Vibration control of beam-model using tuned inerter enhanced TMD

Two vibration control devices using the tuned inerter enhanced TMD are introduced to suppress the vibration of Euler-Bernoulli beam-model in this paper. The two tuned inerter enhanced TMD systems are improved on the basis of the classical TMD system by replacing its damper element with the newly developed tuned viscous mass damper (TVMD) and tuned inerter damper (TID), respectively. The equations of motion and frequency response function of the beam-model subjected to harmonic excitation are derived by the theory of Euler-Bernoulli beam-model. Moreover, the H o , optimization technique and the extended fixed-points theory are employed to obtain the optimal parameters and closed-form solutions of TVMD and TID enhanced TMD systems, and the control performance of two enhanced systems is analyzed compared with the TMD system. The results reveal that TVMD and TID enhanced TMD systems have stronger robustness and wider control range for the resonance response. Furthermore, the enhanced systems have higher control effectiveness at a small mass ratio compared with the TMD system. Finally, the effectiveness of the enhanced systems is verified by a numerical study considering the harmonic and band-limited white noise excitations.