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Modeling chaotic motions of a string from experimental data. (English) Zbl 0899.73008
Summary: Experimental measurements of nonlinear vibrations of a string are analyzed using new techniques of nonlinear modeling. Previous theoretical and numerical work suggested that the motions of a string can be chaotic and a Shil’nikov mechanism is responsible. We show that the experimental data is consistent with a Shil’nikov mechanism. We also reveal a period doubling cascade with a period three window which is not immediately observable because there is sufficient noise, probably of a dynamical origin, to mask the period-doubling bifurcation and the period three window.

MSC:
74-05 Experimental work for problems pertaining to mechanics of deformable solids
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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