Dynamics of autoparametric vibration absorbers using multiple pendulums

This paper analyzes the dynamics of a resonantly excited single-degree-of-freedom linear system coupled to an array of non-linear 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 non-linear response of the system. The stability and bifurcations of 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 double-mode response switches from one pendulum to the other with changing external excitation frequency. The effect of various parameters on the performance is discussed and a strategy is developed to find the most effective parameters for maximum bandwidth of operation. This results in a significant enhancement of the performance of autoparametric vibration absorbers. (C) 2001 Academic Press.