

Keyword(s):

Physical Model ◽

Lumped Parameter Model ◽

Pressure Regulator ◽

Flow Rates ◽

First Order ◽

Runge Kutta Method ◽

Lumped Parameter ◽

Wide Range ◽

Fast Acting ◽

Good Agreement

A generalized physical model describing dynamic behavior of a fast-acting, dome-loaded, gas pressure regulator was developed. The regulator is designed to respond quickly to command changes, and to operate over a wide range of flow rates and pressures. The analytical lumped-parameter model developed consists of a set of nonlinear, first-order, ordinary differential equations with respect to time, accounting for mass and energy conservation at regulator outlet, command dome and internal feedback compartments. It also accounts for the equation-of-motion for the poppet and the control piston-assembly. The numerical solution, based on a Runge–Kutta method, is amenable to an extensive parametric study of regulator performance, and serves as a useful analytical tool for designing new pressure regulators. Several tests were performed on a fast-acting regulator to verify the physical model. Good agreement between predictions and measurements was obtained. The effect of several parameters, geometrical and operational, on regulator performance was studied. [S0022-0434(00)00402-0]

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First-Order Pump Surge Behavior

Journal of Fluids Engineering ◽

10.1115/1.3448708 ◽

1978 ◽

Vol 100 (4) ◽

pp. 459-466 ◽

Cited By ~ 8

Author(s):

P. H. Rothe ◽

P. W. Runstadler

Keyword(s):

Analytical Model ◽

Flow Instability ◽

Lumped Parameter Model ◽

Piping System ◽

Unstable Flow ◽

First Order ◽

Lumped Parameter ◽

Quantitative Basis ◽

Flow Oscillations ◽

Good Agreement

This paper presents the results of an empirical study undertaken to assess the appropriateness and applicability of a simple, analytical model of pump-piping system flow instability. The analysis is used to describe behavior actually observed in a well defined, simple, pump-piping system. The frequency and amplitude of the flow oscillations observed during pump surge and the range of the pump-piping system characteristic parameters for which unstable flow oscillations occurred are in good agreement with the behavior predicted by the analysis. The results of this work provide a quantitative basis for investigating modifications to the lumped-parameter model in order to make it also appropriate for the analysis of more complex pump or compressor system. Although the analytical model displayed here is not new, a direct comparison of model predictions against similar measurements of first-order pump surge has not been published prior to this work.

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