A harmonic-based method for computing the stability of periodic solutions of dynamical systems;Une méthode fréquentielle pour le calcul de stabilité des solutions périodiques des systèmes dynamiques

Comptes Rendus - Mecanique

Volumn 338, Issue 9, 2010, Pages 510-517

  Lazarus, Arnaud ^a   Thomas, Olivier ^a  

^a University of Paris Cité   (France)

Author keywords

Continuation procedure; Dynamical systems; Harmonic balance method; Hill's method; Stability

Indexed keywords

EIGENVALUE; HARMONIC ANALYSIS; NUMERICAL METHOD; STABILITY ANALYSIS;

EID: 77956647722     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crme.2010.07.020     Document Type: Article

References (18)

1. Nayfeh A.H., Balachandran B. Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods 1995, John Wiley & Sons, Inc.
2. Peeters M., Viguié R., Sérandour G., Kerschen G., Golinval J.-C. Nonlinear normal modes. Part II: Toward a practical computation using numerical continuation techniques. Mechanical Systems and Signal Processing 2009, 23:195-216.
3. Hill G.W. On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon. Acta Mathematica 1886, 8(1):1-36.
4. Killingbeck J. On the Hill determinant method. Journal of Physics A: Mathematical and General 1986, 19:2903-2906.
5. Deconinck B., Kutz J.N. Computing spectra of linear operators using the Floquet-Fourier-Hill method. Journal of Computational Physics 2006, 219:296-321.
6. Bonani F., Gilli M. Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 1999, 46:881-890.
7. Villa C., Sinou J.-J., Thouverez F. Stability and vibration analysis of a complex flexible rotor bearing system. Communications in Nonlinear Science and Numerical Simulation 2008, 13:804-821.
8. A. Lazarus, D. Combescure, B. Prabel, A 3D finite element model for the vibration analysis of asymmetric rotating machines, Journal of Sound and Vibration, doi:10.1016/j.jsv.2010.03.029.
9. Cochelin B., Vergez C. A high order purely-based harmonic balance formulation for continuation of periodic solutions. Journal of Sound and Vibration 2009, 324:243-262.
10. Floquet G. Sur la théorie des équations différentielles. Annales Scientifiques de l'École Normale Supérieure 1879, 8:3-132.
11. Hartman P. Ordinary Differential Equations 2002, Society for Industrial and Applied Mathematics.
12. Argyris J., Faust G., Haase M. An Exploration of Chaos. Texts on Computational Mechanics 1994, vol. VII. North-Holland.
13. Nayfeh A.H., Mook D.T. Nonlinear Oscillations 1979, Wiley.
14. Poincaré H. Sur les déterminants d'ordre infini. Bulletin de la Société Mathématique de France 1886, 14:77-90.
15. Zhou J., Hagiwara T., Araki M. Spectral analysis and eigenvalues computation of the harmonic state operators in continuous-time periodic systems. Systems & Control Letters 2004, 53:141-155.
16. Curtis C.W., Deconinck B. On the convergence of Hill's method. Mathematics of Computation 2010, 79:169-187.
17. Szemplinska-Stupnicka W. The Behavior of Nonlinear Vibrating Systems, vol. 1: Fundamental Concepts and Methods: Applications to Single-Degree-of-Freedom Systems 1990, Kluwer Academic Publishers.
18. de Langre E. Frequency lock-in is caused by coupled-mode flutter. Journal of Fluids and Structures 2006, 22:783-791.