A variable-coefficient harmonic balance method for the prediction of quasi-periodic response in nonlinear systems

Mechanical Systems and Signal Processing

Volumn 64-65, Issue , 2015, Pages 233-244

  Zhou, B ^a   Thouverez, F ^b   Lenoir, D ^b  

^a NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS   (China)

^b ECOLE CENTRALE DE LYON   (France)

Author keywords

Harmonic balancing; Quasi periodic response; Time periodic Fourier coefficients

Indexed keywords

DYNAMICAL SYSTEMS; FORECASTING; FOURIER ANALYSIS; FOURIER SERIES; HARMONIC ANALYSIS; NONLINEAR DYNAMICAL SYSTEMS; NONLINEAR SYSTEMS; WAVEFORM ANALYSIS;

BASIC FREQUENCIES; FOURIER COEFFICIENTS; FREQUENCY COMPONENTS; HARMONIC BALANCE METHOD; HARMONIC BALANCING; QUASI-PERIODIC RESPONSE; TRIGONOMETRIC SERIES; VARIABLE COEFFICIENTS;

NUMERICAL METHODS;

EID: 84937974281     PISSN: 08883270     EISSN: 10961216     Source Type: Journal    
DOI: 10.1016/j.ymssp.2015.04.022     Document Type: Article

References (22)

1. R.R. Pusenjak, and M.M. Oblak Incremental harmonic balance method with multiple time variables for dynamical systems with cubic non-linearities Int. J. Numer. Methods Eng. 59 2004 255 292
2. M. Guskov, J.-J. Sinou, and F. Thouverez Multi-dimensional harmonic balance applied to rotor dynamics Mech. Res. Commun. 35 2008 537 545
3. Y.B. Kim, and S.T. Noah Quasi-periodic response and stability analysis for a non-linear Jeffcott rotor J. Sound Vib. 190 1996 239 253
4. O. Gendelman, Y. Starosvetsky, and M. Feldman Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. I: description of response regimes Nonlinear Dyn. 51 2008 31 46
5. A.H. Nayfeh, and B. Balachandran Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods 1995 Wiley New York
6. J. Jiang, and H. Ulbrich Stability analysis of sliding whirl in a nonlinear Jeffcott rotor with cross-coupling stiffness coefficients Nonlinear Dyn. 24 2001 269 283
7. J.P. Chávez, and M. Wiercigroch Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model Commun. Nonlinear Sci. Numer. Simul. 9 2013 2571 2580
8. L. Peletan, S. Baguet, M. Torkhani, and G. Jacquet-Richardet Quasi-periodic harmonic balance method for rubbing self-induced vibrations in rotor-stator dynamics Nonlinear Dyn. 78 2014 2501 2515
9. Y. Starosvetsky, and O.V. Gendelman Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning J. Sound Vib. 315 2008 746 765
10. G. Groll, and D. Ewins The harmonic balance method with arc length continuation in rotor/stator contact problem J. Sound Vib. 241 2001 223 233
11. V. Jaumouillé, J. Sinou, and B. Petitjean An adaptive harmonic balance method for predicting the nonlinear dynamic response of mechanical systems - application to bolted structures J. Sound Vib. 329 2010 4048 4067
12. T.M. Cameron, and J.H. Griffin An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems J. Appl. Mech. 56 1989 149 154
13. R. Seydel Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos 1995 Springer New York
14. B. Cochelin, and C. Vergez A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions J. Sound Vib. 324 2009 243 262
15. A. Grolet, and F. Thouverez On a new harmonic selection technique for harmonic balance method Mech. Syst. Signal Process. 30 2012 43 60
16. J.L. Summers Variable-coefficient harmonic balance for periodically forced nonlinear oscillators Nonlinear Dyn. 7 1995 11 35
17. F. Schilder, W. Vogt, S. Schreiber, and H.M. Osinga Fourier methods for quasi-periodic oscillations Int. J. Numer. Methods Eng. 67 2006 629 671
18. J.J. Sinou, F. Thouverez, and L. Jezequel Stability analysis and non-linear behaviour of structural systems using the complex non-linear modal analysis (CNLMA) Comput. Struct. 84 2006 1891 1905
19. A. Vakakis, and O. Gendelman Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems 2009 Springer Netherlands
20. O.V. Gendelman, D.V. Gorlov, L.I. Manevitch, and A.I. Musienko Dynamics of coupled linear and essentially nonlinear oscillators with substantially different masses J. Sound Vib. 286 2005 1 19
21. Y. Starosvetsky, and O. Gendelman Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: optimization of a nonlinear vibration absorber Nonlinear Dyn. 51 2008 47 57
22. E. Gourdon, N.A. Alexander, C.A. Taylor, C.H. Lamarque, and S. Pernot Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results J. Sound Vib. 300 2007 522 551