Effectiveness of semi-active tuned mass dampers under harmonic excitation

The control effectiveness of a semi-active tuned mass damper (STMD) with variable damping under harmonic excitation is studied. An optimal control law governing the variation of damping of the damper is derived using the optimal control theory. A situation in which the damping can be varied within a certain range is included. Employing the numerical technique, the responses of a single-degree-of-freedom (SDOF) structure coupled with an STMD are investigated. The control effectiveness of the STMD is evaluated by comparing the structureʹs transient and steady-state responses with those of the structure coupled with a tuned mass damper (TMD). It is found that, under harmonic excitation, the vibration suppression by an STMD is significantly superior to that of a conventional passive TMD in both transient and steady-state responses. This improvement is equivalent to an increase of the TMDʹs mass by about four times.