Abstract
In this paper, a system consisting of multiple perfectly tuned identical translational vibration absorbers, having both hardening and softening springs, attached to a main mass under harmonic excitation is considered. The existence of absorbers' synchronous and non-synchronous responses is checked. The method of averaging is employed to reach to the averaged autonomous equations of motion that describe the dynamics of the absorbers. A graphical method is then employed to check the existence of different responses of the absorbers. It is found that for absorbers with hardening springs, only one synchronous response of the absorbers occurs and no other responses take place. However, for the case of absorbers with softening springs, other responses were found to exist. These include multi-valued synchronous responses and a jump instability. These findings are in agreement with those of another study by the author where a similar system was considered using different approach.