Beyond Natural Sciences
Applied Mathematics and Nonlinear Sciences

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Open Access
Available online: March 09, 2018

Analysis of models for viscoelastic wave propagation

Thomas Brown, Shukai Du, Hasan Eruslu, Francisco-Javier Sayas
Volume 3 - Issue 1.     Year 2018.     Pages 55–96.

DOI: 10.21042/AMNS.2018.1.00006

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.

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ISSN:
2444-8656
Category:
Applied Mathematics, Nonlinear Sciences

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