Frequency-dependent viscoelasticity effects on the wave attenuation performance of multi-layered periodic foundations

In this paper, layered periodic foundations (LPFs) are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains. Three different unit-cells, i.e., 2-layer, 4-layer, and 6-layer unit-cells, comprising concrete/rubber, concrete/rubber/steel/rubber, and concrete/rubber/steel/rubber/lead/rubber materials, respectively, are taken into account. Also, the viscoelasticity behavior of the rubber is modeled with two factors, i.e., a frequency-independent (FI) loss factor and a linear frequency-dependent (FD) loss factor. Following the extraction of the complex dispersion curves and the identification of the band gaps (BGs), the simulations of wave transmission in the time and frequency domains are performed using the COMSOL software. Subsequent parametric studies evaluate the effects of the rubber viscoelasticity models on the dispersion curves and the wave transmission for the longitudinal and transverse modes. The results show that considering the rubber viscoelasticity enhances the wave attenuation performance. Moreover, the transverse-mode damping is more sensitive to the viscoelasticity model than its longitudinal counterpart. The 6-layer unit-cell LPF exhibits the lowest BG, ranging from 4.8 Hz to 6.5 Hz.