Computational formulation for periodic vibration of geometrically nonlinear structures - Part 2: Numerical strategy and examples

International Journal of Solids and Structures

Volumn 34, Issue 15, 1997, Pages 1949-1964

  Lewandowski, R ^a  

^a POZNAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; EQUATIONS OF MOTION; MATRIX ALGEBRA; NONLINEAR SYSTEMS; NUMERICAL METHODS; VIBRATIONS (MECHANICAL);

GEOMETRICALLY NONLINEAR STRUCTURES; MATRIX AMPLITUDE EQUATION;

STRUCTURAL ANALYSIS;

EID: 0031139750     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(96)00126-6     Document Type: Article

References (26)

1. Allman, D. J. (1989) On the general theory of the stability of equilibrium of discrete conservative systems. The Aeronautical Journal 93, 29-35.
2. Batoz J. L. and Dhatt G. (1979) Incremental displacement algorithm for nonlinear problems. International Journal of Numerical Methods in Engineering 14, 1262-1267.
3. Cheung, Y. K. and Lau, S. L. (1982) Incremental time-space finite strip method for non-linear structural vibrations. Earthquake Engineering and Structural Dynamics 10, 239-253.
4. Chia, C. Y. (1980) Nonlinear Analysis of Plates. McGraw-Hill, New York.
5. Crisfield, M. A. (1981) A fast incremental/iterative solution procedure that handles snap through. Computers & Structures 13, 55-62.
6. Decker, D. W. and Keller, H. B. (1980) Solution branching - A constructive technique. In New Approaches to Nonlinear Problems in Dynamics, ed. P. J. Holmes. SIAM, Philadelphia, pp. 53-69.
7. Flores, F. G. and Godoy, L. A. (1992) Elastic postbucklmg analysis via finite element and perturbation techniques, Part 1 : formulation. International Journal of Numerical Methods in Engineering 33, 1775-1794.
8. Kouchia, R. and Mikkola, M. (1989) Tracing the equilibrium path beyond simple critical points. International Journal of Numerical Methods in Engineering 28, 2923-2941.
9. Lewandowski, R. (1985) The application of the vector iteration methods to the solution of nonlinear eigen-problems. In Proceedings of the 5th National Congress on Theoretical and Applied Mechanics, Varna. Vol 2, pp. 42-47.
10. Lewandowski, R. (1989) Nonlinear free vibrations of multispan beams on elastic supports. Computers & Structures 32, 305-312.
11. Lewandowski, R. (1991) Nonlinear, steady-state analysis of multispan beams by the finite element method. Computers & Structures 39, 83-93.
12. Lewandowski, R. (1993) Periodic Vibrations of Geometrically Nonlinear Structures. Wydawnictwo Politechniki Poznańskiej, Poznań (in Polish).
13. Lewandowski, R. (1994) Nonlinear free vibration of beams by the finite element and continuation method. Journal of Sound and Vibration. 170, 577-593.
14. Lewandowski, R. (1994) Solutions with bifurcation points for free vibration of beams: an analytical approach. Journal of Sound and Vibration 177, 239-249.
15. Lewandowski, R. (1996) Computational formulation for periodic vibration of geometrically nonlinear structures-part 1 : theoretical background. International Journal of Solids and Structures 34(15), 1925-1947.
16. Lewandowski, R. (1996) On beams, membranes and plates vibration backbone curves in cases of internal resonance. Meccanica 31, 323-346.
17. Mei, C. (1972) Finite element displacements method for large amplitude free flexural vibrations of beams and plates. Computers & Structures 3, 163-174.
18. Rao, G. V., Raju, K. K. and Raju, I. S. (1976) Finite element formulation for the large amplitude vibrations of beams and orthotropic circular plates. Computers & Structures 6, 169-172.
19. Riks, E. (1984) Some computational aspects of the stability analysis of nonlinear structures. Computational Methods in Applied Mechanical Engineering 47, 219-259.
20. Rheinboldt, W. C. (1978) Numerical methods for a class of finite dimensional problems. SIAM Journal of Numerical Analysis 15, 1-11.
21. Seydel, R. (1988) From Equilibrium to Chaos. Practical Bifurcation and Stability Analysis. Elsevier, New York.
22. Spence, A. and Jepson, A. D. (1985) Folds in the solution of two parameter systems and their calculation. Part 1. SIAM Journal of Numerical Analysis 22, 347-368.
23. Srinivasan, A. V. (1969) Large amplitude free oscillations of beams and plates. Journal of AIAA 3, 1951-1953.
24. Szemplińska-Stupnicka, W. (1990) The Behaviour of Nonlinear Vibrating Systems. Kluwer Academic Publishers, Dordrecht.
25. Wellford, L. C., Dib, D. M. and Mindle, W. (1980) Free and steady-state vibrations of non-linear structures using a finite element-nonlinear eigenvalue technique. Earthquake Engineering and Structural Dynamics 8, 97-115.
26. Woinowsky-Krieger, S. (1950) The effect of an axial force on the vibration of hinged bars. Journal of Applied Mechanics 17, 35-36.