Energy Spectrum Study and Optimal Design of an Inerter-Based Structure Considering the Underlying Soil

As a classic inerter system, the tuned viscous mass damper (TVMD) has been proven to be efficient for vibration control. It is characterized by an amplification effect, where the deformation of the dashpot in the TVMD can be larger than that of a single dashpot, providing enhanced energy dissipation. However, the contribution of this system to the enhancement of the energy dissipation quantity and vibration control remains unclear. To deal with this, and considering the underlying soil, this study proposes a systematic energy spectrum analysis framework for the single-degree-of-freedom (SDOF) element controlled by a tuned viscous mass damper (TVMD) in order to reveal the energy characteristics of the TVMD and develop an optimal energy dissipation enhancement-based design. The proposed energy spectrum analysis includes ground motion propagation and energy balance analysis. Considering the underlying soil, energy balance analysis is performed for a series of SDOF elements connected to the TVMD, which yields a fitted input energy spectrum for optimal design of the TVMD. Extensive parametric analysis reveals energy characteristics of the TVMD compared with a single dashpot, yielding an optimal energy dissipation enhancement-based design. The findings of this study show that by considering the soil underneath the inerter-based structure, the developed energy spectrum analysis quantifies the degree of energy dissipation enhancement effect of the TVMD. The proposed design is effective in guaranteeing the target of displacement control, which optimizes the efficiency and quantity of the TVMD for energy dissipation, relieving the energy-dissipation burden on the primary element.