Minimization of the mean square velocity response of dynamic structures using an active-passive dynamic vibration absorber

An optimal design of a hybrid vibration absorber (HVA) with a displacement and a velocity feedback for minimizing the velocity response of the structure based on the H(2) optimization criterion is proposed. The objective of the optimal design is to reduce the total vibration energy of the vibrating structure under wideband excitation, i.e., the total area under the velocity response spectrum is minimized in this criterion. One of the inherent limitations of the traditional passive vibration absorber is that its vibration suppression is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The active element of the proposed HVA helps further reduce the vibration of the controlled structure, and it can provide very good vibration absorption performance even at a low mass ratio. Both the passive and active elements are optimized together for the minimization of the mean square velocity of the primary system as well as the active force required in the HVA. The proposed HVA was tested on single degree-of-freedom (SDOF) and continuous vibrating structures and compared to the traditional passive vibration absorber.