Theoretical investigation on vibration reduction characteristics of a novel foundation metaconcrete beam

The issue of low-frequency vibration problems in foundation beams is becoming increasingly serious. Therefore, it is imperative to find new methods for effectively reducing and controlling these low-frequency vibrations. This study proposes a novel foundation metaconcrete beam to address the challenge of low-frequency vibrations based on locally resonance theory. Additionally, an improved transfer matrix method (ITMM) is proposed to quickly and effectively calculate the bandgap of foundation metaconcrete beam. The validity of the ITMM is verified through the plane wave expansion method (PWEM), and transmission characteristics are fully analyzed using the spectral element method (SEM). Furthermore, the influences of geometric and material parameters of the foundation metaconcrete beam on band structures and transmission functions are investigated in detail. The results show that the proposed foundation metaconcrete beam exhibits multiple bandgaps, and can effectively attenuate low-frequency vibrations. These bandgaps can be tailored by appropriately adjusting relevant parameters. The foundation properties determine the formation of the first bandgap, the damping ratio of the resonator has double effects on band structures, the mass ratio of the resonator is crucial in adjusting these bandgaps, and the axial force can adjust the attenuation capability of the first bandgap.