This paper concludes the theme issue on structural health monitoring (SHM) by discussing the concept of damage prognosis (DP). DP attempts to forecast system performance by assessing the current damage state of the system (i.e. SHM), estimating the future loading environments for that system, and predicting through simulation and past experience the remaining useful life of the system. The successful development of a DP capability will require the further development and integration of many technology areas including both measurement/processing/telemetry hardware and a variety of deterministic and probabilistic predictive modelling capabilities, as well as the ability to quantify the uncertainty in these predictions. The multidisciplinary and challenging nature of the DP problem, its current embryonic state of development, and its tremendous potential for life-safety and economic benefits qualify DP as a 'grand challenge' problem for engineers in the twenty-first century.
We present a nonlinear bifurcation analysis of the dynamics of an automatic dynamic balancing mechanism for rotating machines. The principle of operation is to deploy two or more masses that are free to travel around a race at a fixed distance from the hub and, subsequently, balance any eccentricity in the rotor. Mathematically, we start from a Lagrangian description of the system. It is then shown how under isotropic conditions a change of coordinates into a rotating frame turns the problem into a regular autonomous dynamical system, amenable to a full nonlinear bifurcation analysis. Using numerical continuation techniques, curves are traced of steady states, limit cycles and their bifurcations as parameters are varied. These results are augmented by simulations of the system trajectories in phase space. Taking the case of a balancer with two free masses, broad trends are revealed on the existence of a stable, dynamically balanced steady state solution for specific rotation speeds and eccentricities. However, the analysis also reveals other potentially attracting states-non-trivial steady states, limit cycles, and chaotic motion-which are not in balance. The transient effects which lead to these competing states, which in some cases coexist, are investigated.
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