Non-linear free periodic vibrations of open cylindrical shallow shells

Journal of Sound and Vibration

Volumn 313, Issue 1-2, 2008, Pages 224-245

  Ribeiro, P ^a  

^a UNIVERSITY OF PORTO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); MATHEMATICAL MODELS; NONLINEAR ANALYSIS; VIBRATION ANALYSIS;

ARC-LENGTH CONTINUATION METHOD; CYLINDRICAL SHALLOW SHELLS; HARMONIC BALANCE METHOD;

SHELLS (STRUCTURES);

EID: 40949141544     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2007.11.029     Document Type: Article

References (29)

1. Leissa A.W., and Kadi A.S. Curvature effects on shallow shell vibrations. Journal of Sound and Vibration 16 (1971) 173-187
2. Lau S.L., and Cheung Y.K. Amplitude incremental variational principle for non-linear vibration of elastic systems. Transactions ASME, Journal of Applied Mechanics 48 (1981) 959-964
3. Kobayashi Y., and Leissa A.W. Large amplitude free vibration of thick shallow shells supported by shear diaphragms. International Journal of Non-linear Mechanics 30 (1995) 57-66
4. Sinharay S.C., and Banerjee B. Large amplitude free vibration of shallow spherical shell and cylindrical shell-a new approach. International Journal of Non-linear Mechanics 20 (1985) 69-78
5. Ye Z.M. The non-linear vibration and dynamic instability of thin shallow shells. Journal of Sound and Vibration 202 (1997) 303-311
6. Ribeiro P. A hierarchical finite element for geometrically non-linear vibration of doubly curved, moderately thick isotropic shallow shells. International Journal for Numerical Methods in Engineering 56 (2003) 715-738
7. Przekop A., Azzouz M.S., Guo X., Mei C., and Azrar L. Finite element multiple-mode approach to non-linear free vibrations of shallow shells. AIAA Journal 42 (2004) 2373-2381
8. Amabili M. Non-linear vibrations of circular cylindrical panels. Journal of Sound and Vibration 281 (2005) 509-535
9. Amabili M. Theory and experiments for large-amplitude vibrations of circular cylindrical panels with geometric imperfections. Journal of Sound and Vibration 298 (2006) 43-72
10. Liew K.M., Hung K.C., and Lim M.K. Vibration of shallow shells: a review with bibliography. Applied Mechanics Reviews 50 (1997) 431-444
11. Amabili M., and Paidoussis M.P. Review of studies on geometrically non-linear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Applied Mechanics Reviews 56 (2003) 349-381
12. Han W., and Petyt M. Geometrically non-linear vibration analysis of thin, rectangular plates using the hierarchical finite element method-I: the fundamental mode of isotropic plates. Computers and Structures 63 (1997) 295-308
13. Han W., and Petyt M. Geometrically non-linear vibration analysis of thin, rectangular plates using the hierarchical finite element method-II: 1st mode of laminated plates and higher modes of isotropic and laminated plates. Computers and Structures 63 (1997) 309-318
14. Ribeiro P., and Petyt M. Non-linear vibration of plates by the hierarchical finite element and continuation methods. International Journal of Mechanical Sciences 41 (1999) 437-459
15. Ribeiro P., and Petyt M. Non-linear free vibration of isotropic plates with internal resonance. International Journal of Non-linear Mechanics 35 (2000) 263-278
16. Ribeiro P. A hierarchical finite element for geometrically non-linear vibration of thick plates. Meccanica 38 (2003) 115-130
17. Ribeiro P. Modal interactions in shallow shells. In: van Campen D.H., Lazurko M.D., and van den Oever W.P.J.M. (Eds). Fifth Euromech Nonlinear Dynamics Conference (2005), Eindhoven University of Technology
18. Ventsel E., and Krauthammer T. Thin Plates and Shells. Theory Analysis and Applications (2001), Marcel Dekker, New York
19. Qatu M.S. Vibration of Laminated Shells and Plates (2004), Elsevier, Amsterdam
20. Lewandowski R. Computational formulation for periodic vibration of geometrically non-linear structures-part 1: theoretical background. International Journal of Solids and Structures 34 (1997) 1925-1947
21. Burton T.D., and Hamdan M.N. On the calculation of non-linear normal modes in continuous systems. Journal of Sound and Vibration 197 (1996) 117-130
22. Szemplinska-Stupnicka W. The Behaviour of Non-linear Vibrating Systems (1990), Kluwer Academic Publishers, Dordrecht
23. Bennouna M.M., and White R.G. The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam. Journal of Sound and Vibration 96 (1984) 309-331
24. Benamar R., Bennouna M.M.K., and White R.G. The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures. Part I: simply supported and clamped-clamped beams. Journal of Sound and Vibration 149 (1991) 179-195
25. Szemplinska-Stupnicka W. "Non-linear normal modes" and the generalized Ritz method in the problems of vibration of non-linear elastic continuous systems. International Journal of Non-Linear Mechanics 18 (1983) 149-165
26. Shaw S.W., and Pierre C. Normal modes of vibration for non-linear continuous systems. Journal of Sound and Vibration 169 (1994) 319-347
27. Bardell N.S., Dunsdon J.M., and Langley R.S. On the free vibration of completely free, open, cylindrically curved, isotropic shell panels. Journal of Sound and Vibration 20 (1997) 647-669
28. Leissa A.W., and Narita Y. Vibrations of completely free shallow shells of rectangular planform. Journal of Sound and Vibration 96 (1984) 207-218
29. Seydel R. From Equilibrium to Chaos. Practical Bifurcation and Stability Analysis (1988), Elsevier Science, New York