Purpose

The finite element method (FEM) is used to calculate the two-dimensional anti-plane dynamic response of structure embedded in D’Alembert viscoelastic multilayered soil on the rigid bedrock. This paper aims to research a time-domain absorbing boundary condition (ABC), which should be imposed on the truncation boundary of the finite domain to represent the dynamic interaction between the truncated infinite domain and the finite domain.

Design/methodology/approach

A high-order ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. A new operator separation method and the mode reduction are adopted to construct the time-domain ABC.

Findings

The derivation of the ABC is accurate for the single layer but less accurate for the multilayer. To achieve high accuracy, therefore, the distance from the truncation boundary to the region of interest can be zero for the single layer but need to be about 0.5 times of the total layer height of the infinite domain for the multilayer. Both single-layered and multilayered numerical examples verify that the accuracy of the ABC is almost the same for both cases of only using the modal number excited by dynamic load and using the full modal number of infinite domain. Using the ABC with reduced modes can not only reduce the computation cost but also be more friendly to the stability. Numerical examples demonstrate the superior properties of the proposed ABC with stability, high accuracy and remarkable coupling with the FEM.

Originality/value

A high-order time-domain ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. The proposed ABC is suitable for both linear elastic and D’Alembert viscoelastic media, and it can be coupled seamlessly with the FEM. A new operator separation method combining mode reduction is presented with better stability than the existing methods.

中文翻译：

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粘弹性多层介质中标量波传播模拟的高阶吸收边界条件

目的

采用有限元法(FEM)计算刚性基岩上嵌入D'Alembert粘弹性多层土结构的二维反平面动力响应。本文旨在研究一种时域吸收边界条件（ABC），该条件应施加在有限域的截断边界上，以表示截断的无限域与有限域之间的动态相互作用。

设计/方法/方法

提出了一种用于 D'Alembert 粘弹性多层介质中标量波传播的高阶 ABC。采用新的算子分离方法和模式约简构造时域ABC。

发现

ABC 的推导对于单层是准确的，但对于多层则不太准确。因此，为了获得高精度，从截断边界到感兴趣区域的距离对于单层可以为零，但对于多层需要为无限域总层高的 0.5 倍左右。单层和多层数值例子都验证了仅使用动态载荷激发的模态数和使用无限域的全模态数的情况下 ABC 的精度几乎相同。使用缩减模式的 ABC 不仅可以降低计算成本，而且对稳定性更友好。数值例子证明了所提出的 ABC 具有稳定性、高精度和与 FEM 显着耦合的优越特性。

原创性/价值

提出了一种用于 D'Alembert 粘弹性多层介质中标量波传播的高阶时域 ABC。所提出的 ABC 适用于线弹性和 D'Alembert 粘弹性介质，并且可以与 FEM 无缝耦合。提出了一种新的算子分离方法，结合模式减少，比现有方法具有更好的稳定性。