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Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization.

Publication ,  Journal Article
Zhan, Q; Zhuang, M; Fang, Y; Liu, J-G; Liu, QH
Published in: Proceedings. Mathematical, physical, and engineering sciences
January 2019

A compact Green's function for general dispersive anisotropic poroelastic media in a full-frequency regime is presented for the first time. First, starting in a frequency domain, the anisotropic dispersion is exactly incorporated into the constitutive relationship, thus avoiding fractional derivatives in a time domain. Then, based on the Radon transform, the original three-dimensional differential equation is effectively reduced to a one-dimensional system in space. Furthermore, inspired by the strategy adopted in the characteristic analysis of hyperbolic equations, the eigenvector diagonalization method is applied to decouple the one-dimensional vector problem into several independent scalar equations. Consequently, the fundamental solutions are easily obtained. A further derivation shows that Green's function can be decomposed into circumferential and spherical integrals, corresponding to static and transient responses, respectively. The procedures shown in this study are also compatible with other pertinent multi-physics coupling problems, such as piezoelectric, magneto-electro-elastic and thermo-elastic materials. Finally, the verifications and validations with existing analytical solutions and numerical solvers corroborate the correctness of the proposed Green's function.

Duke Scholars

Published In

Proceedings. Mathematical, physical, and engineering sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

January 2019

Volume

475

Issue

2221

Start / End Page

20180610

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Zhan, Q., Zhuang, M., Fang, Y., Liu, J.-G., & Liu, Q. H. (2019). Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization. Proceedings. Mathematical, Physical, and Engineering Sciences, 475(2221), 20180610. https://doi.org/10.1098/rspa.2018.0610
Zhan, Qiwei, Mingwei Zhuang, Yuan Fang, Jian-Guo Liu, and Qing Huo Liu. “Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization.Proceedings. Mathematical, Physical, and Engineering Sciences 475, no. 2221 (January 2019): 20180610. https://doi.org/10.1098/rspa.2018.0610.
Zhan Q, Zhuang M, Fang Y, Liu J-G, Liu QH. Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization. Proceedings Mathematical, physical, and engineering sciences. 2019 Jan;475(2221):20180610.
Zhan, Qiwei, et al. “Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization.Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 475, no. 2221, Jan. 2019, p. 20180610. Epmc, doi:10.1098/rspa.2018.0610.
Zhan Q, Zhuang M, Fang Y, Liu J-G, Liu QH. Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization. Proceedings Mathematical, physical, and engineering sciences. 2019 Jan;475(2221):20180610.
Journal cover image

Published In

Proceedings. Mathematical, physical, and engineering sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

January 2019

Volume

475

Issue

2221

Start / End Page

20180610

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences