Optimum design for a novel inerter-based vibration absorber with an amplified inertance and grounded stiffness for enhanced vibration control

This article presents the results of the study of a novel inerter-based vibration absorber with an amplified inertance mechanism and grounded stiffness, to control excessive vibrational movements of an excited primary structure. The inerter vibration absorber used in this study acts as a passive tuned inerter damper. An undamped primary structure model with a single degree of freedom controlled by the proposed inerter vibration absorber is developed and used to derive the equations of motion of the coupled system. The optimum frequency ratio and the optimum damping ratio of inerter vibration absorber are found using the fixed point theory for harmonic force-excited primary structures. Then, the optimum grounded stiffness ratio is deduced. Based on the inclusion of an amplified inertance mechanism, it is found that for given inertance mass ratio, the change in the amplification ratio results in three cases for the optimum grounded stiffness ratio, that is, negative, zero, and positive. From these three cases of grounded stiffness, the inerter vibration absorber with positive grounded stiffness has demonstrated the best control performance. Under optimum parameters, the results indicate that the inerter vibration absorber in this article outperforms some existing inerter vibration absorbers under the harmonic excitation, in terms of decreases in the peak vibration response of the primary system and widens the suppression bandwidth. Finally, the further comparison among the inerter vibration absorber under random (white noise) excitation also shows that the model in this article is superior to other inerter vibration absorbers in terms of smallest mean square response and smallest variance of the time history of the primary system.