Abstract
This work overviews and continues recent investigations of the authors [1, 2] on the dynamical integrity of nonlinear mechanical systems and other oscillators. In fact, it has been realized that attractors must be paralleled by uncorrupted basins for safe practical applications [2, 3]. Eroded basins constitute a critical state for the structure corresponding to its impending failure, which can be instantaneous in the presence of perturbations or uncertainties. On the other hand, using the structure only when erosion is prevented may be too much conservative, because it can actually survive safely well above the relevant threshold if the erosion is not sharp.
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References
Lenci, S. and Rega, G., A unified control framework of the nonregular dynamics of mechanical oscillators,” J. Sound Vibr., vol. 278, 1051–1080, 2004.
Rega, G. and Lenci, S., Identifying, Evaluating, and Controlling Dynamical Integrity Measures in Nonlinear Mechanical Oscillators, in press, Nonlinear Analysis, T.M.&A, 2005.
Thompson, J.M.T., Chaotic Behavior Triggering the Escape from a Potential Well, Proc. Royal Soc. London A, vol. 421, 195–225, 1989.
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Lenci, S., Rega, G. (2006). Dynamical Integrity of Nonlinear Mechanical Oscillators. In: Gdoutos, E.E. (eds) Fracture of Nano and Engineering Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4972-2_401
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DOI: https://doi.org/10.1007/1-4020-4972-2_401
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4971-2
Online ISBN: 978-1-4020-4972-9
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