Abstract

This paper analyzes the dynamics of a resonantly excited single degree-of-freedom linear system coupled to an array of nonlinear autoparametric vibration absorbers (pendulums). The case of a 1:1:…:2 internal resonance between pendulums and the primary oscillator is studied. The method of averaging is used to obtain first-order approximations to the nonlinear response of the system. The stability and bifurcations of the equilibria of the averaged equations are computed. It is shown that the frequency interval of the unstable single-mode response, or the absorber bandwidth, can be enlarged substantially compared to that of a single pendulum absorber by adjusting individually the internal mistunings of the pendulums. Use of multiple pendulums is also shown to engender degenerate bifurcations as the coupled-mode response “switches” from one pendulum to the other with changing external excitation frequency. This results in a significant enhancement of the performance of autoparametric vibration absorbers.

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