Analysis of models for viscoelastic wave propagation
Analysis of models for viscoelastic wave propagation
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DOI：
10.21042/amns.2018.1.00006
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发表时间：
2018-02
影响因子：
3.1
通讯作者：
Thomas S. Brown;Shukai Du;H. Eruslu;F. Sayas
中科院分区：
文献类型：
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作者：
Thomas S. Brown;Shukai Du;H. Eruslu;F. Sayas
摘要本文研究粘弹性固体中的波传播问题。对于固体的材料性质，我们认为经典和分数微分在时间版本的齐纳，麦克斯韦，和Voigt模型，在同一个固体内的不同模型的耦合也包括在内。在拉普拉斯域中研究每个模型的稳定性，然后将其转化为时域估计。利用半群理论，给出了一些时域结果，避免了使用拉普拉斯变换，给出了更精确的估计。我们花时间来发展和解释必要的理论，以了解我们在拉普拉斯域中解决的方程与使用因果回火分布语言编写的时域方程之间的关系。最后，我们提供了一些数值实验，突出了模型之间的一些差异，以及不同的参数如何影响结果。
Abstract We consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time versions of the Zener, Maxwell, and Voigt models, where the coupling of different models within the same solid are covered as well. Stability of each model is investigated in the Laplace domain, and these are then translated to time-domain estimates. With the use of semigroup theory, some time-domain results are also given which avoid using the Laplace transform and give sharper estimates. We take the time to develop and explain the theory necessary to understand the relation between the equations we solve in the Laplace domain and those in the time-domain which are written using the language of causal tempered distributions. Finally we offer some numerical experiments that highlight some of the differences between the models and how different parameters effect the results.