Improvement of the semi-analytical method, for determining the geometrically non-linear response of thin straight structures: Part II - First and second non-linear mode shapes of fully clamped rectangular plates

Journal of Sound and Vibration

Volumn 257, Issue 1, 2002, Pages 19-62

  El Kadiri, M ^a   Benamar, R ^a  

^a MOHAMMED V UNIVERSITY   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ASPECT RATIO; BENDING (DEFORMATION); LINEAR SYSTEMS; MATHEMATICAL MODELS; SPECTRUM ANALYSIS; VIBRATIONS (MECHANICAL);

NON-LINEAR MODE SHAPES;

PLATES (STRUCTURAL COMPONENTS);

EID: 0037058134     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.2002.5026     Document Type: Article

References (30)

1. R.G. White 1978 Composites 9, 251-258. A comparison of some statistical properties of the response of aluminium alloy and CFRP plates to acoustic excitations.
2. H. Wolfe 1995 Ph.D. Thesis, University of Southampton. An experimental investigation of non-linear beams and plates exited to high levels of dynamic response.
3. C. Mei and K.R. Wentz 1982 American Institute of Aeronautics and Astronautics Journal 20, 1450-1458. Large-amplitude random response of angle-ply laminated composite plates.
4. R.G. White 1990 Composite Structures 16, 171-192. Developments in the acoustic fatigue design process for composite aircraft structures.
5. L. Azrar 1999 Ph.D. Thesis, University Mohammed V of Rabat. Semi-analytical and asymptotic-numerical methods for non-linear vibrations. Applications to large amplitude vibrations of beams and plates.
6. R. Benamar 1990 Ph.D. Thesis, University of Southampton. Non-linear dynamic behaviour of fully clamped beams and rectangular isotropic and laminated plates.
7. A.W. Leissa 1969 NASA-SP 160, 58-67. Vibration of plates.
8. A.W. Leissa 1973 Journal of Sound and Vibration 31, 257-393. Free vibrations of rectangular plates.
9. C.Y. Chia 1980 Non-linear Analysis of Plates. New York: McGraw-Hill.
10. A.H. Nayfeh and D.T. Mook 1979 Non-linear Oscillations. New York: John Wiley.
11. H.N. Chu and G. Hermann 1956 Journal of Applied Mechanics 23, 532-540. Influence of large amplitudes on free flexural vibrations of rectangular elastic plates.
12. L.W. Rehfield 1973 International Journal of Solids and Structures, 9, 581-590. Non-linear free vibrations of elastic structures.
13. R. Benamar, M.M.K. Bennouna and R.G. White 1991 Journal of Sound and Vibration 149, 179-195. 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.
14. H.N. Chu 1961 Journal of the Aerospace Sciences 28, 602-609. Influence of large amplitudes on flexural vibrations of a thin circular cylindrical shell.
15. W. Han and M. Petyt 1997 Computers and Structures 63, 295-308. Geometrically non-linear vibration analysis of thin, rectangular plates using the hierarchical finite element method-I: the fundamental mode of isotropic plates.
16. W. Han and M. Petyt 1997 Computers and Structures 63, 309-318. 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.
17. P. Ribeiro and M. Petyt 1999 International Journal of Mechanical Sciences 41, 437-459. Non-linear vibration of plates by the hierarchical finite element and continuation methods.
18. L. Azrar, R. Benamar and M. Potier-Ferry 1998 Journal of Sound and Vibration 220, 695-727. An asymptotic-numerical method for large-amplitude free vibrations of thin elastic plates.
19. M. El Kadiri, R. Benamar and R.G. White 1999 Journal of Sound and Vibration 228, 333-358. The non-linear free vibration of fully clamped rectangular plates: second non-linear mode for various plate aspect ratios.
20. M. El Kadiri, R. Benamar and R.G. White 2002 Journal of Sound and Vibration. 249, 263-305. Improvement of the semi-analytical method, for determining the geometrically non-linear response of thin straight structures. Part I: application to clamped-clamped and simply supported-clamped beams.
21. R. Benamar, M.M.K. Bennouna and R.G. White 1991 Journal of Sound and Vibration 164, 399-424. The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures. Part II: fully clamped rectangular isotropic plates.
22. L. Azrar, R. Benamar and R.G. White 1999 Journal of Sound and Vibration 224, 377-395. A semi-analytical approach to the non-linear dynamic response. Problem of S-S and C-C beams at large vibration amplitudes. Part I: general theory and application to the single mode approach to free and forced vibration analysis.
23. L. Azrar, R. Benamar and R.G. White 2002 Journal of Sound and Vibration 255, 1-41. A semi-analytical approach to the non-linear dynamic response problem of beams at large vibration amplitudes. Part II: multimode approach to the forced vibration analysis.
24. R. Benamar, M.M.K. Bennouna and R.G. White 1994 Journal of Sound and Vibration 175, 377-395. The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures. Part III: fully clamped rectangular isotropic plates-measurements of the mode shape amplitude dependence and the spatial distribution of harmonic distortion.
25. B. Harras, R. Benamar and R.G. White 2002 Journal of Sound and Vibration 252, 281-315. Experimental and theoretical investigation of the linear and non-linear dynamic behaviour of a Glare 3 hybrid composite panel.
26. F. Moussaoui, R. Benamar and R.G. White 2000 Journal of Sound and Vibration 232, 917-943. The effect of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic shells. Part I: coupled transverse-circumferential mode shapes of isotropic circular cylindrical shells of infinite length.
27. B. Harras, R. Benamar and R.G. White 2002 Journal of Sound and Vibration 251, 579-619. Geometrically non-linear free vibration of fully clamped symmetrically laminated rectangular composite plates.
28. S. Timoshenko and S. Woinowsky-Krieger 1959. Theory of Plates and Shells, p. 345. New York: McGraw-Hill; second edition.
29. R.G. White 1971 Journal of Sound and Vibration 16, 255-267. Effects of non-linearity due to large deflections in the resonance testing of structures.
30. D. Young 1950 Journal of Applied Mechanics, December, 448-453. Vibration of the rectangular plates by the Ritz method.