Almost-sure stochastic stability of viscoelastic plates in supersonic flow

AIAA journal

Volumn 39, Issue 3, 2001, Pages 465-472

  Ariaratnam, S T ^a   Abdelrahman, N M ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

PLATES (STRUCTURAL COMPONENTS); RANDOM PROCESSES; STOCHASTIC CONTROL SYSTEMS; VISCOELASTICITY;

STOCHASTIC STABILITY; VISCOELASTIC PLATES;

SUPERSONIC FLOW;

EID: 0035280392     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.1328     Document Type: Article

References (25)

1. Hedgepeth, J. M.,"On the Flutter of Panels at High Mach Numbers," Journal of the Aeronautical Sciences, Vol. 23, No. 1, 1956, pp. 563-573.
2. Bolotin, V. V., and Zhinzher, V. V., "Effect of Damping on Stability of Elastic Systems to Non-Conservative Forces," International Journal of Solids and Structures, Vol. 5, No. 9, 1969, pp. 965-989.
3. Volmir, A. S., Stability of Deformable Systems, Nauka, Moscow, 1967.
4. Dowell, E. H., "Review of the Aeroelastic Stability of Plates and Shells," AIAA Journal, Vol. 8, No. 2, 1970, pp. 385-398.
5. Matyash, V. I., "Dynamic Stability of Hinged Viscoelastic Bar," Mechanics of Polymers, Vol. 2, 1964, pp. 293-300 English translation.
6. Stevens, K. K., "On the Parametric Excitation of a Viscoelastic Column." AIAA Journal, Vol. 4, No. 12, 1966, pp. 2111-2116.
7. Szyskowski, W., and Glockner, P. G., "The Stability of Viscoelastic Perfect Columns: A Dynamic Approach." International Journal of Solids and Structures, Vol. 21, No. 6, 1985, pp. 545-559.
8. Glockner, P. G., and Szyskowski, W., "On the Stability of Columns Made of Time Dependent Materials." Encyclopaedia of Civil Engineering Practices Technomic, Vol. 23, No. 1, 1987, pp. 577-626.
9. Plaut, R. H., and Infante, E. F., "On the Stability of Continuous Systems Subjected to Random Excitations." Journal of Applied Mechanics, Vol. 37, No. 3, 1970, pp. 623-628.
10. Kozin, F., Stability of the Linear Stochastic Systems, Lecture Notes in Mathematics No. 294, edited by R. F. Curtain. Springer-Verlag, Berlin, 1972, pp. 186-229.
11. Ahmadi, G., "On the Stability of Systems of Coupled Partial Differential, Equations with Random Excitation," Journal of Sound and Vibration, Vol. 52, No. 1, 1977, pp. 27-35.
12. Potapov, V. D., "Stability of Viscoelastic Plate in Supersonic Flow Under Random Loading." AIAA Journal, Vol. 33, No. 4, 1995, pp. 712-715.
13. Potapov, V. D., and Bonder, P. A., "Stochastic Flutter of Elastic and Viscoelastic Plates in a Supersonic Flow," European Journal of Mechanics A/Solids, Vol. 15, No. 5, 1996, pp. 883-900.
14. Ibrahim, R. A., Orono, P. O., and Madaboosi, S. R., "Stochastic Flutter of a Panel Subjected to Random In-Plane Forces, Part I: Two-Mode Interaction," AIAA Journal, Vol. 28, No. 4, 1989, pp. 694-702.
15. Ibrahim, R. A., and Orono, P. O., "Stochastic Non-Linear Flutter of a Panel Subjected to Random In-Plane Forces," International Journal of Non-Linear Mechanics, Vol. 26, No. 6, 1991, pp. 867-883.
16. Stratonovich, R. L., Topics in the Theory of Random Noise, Vol. 1. Gordon and Breach, New York, 1963.
17. Khasminskii, R. A., "A Limit Theorem for the Solutions of Differential Equations with Random Right-Hand Sides," Theory of Probability and Its Application, Vol. 11. No. 3, 1966, pp. 390-406 English translation.
18. Larianov, G. S., "Investigation of the Vibrations of Relaxing Systems by the Averaging Method," Mechanics of Polymers, Vol. 5, 1969, pp. 714-720 English translation.
19. Khasminskii, R. A., "Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic System," Theory of Probability and Its Application, Vol. 12, No. 1, 1967, pp. 144-147 (English translation).
20. Arnold, L., and Kliemann, W., "Probabilistic Analysis and Related Topics," Qualitative Theory of Stochastic Systems, Vol. 3, Academic Press, New York, 1983.
21. Bolotin, V. V., Non-conservative Problems of the Theory of Elastic Stability, Macmillian, New York, 1962.
22. Drozdov, A. D., Finite Elasticity and Viscoelasticity, World Scientific, New York, 1996.
23. Bolotin, V. V., and Petrovsky, A. V., "Secondary Bifurcations and Global Instability of an Aeroelastic Non-Linear System in the Divergence Domain," Journal of Sound and Vibration, Vol. 191, No. 3, pp. 431-451.
24. Mitchell, R. R., and Kozin, F., "Sample Stability of Second Order Linear Differential Equations with Wide-Band Noise Coefficients," SIAM Journal on Applied Mathematics, Vol. 27, No. 4, 1974, pp. 571-604.
25. Christensen, R. M., Theory of Viscoelasticity: An Introduction, Academic Press, New York, 1982.