Fast Fourier nonlinear vibration analysis

• Published in: Computational mechanics Vol. 22; no. 2; pp. 128 - 142
• Main Authors: CARDONA, A, LERUSSE, A, GERADIN, M
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer 01-08-1998; Berlin Springer Nature B.V
• Subjects: Algorithms; Exact sciences and technology; Fast Fourier transformations; Fourier transforms; Fundamental areas of phenomenology (including applications); Harmonic balance method; Nonlinear analysis; Physics; Solid mechanics; Stability analysis; Structural and continuum mechanics; Vibration analysis; Vibration control; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Predictor corrector method; Vibration; Fast Fourier transformation; Numerical method; Duffing equation; Non linear effect; Harmonic balance; Floquet method; Structural analysis
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s004660050347

We present an implementation of the multi-harmonic balance method (MHB) where intensive use of the Fast Fourier Transform algorithm (FFT) is made at all stages of calculations. The MHB method is not modified in essence, but computations are organized to obtain a very attractive method that can be applied systematically on general nonlinear vibration problems. The resulting nonlinear algebraic problem is solved by a particular implementation of a continuation method. Nonlinear vibration results are analyzed a posteriori by a Floquet method to determine their stability. The technique is applied on a series of problems of different nature, demonstrating the robustness and flexibility of the approach.