Abstract Vibrations propagating underground may have harmful effects on adjacent buildings and human health. Recently, the notion of phononic crystals has been introduced and applied to isolate vibrations below the ground. In this paper, considering the viscoelastic material model, the complex band diagrams are suggested to analyse the transportation of vibrations in the composite foundation consist of soil and different underground structures. In the complex band diagram, the minimum imaginary part of the wave vectors is taken as the index to measure the ability of the pile group to weaken vibrations. Several types of underground barriers, including circular piles, continuous walls, and multi-layer piles, are analysed. The result shows that multi-layer piles can induce local resonance and achieve an attenuation zone at the low-frequency level. The attenuation effect of periodic barriers is then verified by transmission models. The results show that the complex band diagrams can quantitatively evaluate the isolation effect of periodic barriers, which is beyond the capability of classic band diagrams.

中文翻译：

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使用复能带图进行周期性地下屏障的振动衰减分析

摘要 地下传播的振动可能对邻近建筑物和人体健康产生有害影响。最近，声子晶体的概念被引入并应用于隔离地下的振动。在本文中，考虑到粘弹性材料模型，建议使用复杂带图来分析由土壤和不同地下结构组成的复合地基中的振动传递。在复能带图中，以波矢的最小虚部作为衡量桩群减弱振动能力的指标。分析了几种类型的地下屏障，包括圆形桩、连续墙和多层桩。结果表明，多层桩可以引起局部共振并在低频水平上实现衰减区。然后通过传输模型验证周期性屏障的衰减效应。结果表明，复杂能带图可以定量评估周期性势垒的隔离效果，超出了经典能带图的能力。