Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

International Journal of Non-Linear Mechanics

Volumn 43, Issue 6, 2008, Pages 551-561

  Mazzilli, Carlos E N ^a   Sanches, César T ^a   Baracho Neto, Odulpho G P ^a   Wiercigroch, Marian ^b   Keber, Marko ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF ABERDEEN   (United Kingdom)

Author keywords

Axially loaded beams; Non linear multi modes; Non linear normal modes; Vertical risers

Indexed keywords

AXIAL LOADS; COMPUTER SIMULATION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MODAL ANALYSIS; NONLINEAR EQUATIONS; ROBUST CONTROL;

AXIALLY LOADED BEAMS; NON-LINEAR MULTI-MODES; NON-LINEAR NORMAL MODES; VERTICAL RISERS;

LIGHT;

EID: 44649105680     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2008.04.004     Document Type: Article

References (37)

1. C.H. Pak, R.M. Rosenberg, On the existence of normal mode vibrations in nonlinear systems, Q. Appl. Math. 26 (1968) 403-416.
2. Shaw S.W., and Pierre C. Non-linear normal modes and invariant manifolds. J. Sound Vib. 150 1 (1991) 170-173
3. Shaw S.W., and Pierre C. Normal modes for non-linear vibratory systems. J. Struct. 164 1 (1993) 85-124
4. Shaw S.W., and Pierre C. Normal-modes of vibration for nonlinear continuous systems. J. Sound Vib. 169 3 (1994) 319-347
5. Lacarbonara W., and Rega G. Resonant non-linear normal modes. Part I: activation/orthogonality conditions for shallow structural systems. Int. J. Non-linear Mech. 38 (2003) 873-887
6. Gendelman O., Manevitch L.I., Vakakis A.F., and Bergman L. A degenerate bifurcation structure in the dynamics of coupled oscillators with essential stiffness nonlinearities. Nonlinear Dyn. 33 1 (2003) 1-10
7. King M.E., and Vakakis A.F. An energy-based approach to computing resonant nonlinear normal modes. J. Appl. Mech.-Trans. ASME 63 3 (1996) 810-819
8. Lacarbonara W., Rega G., and Nayfeh A.H. Resonant non-linear normal modes. Part I: analytical treatment for structural one-dimensional systems. Int. J. Non-linear Mech. 38 (2003) 851-872
9. Manevitch L.I. The description of localised normalised modes in a chain of nonlinear coupled oscillators using complex variables. Nonlinear Dyn. 25 1-3 (2001) 95-109
10. Manevitch L.I., Gendelman O., Musienko A.I., Vakakis A.F., and Bergman L. Dynamic interaction of a semi-infinite linear chain of coupled oscillators with a strongly nonlinear end attachment. Physica D 178 1-2 (2003) 1-18
11. Mikhlin Y.V. Matching of local expansions in the theory of nonlinear vibrations. J. Sound Vib. 182 4 (1995) 577-588
12. Mikhlin Y.V., and Zhupiev A.L. An application of the Ince algebraization to the stability of non-linear normal vibration modes. Int. J. Non-Linear Mech. 32 2 (1997) 393-409
13. Mikhlin Y.V., and Morgunov B.I. Normal vibrations in near-conservative self-excited and viscoelastic nonlinear systems. Nonlinear Dyn. 25 1-3 (2001) 33-48
14. Vakakis A.F., and Rand R.H. Normal modes and global dynamics of a two-degree-of-freedom non-linear system-I. Low energies. Int. J. Non-Linear Mech. 27 5 (1992) 861-874
15. Vakakis A.F., and Rand R.H. Normal modes and global dynamics of a two-degree-of-freedom non-linear system-II. High energies. Int. J. Non-Linear Mech. 27 5 (1992) 875-888
16. Srinil N., Rega G., and Chucheepsakul S. Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: theoretical formulation and model validation. Nonlinear Dyn. 48 (2007) 231-252
17. Srinil N., and Rega G. Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part II: internal resonance activation, reduced-order models and nonlinear normal modes. Nonlinear Dyn. 48 (2007) 253-274
18. Srinil N., and Rega G. The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables. Int. J. Non-Linear Mech. 42 (2007) 180-195
19. Baracho Neto O.G.P., and Mazzilli C.E.N. Evaluation of non-linear normal modes for finite-element models. Comput. Struct. 80 (2002) 957-965
20. Baracho Neto O.G.P., and Mazzilli C.E.N. Evaluation of multi-modes for finite-element models: systems tuned into 1:2 internal resonance. Int. J. Solids Struct. 42 (2005) 5795-5820
21. Kauderer H. Nichtlineare Mechanik (1958), Springer, Berlin
22. Nayfeh A.H., and Nayfeh S.A. On nonlinear modes of continuous systems. J. Vib. Acoust. 116 (1994) 129-136
23. Nayfeh A.H., Chin C., and Nayfeh S.A. Nonlinear normal modes of a cantilever beam. J. Vib. Acoust. 117 4 (1995) 477-481
24. Singh G., Sharma A.K., and Rao G.V. Large-amplitude free vibrations of beams-a discussion on various formulations and assumptions. J. Sound Vib. 142 1 (1990) 77-85
25. Shaw S.W., Pierre C., and Pesheck E. Modal analysis-based reduced-order models for nonlinear structures-an invariant manifold approach. Shock Vib. Dig. 31 (1999) 3-16
26. C.T. Sanches, C.E.N. Mazzilli, L.D. Cunha, C.P. Pesce, Non-linear modal analysis applied to riser dynamics, in: Proceedings of the 17th International Offshore and Polar Engineering Conference, ISOPE'07, vol. 2, 2007, pp. 1-7.
27. Soares M.E.S., and Mazzilli C.E.N. Nonlinear normal modes of planar frames discretised by the finite element method. Comput. Struct. 77 (2000) 485-493
28. Mazzilli C.E.N., Soares M.E.S., and Baracho Neto O.G.P. Reduction of finite-element models of planar frames using non-linear normal modes. Int. J. Solids Struct. 38 (2001) 1993-2008
29. B.L. Newberry, N.C. Perkins, Analysis of resonant tangential response in submerged cables resulting from 1-to-1 internal resonance, in: Proceedings of the 7th International Offshore and Polar Engineering Conference, ISOPE'97, vol. II, Honolulu, 1997, pp. 157-163.
30. C.P. Pesce, A.L.C. Fujarra, A.N. Simos, E.A. Tannuri, Analytical and closed form solutions for deep water riser-like eigenvalue problem, in: Proceedings of the 9th International Offshore and Polar Engineering Conference, ISOPE'99, vol. 2, 1999, pp. 255-264.
31. Pesce C.P., and Martins C.A. Numerical computation of riser dynamics. In: Chakrabarti S. (Ed). Numerical Modelling in Fluid-Structure Interaction, Advances in Fluid Mechanics Series (2005), WIT Press, Southampton, UK 253-309 (Chapter 7)
32. Pesce C.P., and Martins C.A. Riser-soil interaction: local dynamics at TDP and a discussion on the eigenvalue and the VIV problems. J. Offshore Mech. Arct. Eng. 128 (2006) 39-55
33. Pars L.A. A Treatise on Analytical Dynamics (1965), Heinemann, London
34. Meirovitch L. Methods of Analytical Dynamics (1970), McGraw-Hill, New York
35. Nayfeh A.H., and Mook D.T. Nonlinear Oscillations (1979), Wiley, New York
36. Nayfeh A.H. Nonlinear interactions: analytical, computational and experimental methods. Meccanica 35 6 (2000) 583-586
37. L.M.Y. Silveira, C.A. Martins, L.D. Cunha, C.P. Pesce, An investigation on the effect of tension variation on VIV of risers, in: Proceedings of OMAE, 2007, pp. 1-9.