Geometric amplification of damping: Novel mechanisms for enhanced vibration control

This paper introduces damping amplifiers as an innovative solution to enhance the vibration reduction capabilities of conventional base isolators while addressing their inherent limitations. Four distinct classes of damping amplifiers are presented: ordinary damping amplifiers, compound damping amplifiers, nested damping amplifiers, and levered damping amplifiers. The governing equations of motion for these damping amplifiers and their corresponding damping amplifier base isolators are derived using Newton’s second law. H ∞ optimisation method is utilised to obtain exact closed-form expressions for the optimal design parameters of these novel isolators. A comprehensive parametric study is conducted by applying the optimal design parameters, demonstrating that damping amplifiers can amplify the effective damping of isolators by a factor of 1000 compared to conventional isolators, without introducing additional static damping into the dynamic systems. The transfer matrix is formulated to analyse the dynamic responses of isolated structures in the frequency domain, while the time history analysis is performed to validate the frequency domain results. The Newmark-beta method is mathematically integrated with isolator design to evaluate the time history results under real earthquake ground motions. Results indicate that the novel isolators exhibit an improvement of 84.22 % in performance over conventional isolators. All results are mathematically verified, ensuring the validity of the findings.