Automatic computation and solution of generalized harmonic balance equations

•Automatic generation of poly-harmonic balance equations for a broad class of systems.•Automatic solution of harmonic balance equations using continuation methods.•Automatic generation of Jacobian for use with continuation method solution.•Smart initialization for fast numeric solution validation.•E...

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Bibliographic Details
Published in:Mechanical systems and signal processing 2018-02, Vol.101, p.309-319
Main Authors: Peyton Jones, J.C., Yaser, K.S.A., Stevenson, J.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Continuation methods
Damping
Difference equations
Differential equations
Harmonic balance
Harmonic response
Mathematical analysis
Nonlinear damper
Nonlinear equations
Nonlinear response
Numerical continuation
Numerical methods
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Summary:•Automatic generation of poly-harmonic balance equations for a broad class of systems.•Automatic solution of harmonic balance equations using continuation methods.•Automatic generation of Jacobian for use with continuation method solution.•Smart initialization for fast numeric solution validation.•Example illustrates previously unreported behavior of a nonlinear automotive damper. Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.
ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2017.08.033