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The design of active TMD for multi-degree-of-freedom systems subjected to second order coloured noise excitation is considered using the linear quadratic optimal theory. A detailed numerical study is carried out for a 2-DOF system. It is shown that the effectiveness of active TMD is better than the one of passive TMD.

Among the fundamental concepts for structure control, passive control systems have a significant role since they do not require additional energies produced by actuator. The basic of passive control is to incorporate a secondary system into the primary structure in order to transfer a part of the vibration energy of the primary system into the secondary one. In the paper the design of an optimal tuned mass damper (TMD) for a structure subjected to second order coloured noise excitation is investigated in order to minimize the sum of response mean squares of components of the primary system with a given ranking priority.

A Dynamic Vibration Absorber (DVA) is appropriate equipment for vibration control in many kinds of engineering. In general, there are two main types of DVAs: the passive DVAs and the active DVAs. The paper presents a design of an active mass-spring-inverted pendulum DVA for the inverted pendulum type structure in case the external force is white noise process. The design is based on the optimum passive DVA as carried out in [4] and apply the optimum control force by minimizing the performance index. Numerical simulation which is done for an inverted pendulum structure in the ocean in three cases without DVA, with passive DVA, with active DVA shows that the active DVA is better than the passive one.