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Duan J.-S.,Zhaoqing University | Duan J.-S.,Shanghai Institute of Technology | Rach R.,316 South Maple Street
International Journal of Solids and Structures | Year: 2013

In this paper, the pull-in instability of a cantilever nano-actuator is considered incorporating the influence of surface effects, the fringing field and the Casimir attraction force. The instability parameters of the actuator are determined analytically under the assumption of a second-degree shape function for the beam during deflection. The influence of surface effects, the Casimir force and the fringing field effects on the pull-in parameters is investigated. The results demonstrate that the Casimir force decreases the pull-in deflection and voltage, the fringing field effects increase the pull-in deflection and decrease the pull-in voltage. The critical value of the surface effect parameter decreases monotonically from ηâ̂ -=4 as the Casimir force parameter increases. In the presence of the Casimir force, the surface effects decrease the pull-in deflection and voltage. For the MEMS model, which neglects the intermolecular forces, the surface effects do not influence the pull-in deflection, but decrease the pull-in voltage. For freestanding nanoactuators, the critical values of the tip deflection and the Casimir force parameter are obtained, and the surface effect parameter η decreases linearly with the critical value of the Casimir force parameter. © 2013 Elsevier Ltd. All rights reserved. Source


Duan J.-S.,Shanghai Institute of Technology | Rach R.,316 South Maple Street | Wazwaz A.-M.,Saint Xavier University
Match | Year: 2015

In this paper, we solve a system of two coupled nonlinear differential equations that determine the concentrations of oxygen and the carbon substrate. This system models the excess sludge production from water treatment plants. We will apply the Adomian decomposition method combined with the Duan{Rach modified recursion scheme for analytical approximations of oxygen and the carbon substrate. Our graphs of the objective error analysis demonstrate the rapid rate of convergence of our sequence of analytic approximate solutions without recourse to comparisons with an alternate solution technique. The Adomian decomposition method yields a rapidly convergent, easily computable and readily verifiable sequence of analytic approximations that are convenient for parametric simulations. Source


Farrokhabadi A.,Semnan University | Mokhtari J.,Islamic Azad University at Qom | Rach R.,316 South Maple Street | Abadyan M.,Islamic Azad University
International Journal of Modern Physics B | Year: 2015

The Casimir force can strongly interfere with the pull-in performance of ultra-small structures. The strength of the Casimir force is significantly affected by the geometries of interacting bodies. Previous investigators have exclusively studied the effect of the Casimir force on the electromechanical instability of nanostructures with planar geometries. However no work has yet considered this effect on the pull-in instability of systems with cylindrical geometries such as nanotweezers fabricated from nanotube/nanowires. In our present work, the influence of the Casimir attraction on the electrostatic response and pull-in instability of nanotweezers fabricated from cylindrical conductive nanowires/nanotubes is theoretically investigated. An asymptotic solution, based on scattering theory, is applied to consider the effect of vacuum fluctuations in the theoretical model. The Euler-Bernoulli beam model is employed, in conjunction with the size-dependent modified couple stress continuum theory, to derive the governing equation of the nanotweezers. The governing nonlinear equations are solved by two different approaches, i.e., the modified Adomian-Padé method (MAD-Padé) and a numerical solution. Various aspects of the problem, i.e., the variation of pull-in parameters, effect of geometry, coupling between the Casimir force and size dependency effects and comparison with the van der Waals force regime are discussed. © 2015 World Scientific Publishing Company. Source


Duan J.-S.,Shanghai Institute of Technology | Duan J.-S.,Huaqiao University | Rach R.,316 South Maple Street | Lin S.-M.,Huaqiao University
Mathematical Methods in the Applied Sciences | Year: 2013

We present a new approach to calculate analytic approximations of blow-up solutions and their critical blow-up times. Our approach applies the Adomian decomposition-Padé method to quickly and easily compute the critical blow-up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd. Source


Duan J.-S.,Shanghai Institute of Technology | Duan J.-S.,Huaqiao University | Rach R.,316 South Maple Street | Wazwaz A.-M.,Saint Xavier University
International Journal of Non-Linear Mechanics | Year: 2013

In this paper we solve the common nonlinear boundary value problems (BVPs) of cantilever-type micro-electromechanical system (MEMS) and nano-electromechanical system (NEMS) using the distributed parameter model by the Duan-Rach modified Adomian decomposition method (ADM). The nonlinear BVPs that are investigated include the cases of the single and double cantilever-type geometries under the influence of the intermolecular van der Waals force and the quantum Casimir force for appropriate distances of separation. The new Duan-Rach modified ADM transforms the nonlinear BVP consisting of a nonlinear differential equation subject to appropriate boundary conditions into an equivalent nonlinear Fredholm-Volterra integral equation before designing an efficient recursion scheme to compute approximate analytic solutions without resort to any undetermined coefficients. The new approach facilitates parametric analyses for such designs and the pull-in parameters can be estimated by combining with the Padé approximant. We also consider the accuracy and the rate of convergence for the solution approximants of the resulting Adomian decomposition series, which demonstrates an approximate exponential rate of convergence. Furthermore we show how to easily achieve an accelerated rate of convergence in the sequence of the Adomian approximate solutions by applying Duan's parametrized recursion scheme in computing the solution components. Finally we compare the Duan-Rach modified recursion scheme in the ADM with the method of undetermined coefficients in the ADM for solution of nonlinear BVPs to illustrate the advantages of our new approach over prior art. © 2012 Elsevier Ltd. Source

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