The paper discusses chaotic response behavior of a beam model whose ends are fixed, so that shallow arch action prevails after moderate plastic straining has occurred due to a short pulse of transverse loading. Examples of anomalous displacement-time histories of a uniform beam are first shown. These motivated the present study of a two-degree-of-freedom model of Shanley type. Calculations confirm these behaviors as symptoms of chaotic unpredictability. Evidence of chaos is seen in displacement-time histories, in phase plane and power spectral diagrams, and especially in extreme sensitivity to parameters. The exponential nature of the latter is confirmed by calculations of conventional Lyapunov exponents and also by a direct method. The two-degree-of-freedom model allows use of the energy approach found helpful for the single-degree-of-freedom model (Borino et al., 1989). The strain energy is plotted as a surface over the displacement coordinate plane, which depends on the plastic strains. Contrasting with the single-degree-of-freedom case, the energy diagram illuminates the possibility of chaotic vibrations in an initial phase, and the eventual transition to a smaller amplitude nonchaotic vibration which is finally damped out. Properties of the response are further illustrated by samples of solution trajectories in a fixed total energy plane and by related Poincare section plots.
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December 1992
Research Papers
Chaotic Responses of a Two-Degree-of-Freedom Elastic-Plastic Beam Model to Short Pulse Loading
J.-Y. Lee
,
J.-Y. Lee
Division of Engineering, Brown University, Providence, RI 02912
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P. S. Symonds
,
P. S. Symonds
Division of Engineering, Brown University, Providence, RI 02912
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G. Borino
G. Borino
Division of Engineering, Brown University, Providence, RI 02912
Search for other works by this author on:
J.-Y. Lee
Division of Engineering, Brown University, Providence, RI 02912
P. S. Symonds
Division of Engineering, Brown University, Providence, RI 02912
G. Borino
Division of Engineering, Brown University, Providence, RI 02912
J. Appl. Mech. Dec 1992, 59(4): 711-721 (11 pages)
Published Online: December 1, 1992
Article history
Received:
March 28, 1991
Revised:
January 4, 1992
Online:
March 31, 2008
Citation
Lee, J., Symonds, P. S., and Borino, G. (December 1, 1992). "Chaotic Responses of a Two-Degree-of-Freedom Elastic-Plastic Beam Model to Short Pulse Loading." ASME. J. Appl. Mech. December 1992; 59(4): 711–721. https://doi.org/10.1115/1.2894033
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Cited By
Closure to “Discussions of ‘Creep and Relaxation of Oxygen-Free Copper’” (1943, ASME J. Appl. Mech., 10, pp. A240–A241)
J. Appl. Mech (December 1943)
Discussion: “Creep and Relaxation of Oxygen-Free Copper” (Davis, E. A., 1943, ASME J. Appl. Mech., 10, pp. A101–A105)
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Discussion: “A Principle of Maximum Plastic Resistance” (Sadowsky, M. A., 1943, ASME J. Appl. Mech., 10, pp. A65–A68)
J. Appl. Mech (December 1943)
Discussion: “Creep and Relaxation of Oxygen-Free Copper” (Davis, E. A., 1943, ASME J. Appl. Mech., 10, pp. A101–A105)
J. Appl. Mech (December 1943)
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