Analytical optimal design for the novel grounded three-element inertial damper. (1st December 2022) - Baduidana, Marcial; Kenfack-Jiotsa, Aurelien
Abstract: Vibrations reduction in engineering structures is necessary to ensure their safety. Several studies explore the effect of inertia of mass attached on the structure via a layout of springs and damper to suppress its vibration. However, few studies focus on the inertial amplification mechanism to further improve vibration reduction. To this end, this paper propose a kind of passive grounded three-element inertial damper based on the flywheels architecture with fulcrum fixed at ground. First, the equations of motion of the coupled system are derived. Then the analytical solution governing the primary structure-displacement in the frequency domain is shown and the natural frequencies of the system are obtained. Due to the existence of the fixed points in the frequency response curves of the primary system, the optimum tuning ratios and the optimum damping ratio are found according to the fixed points theory by Den Hartog, and the optimum grounded stiffness ratio directly connected to the earth is deduced. It is found that there are two possible design of the proposed model. However, for given mass ratio, it can be seen that the increase of magnification ratio resulted in three possible values on the grounded stiffness of the proposed designs, i.e., negative, zero, and positive. From theses three cases of grounded stiffness ratio, the designs of the proposed model with positive grounded stiffness has demonstrated the best control performance. Under optimum parameters, the results indicate that the designs of the proposed model in this paper outperforms some existing DVAs under harmonic excitation, in terms of decreases the peak vibration amplitude response of the primary system and widens the suppression bandwidth. Finally, the further comparison under random (white noise) excitation also shows that the designs of the model in this paper is superior to other DVAs in terms of smallest mean square response and smallest variance of the time history of the primary system. Highlights: A novel grounded three-element inertial damper GTEID is proposed. The optimized design parameters are fund through fixed-points theory in terms of H ∞ optimization. The control performance of GTEID with respect to other DVAs are performed in time and frequency domains. The novel GTEID provide more improvements with respect to the considered DVAs with or without negative stiffness. The GTEID in case 3 of grounded stiffness resulted in a much smaller primary system frequency response than its static response without control.