A semi-analytical approach to the non-linear dynamic response problem of beams at large vibration amplitudes, Part II: Multimode approach to the steady state forced periodic response

Journal of Sound and Vibration

Volumn 255, Issue 1, 2003, Pages 1-41

  Azrar, L ^a   Benamar, R ^b   White, R G ^c  

^a ABDELMALEK ESSAADI UNIVERSITY   (Morocco)

^b MOHAMMED V UNIVERSITY   (Morocco)

^c UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BEAMS AND GIRDERS; BENDING MOMENTS; BOUNDARY CONDITIONS; CALCULATIONS; DYNAMIC RESPONSE; EQUATIONS OF MOTION; ESTIMATION; FREQUENCIES; HARMONIC ANALYSIS; ITERATIVE METHODS; MATHEMATICAL MODELS;

HARMONIC BALANCE METHOD; MULTIMODE ANALYSIS; NONLINEAR FREQUENCY;

VIBRATIONS (MECHANICAL);

EID: 0037411940     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.2000.3595     Document Type: Article

References (49)

1. L. Azrar, R. Benamar and R. G. White 1999 Journal of Sound and Vibration 224, 183-207. A semi-analytical approach to the nonlinear 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.
2. R. Benamar 1990 Ph.D. Thesis, University of Southampton. Nonlinear dynamic behaviour of fully clamped beams and rectangular isotropic and laminated plates.
3. R. Benamar, M. M. K. Bennouna and R. G. White 1989 Proceedings of the Seventh International Modal Analysis Conference, Las Vegas, NV, U.S.A. Nonlinear mode shapes and resonance frequencies of fully clamped beams and plates.
4. R. Benamar, M. M. Bennouna and R. G. White 1990 Proceedings of the Eighth International Modal Analysis Conference, Orlando, FL, U.S.A. Harmonic distortion of the nonlinear response of fully clamped beams and plates.
5. 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.
6. R. Benamar, M. M. K. Bennouna and R. G. White 1993 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.
7. 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 spatial distribution of harmonic distortion.
8. L. Azrar and R. Benamar 1995 5ème Colloque Maghrébin sur les Modèles Numériques de l'Ingénieur, E.M.I., Rabat, Maroc, Vol. II, 594-599. Etude des vibrations non linéaires forcées des poutres par une méthode semi-analytique.
9. C. S. Hsu 1960 Quarterly of Applied Mathematics 17, 393-407. On the application of elliptic functions in nonlinear forced oscillations.
10. J. G. Eisley 1964 Zeitschrift für Angewandte Mathematik und Physik 15, 167-175. Nonlinear vibration of beams and rectangular plates.
11. A. V. Srinivasan 1966 International Journal of Nonlinear Mechanics 1, 179-191. Nonlinear vibrations of beams and plates.
12. D. A. Evensen 1968 American Institute of Aeronautics and Astronautics Journal 6, 370-372. Nonlinear vibrations of beams with various boundary conditions.
13. M. M. K. Bennouna and R. G. White 1984 Journal of Sound and Vibration 96, 309-331. The effects of large vibration amplitudes on the fundamental mode shape of a clamped-clamped uniform beam.
14. P. C. Dumir and A. Bhaskar 1988 Journal of Sound and Vibration 123, 517-527. Some erroneous finite element formulations of nonlinear vibrations of beams and plates.
15. M. I. Qaisi 1993 Applied Acoustics 40, 141-151. Application of the harmonic balance principle to the nonlinear free vibration of beams.
16. G. Singh, A. K. Sharma and G. Venkateswara Rao 1990 Journal of Sound and Vibration 142, 77-85. Large amplitude free vibrations of beams. A discussion on various formulations and assumptions.
17. J. A. Bennett and J. G. Eisley 1970 American Institute of Aeronautics and Astronautics Journal 8, 734-739. A multiple degree of freedom approach to nonlinear beam vibrations.
18. H. R. Busby J. and V. I. Weingarten 1972 International Journal of Nonlinear Mechanics 7, 289-303. Nonlinear response of a beam to periodic loading.
19. R. Lewandowski 1987 Journal of Sound and Vibration 114, 91-101. Application of the Ritz method to the analysis of nonlinear free vibrations of beams.
20. C. Mei 1973 Computers and Structures 3, 163-174. Finite element displacement method for large amplitude free flexural vibrations of beams and plates.
21. C. Mei and K. Decha-Umphai 1985 Journal of Sound and Vibration 102, 369-380. A finite element method for nonlinear forced vibrations of beams.
22. C. Mei and K. Decha-Umphai 1985 American Institute of Aeronautics and Astronautics Journal 23, 1104-1110. Finite element method for nonlinear forced vibration of rectangular plates.
23. G. Venkateswara Rao, K. Kanaka Raju, and I. S. Raju 1976 Computers and Structures 6, 169-172. Finite element formulation for large amplitude free vibration of beams and orthotropic circular plates.
24. B. S. Sarma and T. K. Varadan 1983 Journal of Sound and Vibration 86, 61-70. Lagrange-type formulation for finite element analysis of nonlinear beam vibrations.
25. B. Nageswara Rao 1992 Journal of Sound and Vibration 155, 523-527. Large amplitude free vibrations of simply supported uniform beams with immovable ends.
26. S. R. R. Pillai and B. Nageswara Rao 1992 Journal of Sound and Vibration 159, 527-531. On nonlinear free vibrations of simply supported uniform beams.
27. G. Singh, G. Venkateswara Rao and N. G. R. Iyengar 1990 Journal of Sound and Vibration 143, 351-355. Re-investigation of large-amplitude free vibrations of beams using finite elements.
28. Y. K. Cheung and S. L. Lau 1982 Earthquake Engineering and Structural Dynamics 10, 239-253. Incremental time-space finite strip method for non-linear structural vibrations.
29. A. Y. T. Leung 1989 Computational Mechanics 5, 73-80. Nonlinear natural vibration analysis of beams by selective coefficient increment.
30. R. Lewandowski 1994 Journal of Sound and Vibration 170, 577-593. Nonlinear free vibrations of beams by the finite element and continuation methods.
31. L. Azrar, C. Cochelin, N. Damil and M. Potier-Ferry 1998 Structural Dynamic Systems, Computational Techniques and Optimization, Computer-Aided Design and Engineering. Gordon-Breach International Series in Engineering, Technology and Applied Science, Vol. 7, 103-141. As asymptotic-numerical method for nonlinear vibrations of elastic structures.
32. L. Azrar, R. Benamar and M. Potier-Ferry 1999 Journal of Sound and Vibration 220, 695-727. An asymptotic numerical method for large amplitude free vibrations of thin elastic plates.
33. A. K. Noor, C. M. Andersen and J. M. Peters 1993 Computer Methods in Applied Mechanics and Engineering 103, 175-186. Reduced basis technique for nonlinear vibration analysis of composite panels.
34. A. H. Nayfeh and S. A. Nayfeh 1994 Journal of Vibration and Acoustics 116, 129-136. On nonlinear modes of continuous systems.
35. Y. Shi and C. Mei 1996 Journal of Sound and Vibration 193, 453-464. A finite element time domain modal formulation for large amplitude free vibrations of beams and plates.
36. Y. Shi, R. Y. Y. Lee and C. Mei 1997 American Institute of Aeronautics and Astronautics Journal 35, 159-166. Finite element method for nonlinear free vibrations of composite plates.
37. H. F. Wolfe 1995 Ph.D. Thesis, University of Southampton. An experimental investigation of nonlinear behaviour of beams and plates excited to high levels of dynamic response.
38. R. R. Chen, C. Mei and H. F. Wolfe 1996 Journal of Sound and Vibration 195, 719-737. Comparison of finite element nonlinear beam random response with experimental results.
39. E. Riks 1979 International Journal of Solid and Structures 15, 529-551. An incremental approach to the solution of snapping and buckling problems.
40. E. Riks 1984 Computer Methods in Applied Mechanics and Engineering 47, 219-259. Some computational aspects of the stability analysis of nonlinear structures.
41. J. L. Batoz and G. Dhatt 1979 International Journal of Numerical Methods in Engineering 14, 1262-1267. Incremental displacement algorithms for non linear problems.
42. J. L. Batoz, G. Dhatt and M. Fafard 1985 Actes du troisième Colloque de tendances actuelles en calcul des structures, Bastia, 6-8 November, 129-143. Algorithmes de calcul automatique des configurations pré et post-flambement des structures.
43. M. A. Crisfield 1983 International Journal for Numerical Methods and Engineering 19, 1269-1289. An arc-length method including line searchers and accelerations.
44. M. A. Crisfield 1991 Nonlinear finite element analysis of solid structures, Vol. 1, Essentials. New York: John Wiley.
45. W. Wagner and P. Wriggers 1988 Engineering and Computation 5, 103-109. A simple method for the calculation of post-critical branches.
46. E. Carrera 1994 Computer and Structures 50, 217-229. A study on arc-length-type methods and their operation failures illustrated by a simple model.
47. R. Lewandowski 1997 International Journal of Solid and Structures 34, 1925-1947, Computational formulation of periodic vibration of geometrically non-linear structures. Part 1: theoretical background.
48. R. Lewandowski 1997 International Journal of Solid and Structures 34, 1949-1964. Computational formulation of periodic vibration of geometrically non-linear structures. Part 2: numerical strategy and examples.
49. P. Ribeiro and M. Petyt 1999 Journal of Sound and Vibration 224, 591-624. Non-linear vibration of beams with internal resonance by hierarchical finite element method.