A convenient computational form for the Adomian polynomials

AbstractRecent important generalizations by G. Adomian (“Stochastic Systems”, Academic Press 1983) have extended the scope of his decomposition method for nonlinear stochastic operator equations (see also iterative method, inverse operator method, symmetrized method, or stochastic Green's function method) very considerably so that they are now applicable to differential, partial differential, delay, and coupled equations which may be strongly nonlinear and/or strongly stochastic (or linear or deterministic as subcases). Thus, for equations modeling physical problems, solutions are obtained rapidly, easily, and accurately. The methodology involves an analytic parametrization in which certain polynomials An, dependent on the nonlinearity, are derived. This paper establishes simple symmetry rules which yield Adomian's polynomials quickly to high orders

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

On Solutions of Boundary Value Problem for Fourth-Order Beam Equations

In this paper, we consider the fourth-order linear differential equation u(4) +f(x)u = g(x) subject to the mixed boundary conditions u(0) = u(1) = u‘‘(0) = u‘‘(1) = 0. We first establish sufficient conditions on f(x) that guarantee a unique solution of this problem in the Hilbert space by using an a priori estimate. Accurate analytic solutions in series forms are obtained by a new variation of the Duan-Rach modified Adomian decomposition method (DRMA), and then extend this approach to some boundary value problems of fourth-order nonlinear beam equations. Also, a comparison of the two approximate solutions by the ADM with the Green function approach is presented

Modeling the pull-in instability of the CNT-based probe/actuator under the Coulomb force and the van der Waals attraction

Carbon nano-tube (CNT) is applied to fabricate nano-probes, nano-switches, nano-sensors and nano-actuators. In this paper, a continuum model is employed to obtain the nonlinear constitutive equation and pull-in instability of CNT-based probe/actuators, which includes the effect of electrostatic interaction and intermolecular van der Waals (vdW) forces. The modified Adomian decomposition (MAD) method is applied to solve the nonlinear governing equation of the CNT-based actuator. Furthermore a simple and useful lumped parameter model was developed to investigate trends for various pull-in parameters. The influence of the vdW force and the geometrical dimensionless parameter on the pull-in deflection and voltage of the system is investigated. The obtained results are compared with those available in the literature as well as numerical solutions. The results demonstrate that our developed continuum based model is in good agreement with experimental results

Effect of the centrifugal force on the electromechanical instability of U-shaped and double-sided sensors made of cylindrical nanowires

The U-shaped and double-sided nanostructures are promising for developing miniature angular speed sensors. While the electromechanical instability of conventional beam-type nanostructures has been extensively addressed in the literature, few researchers have investigated this phenomenon in the double-sided and U-shaped sensors. In this regard, the present work demonstrates the effect of the centrifugal force on the pull-in performance of the double-sided and U-shaped sensors fabricated from cylindrical nanowire and operated in the van der Waals (vdW) regime. Based on the modified couple stress theory, the size-dependent constitutive equations of the sensors are derived. The governing equations are solved by two different approaches, i.e. the analytic Duan–Adomian method and the numerical differential quadrature method. The influences of the vdW and centrifugal forces, geometric parameters and the size phenomenon on the pull-in parameters are demonstrated

Modeling the static response and pull-in instability of CNT nanotweezers under the Coulomb and van der Waals attractions

In this paper, the static response and pull-in instability of nanotweezers fabricated from carbon nanotubes (CNT) are theoretically investigated considering the effects of the Coulomb electrostatic and van der Waals molecular attractions. For this purpose, a nanoscale continuum model is employed to obtain the nonlinear constitutive equation of this nano-device. The van der Waals attraction is computed from the simplified Lennard-Jones potential. In order to solve the nonlinear constitutive equation of the nanotweezers, three different approaches, e.g. developing a lumped parameter model, applying the analytical modified Adomian decomposition (MAD) and using a commercial numerical integration routine, are employed. The obtained results are in good agreement with experimental measurements as reported in the literature. As a case study, we have investigated a freestanding nanotweezer and have determined the detachment length and minimum initial gap. Furthermore, range of dominancy of the molecular attraction has been discussed. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved