Analytical approximations to nonlinear oscillation of nanoelectro-mechanical resonators

Ismail, Gamal; Abul-Ez, Mahmoud; Farea, N.M.; Saad, Nasser

doi:10.1140/epjp/i2019-12399-2

Cited by 15 publications

(5 citation statements)

References 24 publications

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“…The error analysis of Figure 2b showed that the nanobeam undergoes a linear to weakly nonlinear response for 0 < < 0.35, while a strong nonlinear response was predicted when > 0.475. Equations ( 8) was studied by Ghalambaz et al (2016) using the energy balance method (EBM) while Ismail et al (2019) used the global residue harmonic balance method (GRHBM). The EBM solution was simulated for = 0.01 while the GRHBM was applied for ≤ 0.50.…”

Section: Electrostatically-actuated Nanobeam With Weak Interacting Forcesmentioning

confidence: 99%

Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

Big‐Alabo¹

2021

jasem

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This article proposes a simple energy-based criterion developed to characterize four commonly identified responses, namely: linear, weakly nonlinear, moderately nonlinear and strongly nonlinear regimes. The response of the nonlinear simple pendulum was used for benchmarking the boundary conditions for each of the four response regimes and the test criterion was demonstrated using relevant examples. The test presented in this article is important for clarifying the obscurity surrounding the accuracy and range of validity of recent approximate analytical schemes used to investigate strong nonlinear oscillators. Furthermore, it is meant to create awareness of the need to develop more robust testing criteria. Keywords: strong nonlinear oscillation; periodic oscillation; approximate analytical solution

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Section: Electrostatically-actuated Nanobeam With Weak Interacting Forcesmentioning

confidence: 99%

Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

Big‐Alabo¹

2021

jasem

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“…Recently, several methods have been introduced and developed to obtain approximate solutions for (NDEs) due to their complexity and the difficulty of solving them through traditional perturbation techniques. For example, variational iteration method, 5 homotopy perturbation method, 6 max-min approach, [7][8][9] global residue harmonic balance method (GRHBM) for obtaining higher-order approximate solutions, [10][11][12] modified homotopy perturbation method, [13][14][15] energy balance method, 16,17 Hamiltonian approach, [18][19][20] iteration perturbation technique, 21 coupled homotopy-variational approach, [22][23][24] frequency-amplitude formulation, 25,26 multiple scales technique, 27 parameter expansion method, 28 averaging method, 29 iteration method, 30 and Laplace variational iteration method. 31 The harmonic balance method (HBM) is one of the main techniques for obtaining approximate analytical solutions to NDEs describing oscillatory systems.…”

Section: Introductionmentioning

confidence: 99%

Accurate analytical solution of the circular sector oscillation by the modified harmonic balance method

Farea

Zayed

Ismail

2022

Journal of Low Frequency Noise, Vibration and Active Control

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This paper aims to solve the nonlinear differential equation of the circular sector oscillator analytically via the modified harmonic balance method (MHBM). To assess the reliability and the precision of the present method, we have compared the obtained results with the global residue harmonic balance method, Akbari–Ganji’s method, and numerical Runge–Kutta method which reveals that the MHBM is more reliable than others methods.

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“…The main aim of this paper is to apply the global residue harmonic balance method introduced by Ju and Xue [34][35][36][37] and recently developed through [38][39][40][41][42], in order to obtain analytical approximate solutions to the large-amplitude vibration of electrostatically actuated micro-beams. The higher-order approximations (mainly second-order approximations) have been obtained for the large-amplitude vibration of electrostatically actuated micro-beams, providing the expected accuracy.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of Electrostatically Actuated Microbeam

et al. 2022

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In this paper, an analytical technique based on the global residue harmonic balance method (GRHBM) is applied in order to obtain higher-order approximate analytical solutions of an electrostatically actuated micro-beam. To illustrate the applicability and accuracy of the method, a high level of accuracy was established for the analytical solutions by comparing the results of the solutions with the numerical solution as well as the already published literature, such as the variational approach (VA), Hamiltonian approach (HA), energy balance method (EBM), and homotopy analysis method (HAM). It is shown that the GRHB method can be easily applied to nonlinear problems and provides solutions with a higher precision than existing methods. The obtained analytical expressions are employed to study the effects of axial force, initial gape, and electrostatic load on nonlinear frequency.

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Analytical approximations to nonlinear oscillation of nanoelectro-mechanical resonators

Cited by 15 publications

References 24 publications

Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

Accurate analytical solution of the circular sector oscillation by the modified harmonic balance method

Nonlinear Vibration of Electrostatically Actuated Microbeam

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