Homotopy Perturbation Method for Fractal Duffing Oscillator With Arbitrary Conditions

He, Ji‐Huan; Jiao, Man-Li; He, Chun‐Hui

doi:10.1142/s0218348x22501651

Cited by 42 publications

(21 citation statements)

References 46 publications

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“…This paper adopts simple mathematics concepts to deal with an unsolved problem in MEMS systems with great success. The essence of mathematics is to make the complicated pull-in instability much simpler,if an even higher accuracy is needed to predict the pull-in instability, the homotopy perturbation method 58,59 has to be used.…”

Section: Discussionmentioning

confidence: 99%

A mathematical control for the pseudo-pull-in stability arising in a micro-electromechanical system

Yang

2022

Journal of Low Frequency Noise, Vibration and Active Control

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A micro-electromechanical system’s reliability depends strongly upon its periodic motion; however, the pull-in instability might arise when the applied voltage is high enough. No criterion is available to judge the reliability condition in a simple but effective way. This paper tackles this challenge mathematically. The sufficient conditions for the periodic motion and the pull-in instability of a micro-electromechanical system with a current-carrying conductor are established, respectively. There is an uncertain area, where the system behaves firstly periodic motion, and after a certain number of cycles, the pull-in instability occurs. This new phenomenon is called as a pseudo-pull-in stability (pseudo-periodic motion); its main factors affecting the pseudo-periodic motion are elucidated.

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Section: Discussionmentioning

confidence: 99%

A mathematical control for the pseudo-pull-in stability arising in a micro-electromechanical system

Yang

2022

Journal of Low Frequency Noise, Vibration and Active Control

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“…The drawn curves of Figure 2 are calculated when að¼ 0:5; 1; 2Þ and reveals the temporal history of the solutions (31). These curves behave progressive waves with an increasing of the amplitude during the investigated time interval.…”

Section: Methods Of Solutionmentioning

confidence: 97%

Dynamical analysis of a vertical excited pendulum using He’s perturbation method

Galal

Amer

et al. 2023

Journal of Low Frequency Noise, Vibration and Active Control

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The current paper investigates the nonlinear dynamics of an excited pendulum by a crank-shaft-slider mechanism (CSSM), in which it is restricted to move vertically. He’s method of homotopy is employed to obtain the analytical solution of the governing differential equation. The numerical solution of this equation is obtained using the fourth-order Runge-Kutta method (RKM). The comparison between both solutions demonstrates a high level of consistency, which confirms the precision of the gained analytic solution. The graphical representations of these solutions are presented to reveal the influence of various parameters on the investigated motion.

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“…The fractal derivative can be used to model various discontinuous problems, for example, shallow water waves along an unsmooth boundary, 57 the fractal modification of Chen-Lee-Liu equation, 58 the fractal boundary layer theory, 59 fractal Duffing equation, 60 heat prevention through porous materials, 61,62 and a cement mortar's fluidity. 63 Equation ( 8) is a microelectromechanical system in the fractal space investigated by Tian et al 7,23 The air can be viewed as a porous medium, and the fractal dimension γ indicates the distribution of air.…”

Section: Fractal Mathematical Modelingmentioning

confidence: 99%

Dynamic behaviors for the graphene nano/microelectromechanical system in a fractal space

2023

Journal of Low Frequency Noise, Vibration and Active Control

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The microelectromechanical devices have triggered rocketing interest in various advanced technologies, that is, sensors, material science, and energy harvesting, and now the devices tend to a nanoscale size, making the technology much more attractive in both academic and industrial communities. This paper takes a graphene nano/microelectromechanical system as an example to study its dynamical property, which is the foundation for the optimal design and reliable operation. As the system is inextricably complex with singularity and zero conditions in a fractal space, the iteration perturbation method is used to obtain the periodic solution of the system. The results show clearly the low-frequency property of the system and pull-in instability; furthermore, the fractal dimension affects greatly the system’s dynamical property.

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Homotopy Perturbation Method for Fractal Duffing Oscillator With Arbitrary Conditions

Cited by 42 publications

References 46 publications

A mathematical control for the pseudo-pull-in stability arising in a micro-electromechanical system

A mathematical control for the pseudo-pull-in stability arising in a micro-electromechanical system

Dynamical analysis of a vertical excited pendulum using He’s perturbation method

Dynamic behaviors for the graphene nano/microelectromechanical system in a fractal space

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