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Modelling tools for quieter vehicles: Waves in poro– and visco–elastic continua
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
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 [en]
Vibro-acoutics, poro-elastic, visco-elastic, reduced models, Harmonic expansion, wave guide
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-95205ISBN: 978-91-7501-381-7 (print)OAI: oai:DiVA.org:kth-95205DiVA: diva2:527089
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
List of papers
1. Transverse, tilting and cross-coupling stiffness of cylindrical rubber isolators in the audible frequency range-The wave-guide solution
Open this publication in new window or tab >>Transverse, tilting and cross-coupling stiffness of cylindrical rubber isolators in the audible frequency range-The wave-guide solution
2011 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 330, no 13, 3222-3244 p.Article in journal (Refereed) Published
Abstract [en]

Audio-frequency wave-guide models for antisymmetric dynamic stiffness of arbitrary long elastomer cylinders are presented. The locally non-mixed boundary conditions at the lateral and radial surfaces are simultaneously satisfied by using the modes corresponding to the dispersion relation for axial waves in cylinders satisfying the stress free boundary conditions at the curved radial boundaries, while the displacement conditions on the flat cylinder ends are satisfied by mode matching. The elastomer is modelled as nearly incompressible with deviatoric visco-elasticity based on a fractional derivative, standard linear solid embodying a Mittag-Leffler relaxation kernel, the main advantage being the minimum parameter number required to successfully model the material properties over a broad frequency band. The stiffness is found to depend strongly on frequency: displaying resonances and anti-resonances. The method is compared with and verified against finite element models. In addition, comparison to thin beam theories, i.e. Euler and Timoschenko theory and a simple shear model, is presented, illustrating the limitations of these models.

Place, publisher, year, edition, pages
Elsevier, 2011
Keyword
VIBRATION ISOLATORS; DYNAMIC STIFFNESS; CYLINDERS; PROPAGATION
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-33967 (URN)10.1016/j.jsv.2011.01.020 (DOI)000290068300015 ()2-s2.0-79953686773 (Scopus ID)
Funder
TrenOp, Transport Research Environment with Novel Perspectives
Note

QC 20110531

Available from: 2011-05-31 Created: 2011-05-23 Last updated: 2017-12-11Bibliographically approved
2. Dynamic stiffness of hollowed cylindrical rubber vibrationisolators: The wave-guide solution
Open this publication in new window or tab >>Dynamic stiffness of hollowed cylindrical rubber vibrationisolators: The wave-guide solution
(English)Article in journal (Other academic) Submitted
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-95319 (URN)
Note
QS 2012Available from: 2012-05-22 Created: 2012-05-22 Last updated: 2012-05-22Bibliographically approved
3. Weak formulation of Biot's equations in cylindrical coordinates with harmonic expansion in the circumferential direction
Open this publication in new window or tab >>Weak formulation of Biot's equations in cylindrical coordinates with harmonic expansion in the circumferential direction
2010 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 81, no 11, 1439-1454 p.Article in journal (Refereed) Published
Abstract [en]

A weak symmetric form of Biot's equation in cylindrical coordinates with a spatial Fourier expansion in the circumferential direction is presented. The solid phase displacement and the pore pressure are used as the dependent variables. The original three-dimensional boundary value problem is here, due to the orthogonality of the harmonic functions and the rotationally symmetric geometry, decomposed into independent two-dimensional problems, one for each harmonic function. This formulation provides a computationally efficient procedure for vibroacoustic finite element modelling of rotationally symmetric three-dimensional multilayered structures including porous elastic materials. By numerical Simulations, this method is compared with, and verified against, full three-dimensional Cartesian coordinate system finite element models.

Keyword
Biot's equations, cylindrical coordinates, porous material, Fourier, expansion, weak formulation, poroelastic materials, complex-modes
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-19252 (URN)10.1002/nme.2739 (DOI)000274925300004 ()2-s2.0-74949091356 (Scopus ID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
4. Weak forms for modelling of rotationally symmetric, multilayered structures, including anisotropic poro-elastic media
Open this publication in new window or tab >>Weak forms for modelling of rotationally symmetric, multilayered structures, including anisotropic poro-elastic media
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
Keyword
Biot’s equations, cylindrical coordinates, porous media, Fourier expansion, weak formulation, anisotropic
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-82497 (URN)10.1002/nme.3354 (DOI)000303113500005 ()2-s2.0-84860258278 (Scopus ID)
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

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