Damping ratios and dynamic performance of frame structures with motion amplification devices

This study investigates the damping ratios and dynamic performance of frame structures integrated with motion amplification devices (MADs). Utilizing theoretical analyses, numerical simulations, and empirical formulas, we evaluate the damping ratios through three distinct methodologies: eigenvalue analysis, the Kelvin model, and the Maxwell model. The resulting findings indicate that these methods produce similar results under low damper viscosity; however, as damper viscosity increases, significant differences emerge. The dynamic performance, assessed under pulse-type base excitations, manifests complex trends, contradicting the traditional belief that higher damping ratios directly lead to lower maximum responses. Notably, MADs exert a substantial influence on maximum displacement and acceleration responses, implying that the damping reduction factor applicable to non-MAD structures cannot be directly applied to those with MADs. This research elucidates the nuanced role of MADs in structural dynamics and suggests that optimizing damping ratios does not necessarily minimize maximum responses in MAD systems. This study provides valuable insights for the design and optimization of structures facing dynamic loadings.