Abstract Ground-borne vibrations are disturbing to human beings. In order to model and reduce these vibrations, the calculation of the harmonic Green's-functions of the soil is highly required since the most effective numerical solution to predict ground-borne vibration is to couple the finite-element and the boundary-element methods. In this work, we elaborate a direct space-frequency formulation that is especially suitable of material exhibiting visco-elastic behavior. Moreover, an original formulation of the Proper Generalized Decomposition (PGD) reduction technique was undertaken in the frequency-space domain. This new approach highly shortens time computing costs. It is mainly valuable when a parametric study is concerned. Moreover, the PGD resolution allows providing an off-line solution, thus, the solution is calculated only once.

中文翻译：

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层状土壤调和绿函数的简化建模计算

摘要 地传振动给人类带来了干扰。为了模拟和减少这些振动，非常需要计算土壤的谐波格林函数，因为预测地面振动的最有效数值解决方案是结合有限元和边界元方法。在这项工作中，我们详细阐述了一种直接空间频率公式，该公式特别适用于表现出粘弹性行为的材料。此外，在频空间域中进行了适当广义分解 (PGD) 约简技术的原始公式化。这种新方法大大缩短了时间计算成本。当涉及参数研究时，它主要是有价值的。此外，PGD 分辨率允许提供离线解决方案，因此，该解决方案仅计算一次。