Optimised semi-active tuned mass damper with acceleration and relative motion feedbacks

Abstract This paper presents a semi-active tuned mass damper (STMD) with acceleration and relative motion feedbacks that is optimised in the frequency domain to ensure the same vibration damping efficiency as the Den Hartog’s tuned mass damper (TMD) of up to seven times larger mass. The proposed STMD has attractive features. Firstly, its effectiveness under harmonic excitation is equivalent – also in the case of frequency detuning – to the TMD with K-times larger mass, where K, ranging from 2 to 7, is the main design parameter of the STMD. Secondly, its maximal displacement is not greater than for the TMD having the same mass. Finally, its structure is almost as simple as that of the TMD and it is formed by replacing a viscous damper in the TMD with a controllable damper, for example a magnetorheological damper. The paper presents the tuning of the feedback gains that are introduced along with their correction factors aiming at minimisation of the adverse effect of clipping the active forces. Finding the optimal correction factors together with their polynomial approximations are reported. Due to the practical importance of the proposed STMD, its complete numerical validation as well as in-depth characterisation are provided.