一种模拟弹性波在无界区域传播的简单多方向吸收层法
A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains
摘要：
由于在模型人工边界上反射的虚假波，使得弹性波在无限介质中传播的数值分析变得困难。这一点对于分析波在非均匀或层状固体中的传播是至关重要的。诸如吸收边界条件、无限单元或吸收边界层（例如，完美匹配层）的各种技术导致这种寄生反射的重要减少。本文提出了一种简单的吸收层方法：它是基于瑞利/柯西阻尼公式，这往往是已经在现有的有限元软件。本文首先介绍了Caughey吸收层法的原理（包括流变学解释）。然后，通过一维有限元模拟，考虑均匀和非均匀阻尼的吸收层的方法的效率。随后考虑二维模型，以评估吸收层方法对各种波型和入射波的效率。与PML方法的比较，首先进行纯P波和方法被证明是可靠的，在一个更复杂的二维情况下，涉及各种波型和入射。因此，它可以用于涉及弹性波的各种类型的问题（例如，机器振动，地震波等）。
英文摘要：
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or layered solids. Various techniques such as Absorbing Boundary Conditions, infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this paper, a simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey damping formulation which is often already available in existing Finite Element softwares. The principle of the Caughey Absorbing Layer Method is first presented (including a rheological interpretation). The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences. A comparison with the PML method is first performed for pure P-waves and the method is shown to be reliable in a more complex 2D case involving various wave types and incidences. It may thus be used for various types of problems involving elastic waves (e.g. machine vibrations, seismic waves, etc).
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