Dynamically stable non-linear modes of multiple subharmonic torsional vibration absorbers

Recent studies have demonstrated an arrangement of centrifugal pendulum vibration absorbers that is very effective at reducing torsional vibrations in rotating machinery. The basic system is composed of a pair of identical absorbers that are tuned to a one-half subharmonic order relative to the applied fluctuating torque. These absorbers, when moving in an out of phase manner along a particular path relative to the rotor, are capable of significantly reducing torsional vibrations of a desired order. In this paper we consider the response of systems composed of multiple pairs of these absorbers, with the goal of determining the dynamic stability of the desired response and the effects of small imperfections in the absorbers' paths. The desired response of this system is one in which the N absorbers act as a single pair, with two groups of N/2 each moving with equal amplitude but exactly out of phase with respect to one another. It is shown that this response can be made to be dynamically stable and robust to certain model uncertainties by a slight, identical overtuning of each absorber. The analytical results, obtained by the method of averaging and symmetric bifurcation theory, are confirmed by simulations for the cases with two and three pairs of absorbers.