期刊
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
卷 13, 期 3, 页码 1030-1043出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2011.02.001
关键词
Poroelastic materials; Laplace transforms; Blot's equations; Numerical methods; Fast Fourier transforms
资金
- National Science Foundation [DMS-0920850]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0920850] Funding Source: National Science Foundation
A one-dimensional model of an in vitro experiment, in which a specimen of cancellous bone is immersed in water and insonified by an ultrasonic pulse, is considered. The modification of the poroelastic model of Blot due to Johnson et al. [D.L. Johnson, J. Koplik, R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J. Fluid Mech. 176 (1987) 379-402] is used for the cancellous bone segment. By working with series expansions of the Laplace transform in terms of travel-time exponentials, a series of transfer functions for the reflection and transmission of fast and slow waves at the fluid-poroelastic interfaces are derived. The approach obviates numerical solution beyond the discretization involved in the use of the fast Fourier transform. (C) 2011 Published by Elsevier Ltd
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