Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Hierarchical finite element modelling of Biot's equations for vibro-acoustic modelling of layered poroelastic media
KTH, Superseded Departments, Aeronautical and Vehicle Engineering.
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 [en]
Engineering physics, finite element, hierarchical, Biot, porous material, vibro-acoustic
Keyword [sv]
Teknisk fysik
National Category
Other Engineering and Technologies
Identifiers
URN: urn:nbn:se:kth:diva-95ISBN: 91-7283-927-9 (print)OAI: oai:DiVA.org:kth-95DiVA: diva2:14944
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
List of papers
1. A 3-D hierarchical Fe formulation of Biot's equations for elasto-acoustic modelling of porous media
Open this publication in new window or tab >>A 3-D hierarchical Fe formulation of Biot's equations for elasto-acoustic modelling of porous media
2001 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 245, no 4, 633-652 p.Article in journal (Refereed) Published
Abstract [en]

A three-dimensional hierarchical finite element formulation of Biot's equation for low frequency elasto-acoustic wave propagation in fluid saturated porous media based on a weak formulation with fluid displacement and solid displacement as dependent variables is presented. A global error measure for evaluation of the convergence is proposed. Numerical simulations of an air saturated polyurethane foam material show faster convergence for the hierarchical extensions than for linear and quadratic serendipity finite element mesh refinement extensions.

National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-13419 (URN)10.1006/jsvi.2000.3556 (DOI)000170499800003 ()
Note
QC 20100618Available from: 2010-06-18 Created: 2010-06-18 Last updated: 2017-12-12Bibliographically approved
2. 3D hierarchical hp-FEM applied to elasto-acoustic modelling of layered porous media
Open this publication in new window or tab >>3D hierarchical hp-FEM applied to elasto-acoustic modelling of layered porous media
2005 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 285, no 1-2, 341-363 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents a 3-D hierarchical (p-version) finite element description of the solid displacement-fluid displacement form of Biot's equation for elasto-acoustic modelling of multiple-layered isotropic porous media. The convergence related to mesh refinement extensions for different orders of polynomial approximation is briefly discussed for a homogeneous foam. The highest computational efficiency for reasonable levels of the error in the low-frequency region was obtained for fourth-order polynomial finite element interpolations. The main focus is on coupling conditions and on the convergence of solutions to Biot's equations in cases with multiple layers having different material properties. Simulations of a two-layered porous material with low flow resistivity suggest slow convergence rate of the fluid displacement field close to the interface between the layers.

Keyword
FORMULATION, PROPAGATION, EQUATIONS, 3-D
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-13421 (URN)10.1016/j.jsv.2004.08.032 (DOI)000229701800017 ()2-s2.0-18544381093 (Scopus ID)
Note
QC 20100618Available from: 2010-06-18 Created: 2010-06-18 Last updated: 2017-12-12Bibliographically approved
3. 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
Open this publication in new window or tab >>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
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.

Keyword
weak formulation, finite element, porous material, Biot, acoustics
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-28593 (URN)10.1002/nme.2956 (DOI)000285261600004 ()2-s2.0-78649657604 (Scopus ID)
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
4. A comparative study of three different weak formulations of biot's equations for elasto-acoustic wave propagation in layered poroelastic media using p-version finite elements
Open this publication in new window or tab >>A comparative study of three different weak formulations of biot's equations for elasto-acoustic wave propagation in layered poroelastic media using p-version finite elements
2004 (English)Article in journal (Other academic) Submitted
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-13424 (URN)
Note
QS 20120313Available from: 2010-06-18 Created: 2010-06-18 Last updated: 2012-03-13Bibliographically approved

Open Access in DiVA

fulltext(487 kB)1849 downloads
File information
File name FULLTEXT01.pdfFile size 487 kBChecksum MD5
c725708221625a14c1e427b83f669b0f1be4c8fbee26ba50f5f10aeeac1e8ab6409398c4
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Hörlin, Nils-Erik
By organisation
Aeronautical and Vehicle Engineering
Other Engineering and Technologies

Search outside of DiVA

GoogleGoogle Scholar
Total: 1849 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 999 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf