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A symmetric weak form of Biot's equations based on redundant variables representing the fluid, using a Helmholtz decomposition of the fluid displacement vector field
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
2010 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 84, no 13, 1613-1637 p.Article in journal (Refereed) Published
Abstract [en]

A novel symmetric weak formulation of Biot's equations for linear acoustic wave propagation in layered poroelastic media is presented. The primary variables used are the frame displacement, the acoustic pore pressure, the scalar potential and the vector potential obtained from a Helmholtz decomposition of the fluid displacement. Also a symmetric weak form based on the frame displacement, the pore pressure and the fluid displacement is obtained as an intermediate result. hp finite element simulations of a double leaf partition based on this new weak formulation is verified against simulation results from the classical frame displacement, fluid displacement formulation and a frame displacement pore pressure formulation. All three formulations simulated, displays the same rate of convergence with respect to finite element bases polynomial degree. The novel formulation also extends a previously published frame displacement, pore pressure, scalar fluid displacement potential formulation with an implicit irrotational fluid displacement assumption to a full representation of Biot's equations.

Place, publisher, year, edition, pages
2010. Vol. 84, no 13, 1613-1637 p.
Keyword [en]
weak formulation, finite element, porous material, Biot, acoustics
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-28593DOI: 10.1002/nme.2956ISI: 000285261600004Scopus ID: 2-s2.0-78649657604OAI: oai:DiVA.org:kth-28593DiVA: diva2:388163
Note
QC 20110117. Previous title: A symmetric weak form of Biot's equations based on a Helmholtz decomposition of the fluid displacementAvailable from: 2011-01-17 Created: 2011-01-17 Last updated: 2017-12-11Bibliographically approved
In thesis
1. Hierarchical finite element modelling of Biot's equations for vibro-acoustic modelling of layered poroelastic media
Open this publication in new window or tab >>Hierarchical finite element modelling of Biot's equations for vibro-acoustic modelling of layered poroelastic media
2004 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis concerns three-dimensional finite element modelling of Biot's equations for elasto-acoustic modelling of wave propagation in layered media including porous elastic materials. The concept of hierarchical (p-version) finite elements are combined with various weak forms of Biot's equations. Computationally efficient methods providing accurate solutions of sound propagation in layered porous media are discussed. The research falls within the areas linear acoustics and numerical acoustics. Important applications of the developed methods may be found within vehicle interior acoustics, e.g. engineering design of damping treatment based on multiple layers of porous materials.

Place, publisher, year, edition, pages
Stockholm: KTH, 2004. xiv p.
Series
Trita-AVE, ISSN 1651-7660 ; 2004:46
Keyword
Engineering physics, finite element, hierarchical, Biot, porous material, vibro-acoustic, Teknisk fysik
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:kth:diva-95 (URN)91-7283-927-9 (ISBN)
Public defence
2004-12-12, kollegiesalen, Valhallavägen 79, Stockholm, 14:15
Opponent
Supervisors
Note
QC 20100618Available from: 2004-12-10 Created: 2004-12-10 Last updated: 2012-03-13Bibliographically approved

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