Stability of the Synchronous Response of a System of Multiple Translational Vibration Absorbers

Abstract

In this paper, a system of perfectly tuned multiple nonlinear vibration absorbers attached in parallel to a main mass under harmonic excitation is considered. The absorbers are identical and of translational type with similar cubic nonlinearities in their springs. The averaging method is used to transform the non-autonomous system of equations that describe the absorbers’ dynamics to an averaged autonomous system. The averaged system is then studied to check the stability of absorbers’ synchronous response and existence of other non-synchronous responses. The present work shows that the absorbers’ synchronous response is stable and no other responses exist when the springs in the absorbers are of hardening type. When the springs are of softening type, at certain excitation force amplitude, multi-valued synchronous responses exist. Only one is the desired response where absorbers are functioning well in suppressing vibration of the main mass. The current research work also shows jump instabilities in the synchronous response of softening springs absorbers. These findings are checked against numerical simulations of the nonlinear equations that describe the dynamics of the system considered. The effect of high nonlinearities in absorbers’ springs on their synchronous response is investigated by numerically simulating the systems’ nonlinear equations. In this situation, numerical simulations did observe some non-synchronous responses of the absorbers. This suggests that when designers of vibration absorbers decide to use multiple identical highly nonlinear absorbers, they need to be aware of the absorbers’ non-synchronous responses that may exist and have negative effects on absorbers’ task of suppressing unwanted vibrations.