APPLICATION OF HE’S FREQUENCY FORMULA TO NONLINEAR OSCILLATORS WITH GENERALIZED INITIAL CONDITIONS

Jian-Gang Zhang, Qing-Ru Song, Jian-Qiang Zhang, Fang Wang

DOI Number
https://doi.org/10.22190/FUME230909047Z
First page
701
Last page
712

Abstract


This paper focuses on the vibration periodic property of Duffing oscillator with generalized initial conditions. Firstly, the undamped case is solved by Ji-Huan He’s frequency formulation; Secondly, the formulation is extended to the damped case. Numerical verification shows that the frequency formulation is mathematically simple and physically insightful and practically applicable. This paper paves a novel way for engineers to use the formulation to study nonlinear vibration system with ease and reliability.

Keywords

Duffing equation, He’s frequency formulation, Ancient Chinese mathematics, Residual equation, Nonlinear vibrations

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References


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DOI: https://doi.org/10.22190/FUME230909047Z

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ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

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