Vibration of electrostatically actuated microbeam by means of homotopy perturbation method

Bayat, Mahmoud; Pakar, Iman; Emadi, Alireza

doi:10.12989/sem.2013.48.6.823

Cited by 22 publications

(15 citation statements)

References 18 publications

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“…On one side, semi-analytic methods like: generalized homotopy method (GHM) (Vazquez-Leal 2013 ), homotopy perturbation method (Araghi and Rezapour 2011 ; Araghi and Sotoodeh 2012 ; Bayat et al 2013 , 2014 ; Biazar and Eslami 2011 ; Biazar and Ghanbari 2012 ; Filobello-Nino et al 2012a , 2012b ; He 1999 , 2009 ; Khan et al 2012a , 2012b ; Vazquez-Leal 2012 ; Vazquez-Leal et al 2012a , 2012b , 2012d ), homotopy analysis method (Hassana and El-Tawil 2011 ; He 2004 ; Rashidi et al 2012a , 2012b ; Tan and Abbasbandy 2008 ), variational iteration method (Abbasbandy 2007 ; Chang 2010 ; Khan et al 2012c ), among others (Khan et al 2012d ), need an initial approximation for the sought solutions and the calculus of one or several adjustment parameters. If the initial approximation is properly chosen, the results can be highly accurate, nonetheless, there is not a general method to choose such initial approximation.…”

Section: Numerical Simulation and Discussionmentioning

confidence: 99%

Direct application of Padé approximant for solving nonlinear differential equations

et al. 2014

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This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant.AMS Subject Classification34L30

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Section: Numerical Simulation and Discussionmentioning

confidence: 99%

Direct application of Padé approximant for solving nonlinear differential equations

et al. 2014

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“…From the perspective of analytical methods for a nonlinear vibration system, the HBM which outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude is widely used in the analysis of nonlinear systems (Krack and Gross, 2019). However, it should be noted that other analytical methods can be used to solve highly nonlinear vibration problems successfully when frictional terms, large-amplitude excitation, centrifugal terms, and other typical nonlinear elements are taken into consideration (Bayat et al, 2010, 2013). The base of the dynamic system is excited by an external displacement excitation Z=Z0 cos ωt.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Theoretical and experimental studies of a novel nested oscillator with a high-damping characteristic

Liu¹,

Xiao²,

Zhao³

et al. 2020

Journal of Vibration and Control

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Stiffness and damping of a structure usually show the opposite change so that the resonant frequency and the static load bearing capacity of a mechanical system often exhibit contradiction. To solve this dilemma, a novel high-damping oscillator which is constructed by a nested diamond structure with the purpose of enhancing the damping property is proposed in this study without reducing the overall systematic stiffness. The mathematical model and geometrical relationships are established at first. And then, the steady-state solutions under base excitation are derived by using the harmonic balance method and further verified by numerical simulation. In addition, the effects of some design parameters on the equivalent damping ratio for the high-damping oscillator are studied to reveal the nonlinear characteristic. Besides, the natural frequency of the nonlinear oscillator is also presented and investigated. By using the displacement transmissibility and comparing with the traditional linear isolator with the same overall stiffness, the vibration suppression performance of the high-damping oscillator is addressed. The obtained calculating results demonstrate that the vibration control performance of the high-damping oscillator outperforms the linear counterpart around resonant frequency. Moreover, the influences of systematic parameters of the high-damping oscillator for the base excitation case on the vibration transmissibility are also discussed, respectively. Finally, an experimental campaign is conducted on an in-house-built test rig to corroborate the accuracy of the analytical solutions of the high-damping oscillation system. The results discussed in this study provide a useful guideline, which can help to design this class of high-damping oscillation system.

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“…The analytic and numerical solutions of three different problems are obtained in [15] using HPT and RKM respectively. Another analytic method called Energy Balance Method (EBM) is used to compare the attained results with each other.…”

Section: Introductionmentioning

confidence: 99%

The Vibrational Motion of a Dynamical System Using Homotopy Perturbation Technique

Amer¹,

Galal²,

Elnaggar³

2020

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Vibration of electrostatically actuated microbeam by means of homotopy perturbation method

Cited by 22 publications

References 18 publications

Direct application of Padé approximant for solving nonlinear differential equations

Direct application of Padé approximant for solving nonlinear differential equations

Theoretical and experimental studies of a novel nested oscillator with a high-damping characteristic

The Vibrational Motion of a Dynamical System Using Homotopy Perturbation Technique

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