Open AccessA modified harmonic balance method for solving forced vibration problems with strong nonlinearity
Author(s) -
M. Wali Ullah,
M. Saifur Rahman,
Md Alim Uddin
Publication year - 2020
Publication title -
journal of low frequency noise, vibration and active control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.419
H-Index - 25
eISSN - 2048-4046
pISSN - 1461-3484
DOI - 10.1177/1461348420923433
Subject(s) - harmonic balance , nonlinear system , mathematics , vibration , algebraic equation , harmonic , set (abstract data type) , forcing (mathematics) , mathematical analysis , algebraic number , numerical analysis , control theory (sociology) , physics , computer science , artificial intelligence , programming language , control (management) , quantum mechanics
In this paper, a modified harmonic balance method is presented to solve nonlinear forced vibration problems. A set of nonlinear algebraic equations appears among the unknown coefficients of harmonic terms and the frequency of the forcing term. Usually a numerical method is used to solve them. In this article, a set of linear algebraic equations is solved together with a nonlinear one. The solution obtained by the proposed method has been compared to those obtained by variational and numerical methods. The results show good agreement with the results obtained by both methods mentioned above.
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