Towards chaos in vibrating damaged structures - Part I: Theory and period doubling cascade

Journal of Applied Mechanics, Transactions ASME

Volumn 72, Issue 4, 2005, Pages 511-518

  Carpinteri, Alberto ^a   Pugno, Nicola ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CRACK INITIATION; DYNAMICS; FOURIER TRANSFORMS; FUNCTIONS; INTEGRATION; NATURAL FREQUENCIES; OSCILLATIONS;

HARMONIC LOADING; LINEAR STIFFNESS; NON-DESTRUCTIVE TESTING; NONLINEAR STRUCTURES;

CHAOS THEORY;

EID: 23844445624     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1934582     Document Type: Article

References (14)

1. Gudmundson, P., 1983, "The Dynamic Behaviour of Slender Structures with Cross-Sectional Cracks," J. Mech. Phys. Solids, 31, pp. 329-345.
2. Friswell, M. I., and Penny, J. E. T., 1992, "A Simple Nonlinear Model of a Cracked Beam," Proc. X Int. Modal Analysis Conf., pp. 516-521.
3. Krawczuk, M., and Ostachowicz, W., 1994, "Forced Vibrations of a Cantilever Timoshenko Beam With a Closing Crack," ISMA 19, pp. 1067-1078.
4. Ostachowicz, W., and Krawczuk, M., 1990, "Vibration Analysis of a Cracked Beam," Comput. Struct., 36, pp. 245-250.
5. Crespo, P., Ruotolo, R., and Surace, C., 1996, "Non-Linear Modelling of Cracked Beam," Proc. of XIV Int. Modal Analysis Conf., pp. 1017-1022.
6. Ruotolo, R., Surace, C., Crespo, P., and Storer, D., 1996, "Harmonic Analysis of the Vibrations of a Cantilevered Beam with a Closing Crack," Comput. Struct., 61, pp. 1057-1074.
7. Carpinteri, Al., and Carpinteri, An., 1984, "Softening and Fracturing Process in Masonry Arches," Proc. of the Sixth Int. Brick Masonry Conf., pp. 502-510.
8. Pugno, N., Surace, C., and Ruotolo, R., 2000, "Evaluation of the Non-Linear Dynamic Response to Harmonic Excitation of a Beam with Several Breathing Cracks," J. Sound Vib., 235, pp. 749-762.
9. Brandon, J. A., and Sudraud, C., 1998, "An Experimental Investigation into the Topological Stability of a Cracked Cantilever Beam," J. Sound Vib., 211, pp. 555-569.
10. Carpinteri, A., and Pugno, N., 2002, "Complexity of the Nonlinear Forced Vibrations in Multicracked Structures," Proc. of the IX Int. Con. On Sound & Vibration, July 8-11, Orlando, FL, (CD-ROM N. P114-1).
11. Feigenbaum, M. J., 1978, "Quantitative Universality for a Class of Nonlinear Transformations," J. Stat. Phys., 19 (1), 25-52.
12. Feigenbaum, M. J., 1983, "Universal Behavior in Nonlinear Systems," Physica D, 7, pp. 16-39.
13. Linsay, P. S., 1981, "Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator," Phys. Rev. Lett., 47, pp. 1349-1352.
14. Li, Q. S., 2003, "Vibratory Characteristics of Timoshenko Beams with Arbitrary Number of Cracks," J. Eng. Mech., 129, pp. 1355-1359.