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Weak forms for modelling of rotationally symmetric, multilayered structures, including anisotropic poro-elastic media
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.ORCID iD: 0000-0003-1855-5437
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.ORCID iD: 0000-0001-5760-3919
2012 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 90, no 8, 1035-1052 p.Article in journal (Refereed) Published
Abstract [en]

A weak form of the anisotropic Biot's equation represented in a cylindrical coordinate system using a spatial Fourier expansion in the circumferential direction is presented. The original three dimensional Cartesian anisotropic weak formulation is rewritten in an arbitrary orthogonal curvilinear basis. Introducing a cylindrical coordinate system and expanding the circumferential wave propagation in terms of orthogonal harmonic functions, the original, geometrically rotationally symmetric three dimensional boundary value problem, is decomposed into independent two-dimensional problems, one for each harmonic function. Using a minimum number of dependent variables, pore pressure and frame displacement, a computationally efficient procedure for vibro-acoustic finite element modelling of rotationally symmetric three-dimensional multilayered structures including anisotropic porous elastic materials is thus obtained. By numerical simulations, this method is compared with, and the correctness is verified against, a full three-dimensional Cartesian coordinate system finite element model.

Place, publisher, year, edition, pages
John Wiley & Sons, 2012. Vol. 90, no 8, 1035-1052 p.
Keyword [en]
Biot’s equations, cylindrical coordinates, porous media, Fourier expansion, weak formulation, anisotropic
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-82497DOI: 10.1002/nme.3354ISI: 000303113500005Scopus ID: 2-s2.0-84860258278OAI: oai:DiVA.org:kth-82497DiVA: diva2:498292
Funder
TrenOp, Transport Research Environment with Novel Perspectives
Note

QC 20120524. Accepted 5 October 2011. Manuscript ID: NME-Mar-11-0185.R1- QS 2012

Available from: 2012-02-12 Created: 2012-02-12 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Modelling tools for quieter vehicles: Waves in poro– and visco–elastic continua
Open this publication in new window or tab >>Modelling tools for quieter vehicles: Waves in poro– and visco–elastic continua
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

New modelling tools intended to contribute to the development of components for quieter vehicles are developed. The tools are based on continuum models for wave propagation in poro– and visco–elastic media. By using geometric attributes of the studied components, the computational cost may be radically decreased compared to traditional methods. By assigning known analytical functions for one or two of the spatial directions, the spatial dimension of the remaining numerical problem is reduced. This reduction of spatial dimensions is performed in two di↵erent ways. The first one treats wave propagation in infinitely extended homogeneous and hollowed cylindrical rods, or wave guides, consisting of visco–elastic media. The wave solutions obtained are then used to model rubber vibration isolators of finite length by mode–matching the fields to the radial boundary conditions of interest. The second one is a method for modelling rotationally symmetric multilayered structures consisting of poro–elastic, elastic and fluid domains. By using a harmonic expansion for the azimuthal spatial dependence, the original three–dimensional problem is split up into several, much smaller, two– dimensional ones, radically decreasing the computational load.

Moreover, using a mixed measurement/modelling approach, the audible frequency range characteristics of a viscous damper from a truck is studied, illustrating the influence of the rubber bushings by which it is attached to surrounding structures.

The modelling approaches presented in this thesis are intended as tools aiding the design process of new vehicles, enabling new technology striving for more sustainable vehicle concepts. More specifically, the tools aim to improve the modelling of sound and vibration properties which are often penalised when seeking new, more sustainable vehicle designs.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. ix, 39 p.
Series
Trita-AVE, ISSN 1651-7660 ; 2012:26
Keyword
Vibro-acoutics, poro-elastic, visco-elastic, reduced models, Harmonic expansion, wave guide
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-95205 (URN)978-91-7501-381-7 (ISBN)
Public defence
2012-06-07, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Projects
Centre for Eco2 Vehicle Design
Funder
TrenOp, Transport Research Environment with Novel Perspectives
Note

QC 20120522

Available from: 2012-05-22 Created: 2012-05-16 Last updated: 2013-04-11Bibliographically approved

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Göransson, PeterKari, Leif

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