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Acta Mechanica

, Volume 230, Issue 12, pp 4321–4340 | Cite as

Fractional Burgers wave equation

  • Ljubica Oparnica
  • Dušan ZoricaEmail author
  • Aleksandar S. Okuka
Original Paper
  • 79 Downloads

Abstract

Thermodynamically consistent fractional Burgers constitutive models for viscoelastic media, divided into two classes according to model behavior in stress relaxation and creep tests near the initial time instant, are coupled with the equation of motion and strain forming the fractional Burgers wave equations. The Cauchy problem is solved for both classes of Burgers models using an integral transform method, and an analytical solution is obtained as a convolution of the solution kernels and initial data. The form of the solution kernel is found to be dependent on model parameters, while its support properties imply infinite wave propagation speed for the first class and finite speed for the second class. Spatial profiles corresponding to the initial Dirac delta displacement with zero initial velocity display features which are not expected in wave propagation behavior.

Notes

Acknowledgements

This work is supported by the Serbian Ministry of Education, Science and Technological Development under Grants 174005 and 174024, by the Provincial Secretariat for Higher Education and Scientific Research under Grant 142-451-2102/2019, as well as by FWO Odysseus project of Michael Ruzhansky.

Supplementary material

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EducationUniversity of Novi SadSomborSerbia
  2. 2.Department of Mathematics: Analysis, Logic and Discrete MathematicsUniversity of GentGentBelgium
  3. 3.Mathematical Institute, Serbian Academy of Arts and SciencesBelgradeSerbia
  4. 4.Department of Physics, Faculty of SciencesUniversity of Novi SadNovi SadSerbia
  5. 5.Department of Mechanics, Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

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