Parameter identification using experimental nonlinear dynamics and chaos

Abstract

Parameter identification using experimental nonlinear dynamics and chaos was applied to a piecewise-linear oscillator; application to cracked beams was attempted. Electronic integration circuitry was constructed to provide velocity and displacement data from accelerometer signals mounted on the test specimens. Data acquisition software samples velocity and displacement signals and displays a phase portrait or Poincare map on a computer screen. Experimental data show the chaotic nature of the piecewise- linear system through a phase portrait, Poincare map, frequency spectrum, and bifurcation diagram. Unstable periodic orbits were extracted from each chaotic time series obtained from the system configured with six different parameter values. The movement of the unstable periodic orbits in phase space is used to identify parameter changes in the system. Cracked beams were created by initiating fatigue cracks in aluminum beams. Several attempts to force the beams into chaos revealed how a crack half-way through a beam results in a weakly nonlinear system; such systems rarely display chaos. Recommendations on how to force a cracked beam into chaos are given.