Stability Analysis of Multiple Delayed Resonator Vibration Absorbers

Abstract

Abstract This paper is on the use of multiple identical Delayed Resonator (DR), a recently introduced active vibration absorber, in suppressing tonal vibration of multi-degree-of-freedom mechanical structures. The DR methodology forces the conventional mass-spring-damper passive absorbers into marginally stable resonators which absorb all the vibratory energy at their points of attachment. Control forces in the form of proportional acceleration feedback with variable gains and time delays are considered here. Elimination of tonal vibration, real-time tunability, and stand-alone nature of these actively controlled absorbers are already proven features. The stability of the primary structure combined with multiple DR’s is addressed in this paper, following a stability chart strategy. A “peeling-off” procedure is adopted to eliminate successively the highest order delay terms in the characteristic equation of the system at each step. Consequently, the stability charts are constructed to reveal the operable zones. An example case of two identical DR’s on a 3-DOF system is presented.