The fastest insight into the large amplitude vibration of a string

Qie, Na; Houa, Wei-Fan; He, Ji‐Huan

doi:10.31181/rme200102001q

Cited by 82 publications

(61 citation statements)

References 14 publications

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“…In order to verify our above results, this section introduces briefly He's frequency formulation [38,39]. Considering a nonlinear oscillator in the form…”

Section: He's Frequency Formulationmentioning

confidence: 78%

Periodic Property and Instability of a Rotating Pendulum System

Amer

Elnaggar

et al. 2021

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The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.

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“…In order to verify our above results, this section introduces briefly He's frequency formulation [38,39]. Considering a nonlinear oscillator in the form…”

Section: He's Frequency Formulationmentioning

confidence: 78%

Periodic Property and Instability of a Rotating Pendulum System

Amer

Elnaggar

et al. 2021

Axioms

Self Cite

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“…[4][5][6] However, the analysis of beam structure requires a certain mechanical foundation. [7][8][9][10][11] Since many people are not professional, they often study it only from the perspective of equations or circuits and cannot clearly understand its mechanism. It is necessary to transform it into a popular and concise model.…”

Section: Introductionmentioning

confidence: 99%

Model modification and feature study of Duffing oscillator

Chen

Cao

De-zhi

2021

Journal of Low Frequency Noise, Vibration and Active Control

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With the development of chaos theory, Duffing oscillator has been extensively studied in many fields, especially in electronic signal processing. As a nonlinear oscillator, Duffing oscillator is more complicated in terms of equations or circuit analysis. In order to facilitate the analysis of its characteristics, the study analyzes the circuit from the perspective of vibrational science and energetics. The classic Holmes-Duffing model is first modified to make it more popular and concise, and then the model feasibility is confirmed by a series of rigorous derivations. According to experiments, the influence of driving force amplitude, frequency, and initial value on the system is finally explained by the basic theories of physics. Through this work, people can understand the mechanisms and characteristics of Duffing oscillator more intuitively and comprehensively. It provides a new idea for the study of Duffing oscillators and more.

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“…There are many methods available for obtaining the frequency property of equation (1.1) such as the incremental harmonic balanced method, 6 variational iteration method, 8 Fourier series and Stokes' transformation, 9 homotopy perturbation method, 10,11 and He's frequency formulation. 12 In this study, we will use a new method called the Hamiltonian-based method to determine the frequency property. The overall structure of this study is arranged as follows.…”

Section: Introductionmentioning

confidence: 99%

Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method

Wang

2021

Journal of Low Frequency Noise, Vibration and Active Control

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This article mainly studies the vibration of the carbon nanotubes embedded in elastic medium. A new novel method called the Hamiltonian-based method is applied to determine the frequency property of the nonlinear vibration. Finally, the effectiveness and reliability of the proposed method is verified through the numerical results. The obtained results in this work are expected to be helpful for the study of the nonlinear vibration.

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The fastest insight into the large amplitude vibration of a string

Cited by 82 publications

References 14 publications

Periodic Property and Instability of a Rotating Pendulum System

Periodic Property and Instability of a Rotating Pendulum System

Model modification and feature study of Duffing oscillator

Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method

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