Dynamic Analysis of Nonlinear Oscillator Equation Arising in Double-Sided Driven Clamped Microbeam-Based Electromechanical Resonator

Khan, Yasir; Akbarzade, M.

doi:10.5560/zna.2012-0043

Cited by 21 publications

(10 citation statements)

References 10 publications

(21 reference statements)

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“…The perturbation method is not applied when a small parameter is not present in a nonlinear problem. There are many methods (Amore and Aranda, 2005;Cheung et al, 1991;He, 2002;Khan et al, 2012a;Khan and Mirzabeigy, 2014;Saha and Patra, 2013;Yazdi et al, 2010;Khan et al, 2011;Yildirim et al, 2011a;Yildirim et al, 2011b;Khan and Akbarzade, 2012;Khan et al, 2012b;Akbarzade and Khan, 2012;Yildirim et al, 2012;Khan et al, 2013) which are used to solve strongly nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

An analytical approximate technique to investigate a finite extensibility nonlinear oscillator

Razzak

2017

Journal of the Association of Arab Universities for Basic and A

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In this paper, an analytical approximate technique based on modified harmonic balance method is presented to study about the dynamics of a finite extensibility nonlinear oscillator described by Febbo (2011) and Bele´ndez et al. (2012). Generally, a second-order approximation is only considered in this paper. In the proposed method, the approximate period of oscillations and the corresponding periodic solutions are determined, which are valid for both range of amplitudes 0 < A 0.9 and 0.9 < A < 1 of oscillation. The approximate periods obtained in this paper are compared with numerical result (considered to be exact) and other existing results. Firstly, the results are obtained for the amplitude 0 < A 0.9 and show that the present method gives high accuracy than other existing results. Moreover, the results are also obtained for the rest of the amplitude 0.9 < A < 1. The relative error measure in this paper is 0.03% for A = 0.9 while the relative errors obtained by Febbo (2011) and Bele´ndez et al. (2012), were 3.53% and 0.60% respectively. On the other hand, Belendez et al. (2012) did not obtain approximate period for 0.9 < A < 1. In this article, the approximate periods have been determined in the range of value 0.9 < A < 1 and they have provided better results than the existing result of Febbo (2011).

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Section: Introductionmentioning

confidence: 99%

An analytical approximate technique to investigate a finite extensibility nonlinear oscillator

Razzak

2017

Journal of the Association of Arab Universities for Basic and A

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“…Nonlinear ordinary differential equations are frequently used to model a wide class of problems in many areas of scientific fields: chemical reactions, spring-mass systems bending of beams, resistor-capacitor-inductance circuits, pendulums, the motion of a rotating mass around another body, and so forth [1,2]. Also, nonlinear equations which can be modeled by the oscillator equations are of crucial importance in all areas of engineering sciences [3][4][5][6][7]. Thus, methods of solution for these equations are of great importance to engineers and scientists.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

Bülbül

Sezer

2013

Journal of Applied Mathematics

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We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems.

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“…Fu et al [16] employed the energy balance approach for modeling the oscillation of double-sided microbridges. Khan and Akbarzade employed several analytical methods to study a nonlinear oscillator equation arising in the driven, double-sided, electromechanical resonator [19]. More useful information about double-sided NEMS can be found in Refs.…”

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confidence: 99%

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

Keivani

Gheisari

Kanani

et al. 2016

J Braz. Soc. Mech. Sci. Eng.

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Beam-type micro/nano-electromechanical systems (MEMS/NEMS) are increasingly used in several branches of engineering and science, i.e. mechanics, chemistry, optics, biology, photonics, electronics, etc. Modeling of the electromechanical stability of NEMS is crucial for the reliable design, fabrication and operation of these devices. Many researchers have investigated the pull-in instability of NEMS devices [1-5]. Although there are many articles focused on modeling the pull-in instability of the conventional NEMS with a simple beam-type electrode [6, 7], few efforts have been made for modeling this phenomenon in less conventional systems such as the U-shaped and double-sided NEMS. In this regard, the present research is devoted to the theoretical study of the electromechanical performance of U-shaped and double-sided cantilever NEMS sensors. The U-shaped configuration consists of two parallel cantilever micro/nano-beams with a rigid plate attached to their free ends. Recently, several studies have investigated the limitations and potential of the U-shaped MEMS/ NEMS as sensors [8], actuators [9], and switches [8-11]. Qian et al. [10] developed a U-shaped nanoelectromechanical switch consisting of a capacitive plate supported by two silicon nanowires. They presented several remarkable advantages of the U-shaped switch such as decreasing the Abstract 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 Communicated by Eduardo Alberto Fancello.

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Dynamic Analysis of Nonlinear Oscillator Equation Arising in Double-Sided Driven Clamped Microbeam-Based Electromechanical Resonator

Cited by 21 publications

References 10 publications

An analytical approximate technique to investigate a finite extensibility nonlinear oscillator

An analytical approximate technique to investigate a finite extensibility nonlinear oscillator

Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

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

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