zbMATH — the first resource for mathematics

Identifying, evaluating, and controlling dynamical integrity measures in non-linear mechanical oscillators. (English) Zbl 1153.70307
Summary: The erosion curves for the Helmholtz, the Duffing and rigid block oscillators are constructed to investigate the loss of integrity in different mechanical systems. Various definitions of safe basin and integrity measures are reviewed, compared with each other and applied to the considered cases. A control method aimed at shifting the erosion profiles towards larger excitation amplitudes is considered, too, and its main features are discussed in depth.

70K99 Nonlinear dynamics in mechanics
93C85 Automated systems (robots, etc.) in control theory
Full Text: DOI
[1] Fielder, W.T.; Virgin, L.N.; Plaut, R.H., Experiments and simulation of overturning of an asymmetric rocking block on an oscillating foundation, Eur. J. mech. A, 16, 905-923, (1997) · Zbl 0894.73125
[2] Lansbury, A.N.; Thompson, J.M.T.; Stewart, H.B., Basin erosion in the twin-well Duffing oscillatortwo distinct bifurcation scenarios, Int. J. bifurcat. chaos, 2, 505-532, (1992) · Zbl 0878.34034
[3] Lenci, S.; Rega, G., Optimal control of homoclinic bifurcationtheoretical treatment and practical reduction of safe basin erosion in the Helmholtz oscillator, J. vib. control, 9, 281-316, (2003) · Zbl 1156.70314
[4] Lenci, S.; Rega, G., Optimal control of nonregular dynamics in a Duffing oscillator, Nonlinear dyn., 33, 71-86, (2003) · Zbl 1038.70019
[5] S. Lenci, G. Rega, Overturning thresholds of a rigid block subjected to harmonic excitation: computer simulations and analytical treatment, in: Proceedings of the 2003 ASME International Mechanical Engineering Congress and R&D Expo, Washington, DC, USA, November 16-21, 2003 (CD-Rom).
[6] S. Lenci, G. Rega, A dynamical systems analysis of the overturning of rigid blocks, in: CD-Rom Proceedings of the XXI International Conference of Theoretical and Applied Mechanics, IPPT PAN, ISBN 83-89687-01-1, Warsaw, Poland, August 15-21, 2004. · Zbl 1084.70003
[7] S. Lenci, G. Rega, Numerical aspects in the optimal control and anti-control of rigid block dynamics, in: Proceedings of the Sixth World Conference on Computational Mechanics, WCCM VI, Beijing, China, September 5-10, 2004. · Zbl 1060.93527
[8] Soliman, M.S.; Thompson, J.M.T., Integrity measures quantifying the erosion of smooth and fractal basins of attraction, J. sound vib., 135, 453-475, (1989) · Zbl 1235.70106
[9] Szemplinska-Stupnicka, W., Cross-well chaos and escape phenomena in driven oscillators, Nonlinear dyn., 3, 225-243, (1992)
[10] Thompson, J.M.T., Chaotic behavior triggering the escape from a potential well, Proc. roy. soc. London A, 421, 195-225, (1989) · Zbl 0674.70035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.