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On the propagation of waves through porous solids
Published in Elsevier BV
Volume: 40
Issue: 2-3
Pages: 373 - 380

This note reexamines Biot's model for the propagation of acoustic waves in a material such as cohensionless sand, infused with a fluid, within the context of mixture theory. Instead of the standard entropy equation that is used in mixture theory, an inequality for the viscous dissipation is employed here due to a conceptual difficulty that one encounters in applying the standard equation to a mixture of sand and a fluid. The wave equations are reformulated by taking the velocity field, instead of the displacement, for the fluid as a primary quantity. By recognizing and thereby exploiting the dependence of the stored energy of the sand on the pore fluid pressure and choosing an appropriate form for the rate of dissipation, a set of governing equations are obtained which are equivalent to those derived by Biot [J. Acoust. Soc. Am. 28(1956) 168, 179; J. Appl. Phys. 33(1962) 1482]. A differential equation for the pore fluid pressure is derived and the effects of drag and virtual mass are dealt with in a unified fashion. The procedure allows us to develop generalizations to Biot's equations in a rational manner.

About the journal
JournalData powered by TypesetInternational Journal of Non-Linear Mechanics
PublisherData powered by TypesetElsevier BV
Open AccessNo