Experimental measurements of dimensionality and spatial coherence in the dynamics of a flexible-beam impact oscillator

Abstract

Experiments on a flexible-beam impact oscillator are described in which the spatial structure of typical motions is explored. The beam is held in a fixed mount with clamped-free boundary conditions, and the beam is driven by impacts between its free end and a sinusoidally driven impactor. Bifurcation diagrams using impactor frequency and offset as the bifurcation parameter are obtained using a computer-driven data acquisition system. The dimensionality of the system is studied by analysis of delay-reconstructed time series of experimental data. Valid delay reconstructions are obtained using mutual information and false nearest neighbour algorithms, and the correlation dimensions is estimated for the resulting experimental attractors. The relation of these topological characterizations of the system to the spatial structure of the vibrations is studied using two-point spatial correlation measurements and the proper orthogonal decomposition. It is shown that over 90% of the mean square response amplitude is captured by the first proper orthogonal mode for the cases examined and that the spatial coherence measurements can be used to distinguish between responses with similar dimensionality.