The nonlinear dynamic response of a centrifugal pendulum vibration absorber with damping in both the primary system and the pendulum is analyzed using the methods of harmonic balance and Floquet theory. Periodic solutions are approximated by the first harmonic of the response and it is shown that for low and moderate response amplitudes the resulting frequency response curves agree well with results from simulations of the full nonlinear equations of motion. Particular attention is paid to the response at the anti-resonance frequency, that is, the operating frequency for which the absorber is tuned. Cases are demonstrated for which there exists more than one stable steady-state periodic motion of the system at the anti-resonance frequency; this particular property of the system is due to nonlinear effects and cannot be captured through the traditional linear analysis. Furthermore, it is shown that for certain ranges of parameter values the only stable periodic response of the system at the anti-resonance frequency is one of large amplitude, and it cannot be predicted by linear analysis. The effects of system parameters on the shifting of the anti-resonance frequency and on the corresponding carrier amplitude are also considered.

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