Abstract
The dynamic response of a system composed of a rotor subject to engine-order torsional excitation and fitted with multiple identical centrifugal pendulum vibration absorbers is considered. The absorbers' desired synchronous response can lose stability in two ways: a jump behavior, which maintains the symmetry associated with absorber synchronicity, and loss of synchronicity via a symmetry-breaking response bifurcation. In this paper, we review the loss of stability of the synchronous response and consider the post-critical system response for the case of general path absorbers. We investigate the resulting post-bifurcation responses, which consist of two groups of absorbers each of which respond in a mutually synchronous manner within the group. By considering permutations of these responses, it is found that there are many such responses with some being dynamically stable. This analytical study is based on the method of averaging applied to a dimensionless form of the equations of motion. It is found that the initial symmetry-breaking bifurcations are generally subcritical, and the subsequent bifurcations can result in situations where several steady-state responses are possible over a wide range of operating conditions. Some of these responses are localized in nature leading to a significant reduction in feasible operating range of the system. It is shown that non-synchronous responses can exist at very small torque levels. Absorber overtuning widens the range of stable synchronous response, but it also widens the range where stable non-synchronous responses coexist with the stable synchronous response. These results provide important considerations for the tuning of identical absorber systems.