Dynamic pull-down theory for the Toda oscillator

Feng, Guang-Qing

doi:10.1142/s0217979224502928

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…Recently scientists worldwide have intensified efforts to insight into some striking oscillation phenomena arising in even nonlinearities, especially the pull-down instability, 1,2 which offers striking benefits in designing shallow arches, ship rolls, and electrical circuits to improve operation reliability and extend the lifetime of a nonlinear vibration system, but much work is still needed to investigate its main factors affecting the pull-down instability.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-breaking and pull-down motion for the Helmholtz–Duffing oscillator

Niu,

He,

Alsolami

2023

Journal of Low Frequency Noise, Vibration and Active Control

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An accurate frequency of the Helmholtz–Duffing oscillator is obtained by a sophisticated modification of He’s frequency formulation. The pull-down instability existing in the symmetric breaking phenomenon is a newly discovered dynamic motion for oscillators with even nonlinearities. A criterion for predicting the asymmetrical amplitude motion and the pull-down instability is built by measuring the amplitude change. The good matching performance between the analytic results and numerical ones indicates that the criterion offers a starting point for future research into the pull-down phenomenon, and opens a new path for studying more complex nonlinear oscillators with even nonlinearities.

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Section: Introductionmentioning

confidence: 99%

Symmetry-breaking and pull-down motion for the Helmholtz–Duffing oscillator

Niu,

He,

Alsolami

2023

Journal of Low Frequency Noise, Vibration and Active Control

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“…Guojuan et al 38 established the straightforward technique for solving nonlinear oscillator problems with the application of fractal space. Feng 39 investigated the pull-down theory of Toda oscillator as its pseudo-periodic property is also considered for studying the pull-down instability. Wang et al 40 gave the idea that the unique hierarchical anatomy of polar hairs with golden ratio fractal proportions endows the organism with exceptional cool protection.…”

Section: Introductionmentioning

confidence: 99%

An application to formable transform: Novel numerical approach to study the nonlinear oscillator

Basit,

Tahir,

Shah

et al. 2023

Journal of Low Frequency Noise, Vibration and Active Control

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Numerical methods in the area of nonlinear systems are extensively implemented for computing their approximate solutions because these systems are very difficult to tackle analytically. There are various numerical techniques available in the literature to find the solutions of nonlinear oscillators. Variational iteration method (VIM) is one of these approaches which is convenient to implement for these kinds of problems. In this work, our study aims to identify the numerical solution of nonlinear oscillator by making use of variational iteration method associated with Formable transformation. For the smooth utilization of this approach, we have to formulate the Lagrange multiplier through variational theory. Furthermore, we develop a new unified iterative scheme for the correction functional of VIM, considering the Formable transformation. Several new schemes of correction functional can be deduced from the newly proposed method considering the duality relation of Formable transform. In support of our primary finding, we discuss numerical example as application. A number of Physical applications of nonlinear oscillators are available in the field of vibrations and oscillations but in recent times nonlinear oscillators are used to describe complicated systems or to address mechanical, electrical, and other engineering phenomenon.

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Fractal Pull-in Motion of Electrostatic Mems Resonators by the Variational Iteration Method

FENG,

ZHANG,

TANG

2023

Fractals

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The dynamic pull-in instability of a microstructure is a vast research field and its analysis is of great significance for ensuring the effective operation and reliability of micro-electromechanical systems (MEMS). A fractal modification for the traditional MEMS system is suggested to be closer to the real state as a practical application in the air with impurities or humidity. In this paper, we establish a fractal model for a class of electrostatically driven microstructure resonant sensors and find the phenomenon of pull-in instability caused by DC bias voltage and AC excitation voltage. The variational iteration method has been extended to obtain approximate analytical solutions and the pull-in threshold value for the fractal MEMS system. The result obtained from this method shows good agreement with the numerical solution. The simple and efficient operability is demonstrated through theoretical analysis and results comparisons.

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Dynamic pull-down theory for the Toda oscillator

Cited by 3 publications

References 29 publications

Symmetry-breaking and pull-down motion for the Helmholtz–Duffing oscillator

Symmetry-breaking and pull-down motion for the Helmholtz–Duffing oscillator

An application to formable transform: Novel numerical approach to study the nonlinear oscillator

Fractal Pull-in Motion of Electrostatic Mems Resonators by the Variational Iteration Method

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