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DAMPING ESTIMATES FROM EXPERIMENTAL NON-LINEAR TIME-SERIES

โœ Scribed by J.M. NICHOLS; L.N. VIRGIN; H.P. GAVIN

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
345 KB
Volume
246
Category
Article
ISSN
0022-460X

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โœฆ Synopsis

This paper seeks to illustrate the utility of the Lyapunov spectrum in estimating the damping of an experimental non-linear system. A mechanical model of Du$ng's equation operating in the chaotic regime is used to generate a single observable. Using standard techniques from non-linear time-series analysis, the complete Lyapunov spectrum is estimated. The sum of these exponents may, via the divergence theorem, be related directly to the coe$cient of viscous damping. Estimations are performed in this manner for both a three-and four-dimensional response and results are compared to estimates taken from two linear-based techniques. The indication is that use of the Lyapunov spectrum to obtain quantitative damping estimates is a comparable alternative to methods requiring transient data or detailed knowledge of the dynamics.

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