An inerter-equipped vibrating barrier for non-invasive motion control of seismically excited structures

The vibrating barrier (ViBa) is a large-scale oscillating mass-spring-damper unit contained in the ground and tuned to mitigate the motion of surrounding structures under earthquake-induced ground shaking, without being directly in contact to them, through a structure–soil–structure interaction mechanism. Previous research showed that ViBa achieves significant seismic structural response reductions, but in doing so, it requires excessive vibrating mass, equal to the mass of the structure that aims to control or more, which hinders its practical applicability. This paper considers coupling ViBa with a grounded inerter acting as a mass amplifier to reduce ViBa mass/weight in suppressing seismically induced structural response. Attention is focused on structures amenable to modelling as single-degree-of-freedom (SDOF) damped oscillators by establishing equations of motion of a 5-DOF dynamical system of a grounded inerter-equipped ViBa (IViBa) fused with an SDOF structure and accounting for soil-structure interaction effects due to soil compliance. Optimal closed-form H _∞ and numerical H ₂ IViBa tuning are addressed minimizing the response of SDOF structure subject to harmonic resonant and to broadband/white base excitation, respectively. Numerical results pertaining to a small-scale physical ViBa prototype specimen are furnished quantifying the trade-off between IViBa mass and inertance considering non-rigid/compliant inerter-to-ground connectivity. Monotonic IViBa mass/weight reduction trend is found for fixed targeted structural performance under white stationary as well as coloured nonstationary seismic excitation for increasing inertance and for sufficiently rigid inerter-to-ground connection. It is concluded that careful engineering design of the inerter-to-ground connection minimizing compliance is most critical in fully exploiting the beneficial effects of grounded inerter for mass/weight IViBa reduction facilitating, thus, its practical implementation.