Semi-active tuned mass dampers with nonlinear control

A semi-active tuned mass damper (TMD) is proposed for controlling the free-vibration impulse response of structures. It is assumed that (i) the initial displacement for the TMD spring can be set to non-zero values and (ii) the viscous damping coefficient for the TMD damping can be adjusted. The contribution of the paper is in developing an analytically-based theory for the optimal control algorithms for TMDs to suppress transient vibrations. The extensive use of closed-form analytical results provides useful insight into the complex interaction between the structure and TMD. The algorithms are nonlinear, but given by simple expressions explicitly in terms of the current state of the system. The semi-active TMD is found to be far more effective than conventional passive devices.