Stability analysis of periodic systems by truncated point mappings

Journal of Sound and Vibration

Volumn 189, Issue 1, 1996, Pages 33-54

  Guttalu, R S ^a   Flashner, H ^a  

^a University of Southern California ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BIFURCATION (MATHEMATICS); CONFORMAL MAPPING; CONVERGENCE OF NUMERICAL METHODS; DEGREES OF FREEDOM (MECHANICS); INTEGRATION; PERTURBATION TECHNIQUES; SYSTEMS ANALYSIS; TIME VARYING SYSTEMS;

MATHIEU EQUATION; STABILITY ANALYSIS; TRUNCATED POINT MAPPINGS;

SYSTEM STABILITY;

EID: 0030562018     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1996.0004     Document Type: Article

References (31)

1. V. V. BOLOTIN 1964 The Dynamic Stability of Elastic Systems. San Francisco: Holden-Day.
2. V. A. YAKUBOVITCH and V. M. STARZHINSKI 1975 Linear Differential Equations with Periodic Coefficients, Vols. I and II. New York: John Wiley.
3. K. G. LINDH and P. W. LIKINS 1970 American Institute of Aeronautics and Astronautics Journal 8, 680-686. Infinite determinant methods for stability analysis of periodic-coefficient differential equations.
4. J. A. RICHARDS 1983 Analysis of Periodically Time-varying Systems. San Francisco: Holden-Day.
5. A. H. NAYFEH 1973 Perturbation Methods. New York: John Wiley.
6. A. H. NAYFEH and D. T. MOOK 1979 Non-linear Oscillations. New York: John Wiley.
7. J. K. HALE 1963 Oscillations in Nonlinear Systems. New York: McGraw-Hill.
8. J. J. STOKER 1950 Non-linear Vibrations. New York: Academic Press.
9. N. N. BOGOLIUBOV and Y. A. MITROPOLSKI 1961 Asymptotic Methods in the Theory of Nonlinear Oscillations. New York: Gordon and Breach.
10. L. MEIROVITCH 1970 Analytical Methods in Vibrations. New York: McGraw-Hill.
11. S. C. SINHA, D.-H. WU, V. JUNEJA, and P JOSEPH 1993 American Society of Mechanical Engineers Journal of Vibrations and Acoustics 115, 96-102. Analysis of dynamic systems with periodically varying parameters via Chebyshev polynomials.
12. S. C. SINHA and D.-H. WU 1991 Journal of Sound and Vibration 151, 91-117. An efficient computational scheme for the analysis of periodic systems.
13. S. C. SINHA, C. C. CHOU and H. H. DENMAN 1979 Journal of Sound and Vibration 64, 515-527. Stability analysis of systems with periodic coefficients: an approximate approach.
14. P. FRIEDMANN, C. E. HAMMOND and T. H. WOO 1977 International Journal for Numerical Methods in Engineering 11, 1117-1136. Efficient treatment of periodic systems with application to stability problems.
15. P. P. FRIEDMANN 1986 Computers and Mathematics with Applications 12A, 131-148. Numerical methods for determining the stability and response of periodic systems with applications to helicopter rotor dynamics and aero-elasticity.
16. G. H. GAONKAR, D. S. SIMHA PRASAD and D. SASTRY 1981 Journal of American Helicopter Society 26, 56-61. On computing Floquet transition matrices of rotorcraft.
17. J. DUGUNDJI and J. H. WEDELL 1983 American Institute of Aeronautics and Astronautics Journal 21, 890-897. Some analysis methods for rotating systems with periodic coefficients.
18. H. POINCARE 1891 Leas Methodes Nouvelles de la Mechanique Celeste. Paris: Gauthier-Villars.
19. C. S. HSU and W. H. CHENG 1973 American Society of Mechanical Engineers Journal of Applied Mechanics 40, 78-86. Application of the theory of impulsive parametric excitation and new treatment of general parametric excitation problems.
20. C. S. HSU 1974 Journal of Mathematical Analysis and Application 45, 234-251. On approximating a general linear periodic system.
21. J. BERNUSSOU, and H. LIU and C. MIRA 1976 International Journal of Nonlinear Mechanics 11, 151-170. On non-linear periodic differential equations and associated point mappings: application to stability problems.
22. J. BERNUSSOU 1977 Point Mapping Stability. Oxford: Pergamon.
23. H. FLASHNER 1979 Ph.D. Dissertation, Department of Mechanical Engineering, University of California, Berkeley. A point mapping study of dynamical systems.
24. H. FLASHNER and C. S. HSU 1983 International Journal for Numerical Methods in Engineering 19, 185-215. A study of nonlinear systems via the point mapping method.
25. R. S. GUTTALU and H. FLASHNER 1989 Journal of Sound and Vibration 129, 291-311. Periodic solutions of non-linear autonomous sytems by approximate point mappings.
26. H. FLASHNER and R. S. GUTTALU 1989 International Journal of Non-linear Mechanics 24, 327-344. Analysis of non-linear and non-autonomous systems by truncated point mappings.
27. E. I. JURY 1974 Inners and Stability of Dynamic Systems. New York: John Wiley.
28. C. S. HSU 1977 Advances in Applied Mechanics 17, 245-301. On nonlinear parametric excitation problems.
29. P. HENRICI 1962 Discrete Variable Methods in Ordinary Differential Equatons. New York: John-Wiley and Sons.
30. N. W. MCLACHLAN 1947 Theory and Application of Mathieu Functions. Oxford: Clarendon Press.
31. H. LEIPHOLZ 1970 Stability Theory. New York: Academic Press.