A new analytic solution for buckling of doubly clamped nano-actuators with integro differential governing equation using Duan–Rach Adomian decomposition method

Ghalambaz, Mohammad; Ghalambaz, Mehdi; Edalatifar, Mohammad

doi:10.1016/j.apm.2016.03.016

Cited by 8 publications

(11 citation statements)

References 24 publications

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“…The obtained solutions can be compared to those of Ref. [1] and references therein. All approximate solutions reported here are obtained, in few seconds by MATLAB software programme, and therefore the method is highly robust.…”

Section: Numerical Experiments and Comparisonmentioning

confidence: 92%

“…Consider the following generalized form of the governing problem of a nano-actuator beam, augmented to boundary conditions, and containing the influence of axial loads and other various kind of nonlinear forces [1]:…”

Section: Preliminaries and Mathematical Formulationmentioning

confidence: 99%

“…The actuator contains a beam * corresponding author; e-mail: shivanian@sci.ikiu.ac.ir hung over a substratum in nano/micro mechanical actuators, or in nano/micro mechanical sensors. Electrostatic field is induced by imposing a voltage difference among the substrate and beam, and therefore, the electrostatic forces captivate the beam into the substrate [1]. Furthermore, beam and substrate play the role of a condenser, where the movement of the beam could be discerned by the capacitive alteration as a signal [2].…”

Section: Preliminaries and Mathematical Formulationmentioning

confidence: 99%

“…The BVP (1), (2) in the general form has been analyzed by a modification of Adomian decomposition method (ADM), more specifically Duan-Rach Adomian decomposition method [1]. ADM and its modifications are some kinds of semi-analytical methods [18][19][20].…”

Section: Preliminaries and Mathematical Formulationmentioning

confidence: 99%

“…In current section, we present the results obtained for some case studies, which have been adopted from Ref. [1], using proposed method described in the previous sections. In these examples, the number of total nodal points covering [−1, 1], N = 20, and they are regularly distributed.…”

Section: Numerical Experiments and Comparisonmentioning

confidence: 99%

See 4 more Smart Citations

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

Shivanian

Ansari

2019

Acta Phys. Pol. A

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In current work, a novel intelligent computational technique is adopted for searching the behaviour of the problem of buckling of nano-actuators in the presence of various nonlinear forces. In order to accomplish this aim, the governing integro-differential equation in general form is taken into account for nano-actuators, which contains various nonlinear forces as well. This generalized form for the nano-actuators is in fact a non-linear fourth-order Fredholm integro-differential boundary value problem. The boundary value problem is transformed into an equivalent problem whose boundary conditions are such that it is convenient to apply reformed version of the Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an uninspected error which is minimized through adjusting weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem. This numerical technique enables us to overcome all kind of nonlinearities in the mentioned boundary value problem, and then to obtain an accurate solution. Thus, it can expedite the design of nano-actuators.

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Section: Numerical Experiments and Comparisonmentioning

confidence: 92%

Section: Preliminaries and Mathematical Formulationmentioning

confidence: 99%

Section: Preliminaries and Mathematical Formulationmentioning

confidence: 99%

Section: Preliminaries and Mathematical Formulationmentioning

confidence: 99%

Section: Numerical Experiments and Comparisonmentioning

confidence: 99%

See 3 more Smart Citations

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

Shivanian

Ansari

2019

Acta Phys. Pol. A

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A Numerical Investigation of the Buckling of Doubly Clamped Nano-Actuators Governed by an Integro-Differential Equation

Abdelrahman

Khuri²,

Louhichi³

2022

J Math Sci

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In this article, a fixed point iterative scheme involving the Green's function is applied to reach a solution for the buckling of nano-actuators under nonlinear forces. Our solution is convergent. The nano-actuators problem under consideration is governed by a general type equation that contains nonlinear forces and integro-differential terms. The equation, we adopted and which governs the nano-actuators, is a nonlinear integro-differential BVP of the fourth order. Our scheme enjoys important features such as high accuracy, robustness and fast convergence. Numerical tests are performed and compared with other results that exist in the current literature.

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Parameter-splitting perturbation method for the improved solutions to strongly nonlinear systems

2019

Nonlinear Dyn

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A new analytic solution for buckling of doubly clamped nano-actuators with integro differential governing equation using Duan–Rach Adomian decomposition method

Cited by 8 publications

References 24 publications

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

Buckling of Doubly Clamped Nano-Actuators in General Form through Optimized Chebyshev Polynomials with Interior Point Algorithm

A Numerical Investigation of the Buckling of Doubly Clamped Nano-Actuators Governed by an Integro-Differential Equation

Parameter-splitting perturbation method for the improved solutions to strongly nonlinear systems

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