Abstract
The characteristics of two nonlinear vibration absorbers simultaneously attached to structures under harmonic excitation are investigated. The frequency response curves are theoretically determined using Andronov and Witt's method. It is found from the theoretical analysis that pitchfork bifurcations may appear on a part of response curves which are stable in a system with one nonlinear dynamic absorber. Three steady state solutions with different amplitude appear just after the pitchfork bifurcation. After that, Hopf bifurcations may occur depending on the values of the system parameters and amplitude modulated motion including a chaotic vibration appears after the Hopf bifurcation. The Lyapunov exponent is numerically calculated to prove the chaotic vibration. In addition, it is also found that only Hopf bifurcations, not pitchfork bifurcations, can occur even when the linear and nonlinear dynamic absorbers are combined.
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