DAMPING ESTIMATES FROM EXPERIMENTAL NON-LINEAR TIME-SERIES

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 Duffingʹs 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 coefficient 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.