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Chaotic Behavior of an Inelastic Beam

Published online by Cambridge University Press:  05 May 2011

Jiin-Po Yeh
Jiin-Po Yeh*
Affiliation:
Department of Civil Engineering, I-Shou University, Kaohsiung, Taiwan, R.O.C.
*
*Associate Professor
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Abstract

The dynamical system considered in this paper is an inelastic beam whose supports are subjected to a harmonic excitation. This paper first explores whether the system has chaotic motion. The appearance of the irregular time history, strange attractor on the Poincaré map as well as period-doubling bifurcation phenomenon strongly indicates that chaos indeed exist in this system. After finding the chaos phenomenon, this paper continues to investigate the relationship between the decay time of the autocorrelation function and the largest Lyapunov exponent. The Poincaré mapping points are chosen to be the sampled function of the discrete autocorrelation function. It's found that a power model of regression analysis can fit with good accuracy the data points, which are composed of the mapping times for the autocorrelation to decay into the square of the mean of the Poincaré points and the corresponding largest Lyapunov exponent.

Keywords

Inelastic beamChaotic motionAutocorrelation function, Lyapunov exponent
Type
Articles
Information
Journal of Mechanics , Volume 14 , Issue 4 , December 1998 , pp. 217 - 221
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1998

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References

REFERENCES

1.Moon, F. C. and Holmes, P. J., “A Magnetoelastic Strange Attractor,” Journal of Sound and Vibration, Vol. 65. No. 2, pp. 275–296 (1979).CrossRefGoogle Scholar
2.Moon, F. C. and Shaw, S. W., “Chaotic Vibrations of Beam with Non–Linear Boundary Conditions,” International Journal of Non–Linear Mechanics, Vol. 18, No. 6, pp. 465–477 (1983).Google Scholar
3.Yang, C. Y.Random Vibration of Structures, John Wiley and Sons, New York, pp. 23–59 (1986).Google Scholar
4.Moon, F. C, Chaotic and Fractal Dynamics, An Introduction for Applied Scientists and Engineers, John Wiley & Sons, Inc., New York, pp. 263–324 (1992).CrossRefGoogle Scholar
5.Singh, P. and Joseph, D. D., “Autoregressive Methods for Chaos on Binary Sequences for the Lorenz Attractor,” Physics Letters A, Vol. 135, No. 4, 5, pp. 247–253 (1989).CrossRefGoogle Scholar
6.Feeny, B. F. and Moon, F. C, “Autocorrelation on Symbol Dynamics for a Chaotic Dry–Friction Oscillator,” Physics Letters A, Vol. 141, No. 8, 9. pp. 397–400(1989).Google Scholar
7.Yeh, J. and DiMaggio, F., “Chaotic Motion of Pendulum with Support in Circular Orbit,” Journal of Engineering Mechanics, ASCE, Vol. 117, No. 2, pp. 329–347 (1991).CrossRefGoogle Scholar
8.Brigham, E. O., The Fast Fourier Transform and Its Application, Prentice-Hall, Inc., New Jersey, pp. 89–117 (1988).Google Scholar
9.Bergé, P., Pomean, Y., and Vidal, C, Order Within Chaos, Towards a Deterministic Approach to Turbulence, John–Wiley & Sons, New York, pp. 191–221 (1984).Google Scholar
10.Ayyub, B. M. and McCuen, R. H., Numerical Methods for Engineers, Prentice-Hall International, Inc., London, pp. 293–352 (1996).Google Scholar