Multi-parameter linear periodic systems: sensitivity analysis and applications

Journal of Sound and Vibration

Volumn 229, Issue 1, 2000, Pages 89-111

  Seyranian, Alexander P ^a   Solem, Frederik ^b   Pedersen, Pauli ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; INTEGRATION; LINEAR SYSTEMS; MATRIX ALGEBRA; SENSITIVITY ANALYSIS; STABILITY;

DEGREE OF FREEDOM; FLOQUET MATRIX; FLOQUET METHOD; MULTIPARAMETER LINEAR PERIODIC SYSTEMS; STABILITY ANALYSIS;

TIME VARYING SYSTEMS;

EID: 0034610672     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1999.2478     Document Type: Article

References (22)

1. BOLOTIN V. V. The Dynamic Stability of Elastic Systems. 1964;Holden-Day, San-Francisco.
2. NAYFEH A. H., MOOK D. T. Nonlinear Oscillations. 1979;John Wiley & Sons, New York.
3. PEDERSEN P. On stability diagrams for damped Hill equations. Quarterly of Applied Mathematics. 42:1985;477-495.
4. FLOQUET G. Sur les Equation Différentielles Linéaires à Coefficients Périodiques. Annales de École Normal Superior, Paris. 2:1883;47-89.
5. CESARI L. Asymptotic Behaviour and Stability Problems in Ordinary Differential Equations. 1964;Academic Press, New York.
6. FU F. C. L., NEMAT-NASSER S. Stability of solution of systems of linear differential equations with harmonic coefficients. AIAA Journal. 10:1972;30-36.
7. HANSEN J. M. Stability diagrams for coupled, Mathieu-equations. Ingenieur-Archiv. 55:1985;463-473.
8. LINDH K. G., LIKINS P. W. Infinite determinant methods for stability analysis of periodic-coefficient differential equations. AIAA Journal. 8:1970;680-686.
9. WEYH B., KOSTYRA H. Direct Floquet method for stability limits determination - I. Theory. Mechanism and Machine Theory. 26:1991;123-131.
10. KOSTYRA H., WEYH B. Direct Floquet method for stability limits determination - II. Application and phenomena. Mechanism and Machine Theory. 26:1991;133-144.
11. FRIEDMANN P., HAMMOND C. E., WOO T.-H. Efficient numerical treatment of periodic systems with application to stability problems. International Journal for Numerical Methods in Engineering. 11:1977;1117-1136.
12. SINHA S. C., WU D.-H. An efficient computational scheme for the analysis of periodic systems. Journal of Sound and Vibration. 151:1991;91-117.
13. PEDERSEN P., SEYRANIAN A. P. Sensitivity analysis for problems of dynamic stability. International Journal of Solids Structures. 9:1983;315-335.
14. YAKUBOVITCH V. A., STARZHINSKII V. M. Linear Differential Equations with Periodic Coefficients? 1975;Wiley, New York.
15. GRIMSHAW R. Nonlinear Ordinary Differential Equations? 1990;Blackwell Scientific Publications, London.
16. YAKUBOVITCH V. A., STARZHINSKII V. M. Parametric Resonance in Linear Systems. 1987;Nauka (in Russian), Moscow.
17. VAINBERG M. M. Variational Methods for the Study of Nonlinear Operators. 1964;Holden-Day, San Francisco.
18. SEYRANIAN A. P. Sensitivity analysis of multiple eigenvalues. Mechanics of Structures and Machines. 21:1993;261-284.
19. FORYS A. S. Optimization of an axially loaded beam on a foundation. Journal of Sound and Vibration. 178:1994;607-613.
20. IWATSUBO T., SAIGO M., SUGIAMA Y. Parametric instability of clamped-clamped and clamped-simply supported columns under periodic axial load. Journal of Sound and Vibration. 30:1973;65-77.
21. PEDERSEN P. Design with several eigenvalue constraints by finite elements and linear programming. Journal of Structural Mechanics. 10:1982-83;243-271.
22. PEDERSEN P. A quantitative stability analysis of the solutions to the Carson-Cambi equations. Journal of the Franklin Institute. 309:1980;359-367.