Steady-State Responses in Systems of Nearly-Identical Torsional Vibration Absorbers

In this paper we consider the steady-state response of a rotor fitted with a system of nearly identical torsional vibration absorbers. The absorbers are of the centrifugal pendulum type, which provide an effective mean of attenuating torsional vibrations of the rotor at a given order. The model considered employs absorbers that are tuned close to the order of the excitation, with an intentional mistuning that is selected by design, and imperfections among the absorbers which arise from manufacturing, wear, and other effects. It is shown that these systems can experience localized responses in which the response amplitude of one or more absorbers can become relatively large as compared to the response of the corresponding system with identical absorbers. The results are based on an exact steady-state analysis of the mathematical model, and they show that the strength of the localization depends on the average level of absorber mistuning (a design parameter), the magnitude of the relative imperfections among the absorbers, and the absorber damping. It is found that the most desirable situation is one in which the relative imperfections are kept as small as possible, and that this becomes more crucial when the levels of mistuning and damping are very small. The results of the analysis are confirmed by simulations of the fully nonlinear equations of motion of the rotor/absorber system. It is concluded that the presence of localization should be accounted for in absorber designs, since its presence makes the absorbers less effective in terms of vibration reduction and, perhaps more significantly, it can drastically reduce their operating range, since such absorbers typically have limited rattle space.