Analytical Research on a Locally Resonant Periodic Foundation for Mitigating Structure-Borne Vibrations from Subway

TL;DR

This paper proposes a locally resonant periodic foundation with negative stiffness to effectively reduce ultra-low frequency vibrations from subways, considering soil and superstructure interactions, providing an analytical approach for vibration mitigation.

Contribution

It introduces a novel LRPF with negative stiffness for subway vibration mitigation and develops an analytical model considering soil and superstructure coupling.

Findings

The LRPF can create a quasi-static band gap at ultra-low frequencies.

Adjusting negative stiffness effectively attenuates superstructure vibrations.

Soil compliance influences the coupled resonance frequencies and mitigation performance.

Abstract

Filtering properties of locally resonant periodic foundations (LRPFs) have inspired an innovative direction towards the mitigation of structural vibrations. To mitigate the structure-borne vibrations from subways, this study proposes an LRPF equipped with a negative stiffness device connecting the resonator and primary structure. The proposed LRPF can exhibit a quasi-static band gap covering the ultra-low frequency range. These frequency components have the properties of strong diffraction and low attenuation and contribute the most to the incident wave fields impinging on nearby buildings. By formulating the interaction problem between the tunnel-ground and LRPF-superstructure systems, the mitigation performance of the proposed LRPF is evaluated considering the effects of soil compliance and superstructure. The performance depends on the dynamic properties of the ground, foundation, and superstructure as well as their coupling. Transmission analyses indicate that the superstructure responses can be effectively attenuated in the quasi-static band gap by adjusting the negative stiffness. Considering the coupling of the flexible ground, the peak responses of the LRPF-superstructure system occur not only at its eigenfrequencies but also at coupled resonance frequencies due to the contribution of the soil compliance. This study provides an analytical tool for mitigating the structure-borne vibrations from subways with the LRPF.