DYNAMICS OF AUTOPARAMETRIC VIBRATION ABSORBERS USING MULTIPLE PENDULUMS

• Published in: Journal of sound and vibration Vol. 246; no. 1; pp. 115 - 135
• Main Authors: VYAS, A., BAJAJ, A.K.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 06-09-2001; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Parametric excitation; Averaging method; Equation of motion; Self excitation; Dynamic stability; Vibration damper; Vibration control; Passive system; Hopf bifurcation; Modeling; Steady state
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.2001.3616

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.