Abstract
The characteristics of three nonlinear dynamic absorbers attached to structures under horizontal-harmonic excitation are investigated. The frequency response curves are theoretically determined using van del Pol's method. It is clarified from the theoretical analysis that a part of response curves, which are stable in a system with one nonlinear dynamic absorber, change to be unstable and that five branches for steady state solutions may appear. The absorbers vibrate in different amplitude and the system may encounter saddle-node bifurcations and Hopf bifurcations depending on the values of the system parameters. The excitation frequency range and the values of the system parameters for amplitude modulated motion appearing after Hopf bifurcations can be determined by bifurcation sets.
