Semi-active dynamic vibration absorbers have one or both of the following capabilities: (a) initial displacements set to non-zero values and (b) damping adjustable in real time. Such devices are feasible because of the development of electro-rheological fluids and electromagnetic dampers. Experimental tests have shown that semi-active vibration absorbers are suitable for controlling the impulse response of structures. The contribution of this paper is in developing an analytical theory for the optimal control algorithms for semi-active absorbers. The theory is first developed for a single-degree-of-freedom structure, and is then generalized to continuous structures. Closed form analytical results are derived to provide insight into the complex interaction between the structure and absorber. The results are used directly to solve the design problem without recourse to numerical optimization.
The control algorithms are described by simple expressions which are explicitly in terms of the current state of the system. Several algorithms are proposed which differ according to the information required on the impact load and system state. Semi-active vibration absorbers are found to be substantially more effective than conventional passive vibration absorbers. They are limited primarily by the maximum displacement of the absorber and the accuracy of the modal state measurements of the structure. The devices are proven to be unconditionally stable, regardless of the accuracy of the modal state information.