Residual calculation in He’s frequency–amplitude formulation

He’s frequency–amplitude formulation and its modifications mainly depend upon the residual calculation. A suitable choice of a residual leads to an ideal result. This paper discusses some effective methods for the residual calculation, and a modification with a free parameter is suggested to effecti...

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Bibliographic Details
Published inJournal of low frequency noise, vibration, and active control Vol. 40; no. 2; pp. 1040 - 1047
Main Authors Wu, Yue, Liu, Yan-Ping
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.06.2021
Sage Publications Ltd
SAGE Publishing
Subjects
Amplitudes
Mathematical analysis
Parameter estimation
Parameter modification
semi-inverse method
residual equation
Duffing oscillator
variational theory
He’s frequency–amplitude formulation
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Summary:He’s frequency–amplitude formulation and its modifications mainly depend upon the residual calculation. A suitable choice of a residual leads to an ideal result. This paper discusses some effective methods for the residual calculation, and a modification with a free parameter is suggested to effectively estimate the frequency of a nonlinear oscillator. Furthermore, an energy-based residual calculation is also suggested, which is deduced from a variational principle.
ISSN:1461-3484
2048-4046
DOI:10.1177/1461348420913662