Starting from the two-component representation technique for damping of structures the possible increase in damping efficiency obtained by introducing collocated active damping is illustrated. The two-component representation of the damped vibration mode is constructed as a linear combination of the undamped mode shape and the mode shape obtained by locking the damper. This leads to a simple set of equations of motion, which in the frequency domain gives an accurate solution for the complex-valued natural frequency, and thereby for the modal damping. This solution shows that attainable damping increases with the phase angle of the damper, and that improved damping efficiency thus follows from the ability of an active device to produce a force acting ahead of velocity. Phase lead is equivalent to negative stiffness, and the effect of negative stiffness is illustrated by a radiation condition on a cable. Simple linear filters, with desirable low-pass properties, are presented as simple means for implementing phase lead.
Journal of Sound and Vibration, 2006, Vol 293, Issue 1-2