Quantitative Analysis of Phase Trajectory as the Information about Technical Condition of the Object

The paper aims to describe the potential use of phase trajectory for damage detection of structural components. The attractor of the examined trajectory is a static equilibrium point of the element being diagnosed. Two different damage indices are proposed to evaluate the severity of damage in the diagnosed component. The first one refers to distance between a point on a trajectory and the point which is the attractor of the trajectory. The other one relates to linearity of the Poincaré map. Effectiveness of the proposed method was evaluated on: a simple model with two degrees of freedom, data from the finite element method model of a cantilever beam with a crack, and experimental data for a cracked plate. With the proposed method, the damage can be quickly and effectively detected. By comparing the current trajectory with that from the previous diagnostic test, it is possible to establish if the nature of crack is either propagating or stationary.