Anomalous dynamic elastic-plastic response of a Galerkin beam model

International Journal of Mechanical Sciences

Volumn 38, Issue 7, 1996, Pages 687-708

  Qian, Yin ^a   Symonds, P S ^a  

^a Brown University   (United States)

Author keywords

Anamalous; Beam; Chaotic; Elastic plastic; Pulse load

Indexed keywords

COMPUTATIONAL METHODS; DEGREES OF FREEDOM (MECHANICS); DYNAMIC RESPONSE; ELASTICITY; LYAPUNOV METHODS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE DIAGRAMS; PLASTIC DEFORMATION;

ELASTIC PLASTIC RESPONSE; GALERKIN METHOD; GEOMETRIC NONLINEARITY; POWER SPECTRAL DENSITY; PULSE LOAD;

BEAMS AND GIRDERS;

EID: 0030197896     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7403(95)00082-8     Document Type: Article

References (34)

1. P. S. Symonds and T. X. Yu, Counterintuitive behavior in a problem of elastic-plastic beam dynamics. ASME J. Appl. Mech. 52, 517-522 (1985).
2. P. S. Symonds, U. Perego, G. Borino and F. Genna, Anomalous Elastic-Plastic Response to Short Pulse Loading - An Outline of Recent Progress (edited by U. Andreus et al.). Omaggio a Giulio Ceradini - Note Scientifiche in Occasione del 70° Compleano, Dept. of Struct. and Geotechnical Engr., Univ. of Rome "La Sapienza", pp. 641-668 (1988).
3. P. S. Symonds and J. Y. Lee, Anomalous and unpredictable response to short pulse loading, in Recent Advances in Impact Dynamics of Engineering Structures (edited by D. Hui and N. Jones), Vol. 105, pp. 31-38. ASME, New York, AMD (1989).
4. J. Y. Lee, P. S. Symonds and G. Borino, Chaotic response of a two-degree-of-freedom elastic-plastic beam model to short pulse loading. ASME J. Appl. Mech. 59, 711-721 (1992).
5. G. Borino, U. Perego and P. S. Symonds, An energy approach to anomalous damped elastic-plastic response to short pulse loading. ASME J. Appl. Mech. 56, 430-438 (1989).
6. P. S. Symonds, F. Genna and A. Ciullini, Special cases in study of anomalous dynamic elastic-plastic response of beams by a simple model. Int. J. Solids Struct. 27, 299-314 (1991).
7. J. Y. Lee and P. S. Symonds, Extended energy approach to chaotic elastic-plastic response to impulsive loading. Int. J. Mech. Sci. 34, 139-157 (1992).
8. P. S. Symonds and J. Y. Lee, Fractal dimensions in elastic-plastic beam dynamics, Proc. 14th Biennial ASME Conf. on Vibrations and Noise, Albuquerque, NM, 19-22 Sept. (1993).
9. A. Carini, L. Castiglioni and P. S. Symonds, Regular and chaotic responses of a fixed-ended beam model with assigned plastic strains: (1) Illustrative examples for a Hamiltonian system. In preparation.
10. P. J. Holmes, A nonlinear oscillator with a strange attractor. Phil Trans. Roy. Soc. Lond. A292, 419-448 (1979).
11. E. H. Dowell, Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system. J. Sound Vib. 85, 333-344 (1982).
12. E. H. Dowell, Observation and evolution of chaos for an autonomous system. ASME J. Appl. Mech. 51, 664-673 (1984).
13. M. P. Paidoussis, G. X. Li and F. C. Moon, Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. J. Sound Vibr. 135, 1-19 (1989).
14. W. Duncan, Galerkin's method in mechanics and differential equations, Great Britain Aero Res. Counc., London, Report and Memo. No. 1798 (1937).
15. W. Duncan, The principles of Galerkin's method, Great Britain Aero Res. Counc., London, Report and Memo. No. 1848 (1938).
16. S. H. Crandall, Engineering Analysis, A Survey of Numerical Procedures. McGraw-Hill, New York (1956).
17. B. A. Finlayson, The Method of Weighted Residuals and Variational Principles. Math. Sci. and Engng Vol. 87. Academic Press, New York (1972).
18. Ü. Lepik, Dynamic response of elastic-plastic beams with axial constraints. Int. J. Impact Engng 15, 3-16 (1994).
19. Ü. Lepik, Impulsively loaded fully fixed-ended elastic-plastic beams by Galerkin's method. Int. J. Impact Engng 15, 17-23 (1994).
20. Y. Qian, Anomalous and chaotic responses to short pulse loading of an elastic-plastic beam by Galerkin models. Ph.D. Thesis, Division of Engineering, Brown University, Providence, RI 02912 (1994).
21. D. T. Greenwood, Principles of Dynamics, Prentice-Hall, Englewood Cliffs, NJ (1965).
22. Y. Qian and P. S. Symonds, The role of damping in chaotic oscillation of the Galerkin model of an elastic-plastic beam. In preparation.
23. P. S. Symonds and Y. Qian, Chaotic unpredictability of elastic-plastic response to impact loading, presented at Conf. on Nonlinear Vibrations, Stability, and Dynamics of Structures, Virginia Polytechnic Institute and State University, Blacksburg, VA (1994).
24. W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing. CUP, Cambridge (1990).
25. G. D. Hahn, J. F. Carney and M. H. Ray, On the numerical evaluation of the unforced response of a Duffing oscillator. ASME J. Appl. Mech. 59, 228-230 (1992).
26. Q. M. Li, L. M. Zhao and G. T. Yang, Experimental results on the counterintuitive behaviors of thin clamped beams subjected to projectile impact. Int. J. Impact Engng 11, 341-348 (1991).
27. H. Kolsky, P. Rush and P. S. Symonds, Some experimental observations of anomalous response of fully clamped beams. Int. J. Impact Engng 11, 445-456 (1991).
28. ABAQUS User's Manual, Version 5.2. Hibbitt, Karlsson & Sorensen, Inc., 1080 Main Street, Pawtucket, RI 02860 (1992).
29. M. Tabor, Chaos and Integrability in Nonlinear Dynamics, An Introduction. John Wiley, New York (1989).
30. G. Benettin, L. Galgani and J.-M. Strelcyn, Kolmogorov entropy and numerical experiments. Phys. Rev. A14, 2338-2345 (1980).
31. A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano, Determining Lyapunov exponents from a time series. Physica 16D, 285-317 (1985).
32. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd edition. Springer-Verlag, New York (1992).
33. J. W. Cooley, P. A. W. Lewis and P. D. Welch, The fast Fourier transform and its applications. IEEE Trans. Educ. 12, 27-34 (1969).
34. N. R. Lomb, Least-squares frequency analysis of unevenly spaced data. Astrophys. Space Sci. 39, 447-462 (1976).