STRUCTURE-ACOUSTIC ANALYSIS; FINITE ELEMENT

195 Pages·2004·6.91 MB·English

STRUCTURE-ACOUSTIC ANALYSIS;
FINITE ELEMENT MODELLING AND
REDUCTION METHODS
PETER DAVIDSSON
Structural
Doctoral Thesis
Mechanics
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Structural Mechanics
ISRN LUTVDG/TVSM--04/1018--SE (1-180)
ISBN 91-628-6176-X ISSN 0281-6679
STRUCTURE-ACOUSTIC ANALYSIS;
FINITE ELEMENT MODELLING AND
REDUCTION METHODS
Doctoral Thesis by
PETER DAVIDSSON
Copyright © Peter Davidsson, 2004.
Printed by KFS i Lund AB, Lund, Sweden, August 2004.
For information, address:
Division of Structural Mechanics, LTH, Lund University, Box 118, SE-221 00 Lund, Sweden.
Homepage: http://www.byggmek.lth.se
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Preface
The work presented in this thesis has been carried out at the Division of Structural
Mechanics at Lund University. I would like to express my gratitude to my supervisor
Professor G˜oran Sandberg, both for the opportunity to conduct my research studies at
thisdivisionandforthesupportprovided. Thefriendshipandsupportofallcolleaguesat
thedivisionareveryappreciated. IalsowouldliketothankmycolleaguesattheDivision
of Engineering Acoustics, especially Dr. Jonas Brunskog, for the invaluable discussions
and help during the course of this work. A special thanks to Mr. Bo Zadig for the help
on creating a variety of the flgures.
The work was initiated by and conducted as a part of the national research programme
Integral Vehicle Structures (IVS), which concerns the development of future generations
ofvehicles. IVSisflnancedbytheSwedishFoundationforStrategicResearch(SSF).This
flnancialsupportaswellasthecoursesandothereventswithintheprogrammehavebeen
very appreciated.
Paper 5 presents work carried out in cooperation with Dr. Gunnar Bj˜orkman and Johan
Svenningstorp at Volvo Technological Development in G˜oteborg. I very much appreciate
their efiorts on introducing me to the modelling environment described in the paper.
The work conducted in Papers 6 and 7 was partly flnanced by Lindab Proflle AB, which
is gratefully acknowledged.
I would also like to thank my friends and family. Especially, thank you ”Asa for your love
and support.
Lund, August 2004,
Peter Davidsson
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Overview of the thesis
This thesis investigates structure-acoustic problems, which involves a (cid:176)exible structure
coupled to an enclosed acoustic (cid:176)uid. In the literature, this type of problems are usually
referred to as vibroacoustic problems or structural-acoustic problems with (cid:176)uid interac-
tion. The thesis consists of two parts. The flrst part provides an introduction into the
fleld of structure-acoustic analysis within the flnite element framework, including the de-
scription of porous materials. The second part of the thesis comprises seven papers in
which analysis procedures for modal reduction of structure-acoustic systems are devel-
oped. Two of the included papers also investigate the sound transmission loss of double
walls.
Included papers
Paper 1 G˜oranSandbergandPeterDavidsson,Astrategyformodalreductionofstruc-
ture-acoustic systems, 2002.
Paper 2 Peter Davidsson and G˜oran Sandberg, Reduction of structure-acoustic prob-
lems that include hysteretic damping, 2002.
Paper 3 Peter Davidsson and G˜oran Sandberg, Substructuring and modal reduction of
flniteelementformulatedporoelasticsystems,SubmittedtoComputermethods
in applied mechanics and engineering, 2004.
Paper 4 Peter Davidsson and G˜oran Sandberg, A reduction procedure for structure-
acoustic and poroelastic{acoustic problems using interface-dependent Lanczos
vectors,SubmittedtoComputermethodsinappliedmechanicsandengineering,
2004.
Paper 5 Peter Davidsson, G˜oran Sandberg, Gunnar Bj˜orkman and Johan Svennings-
torp, Structure-acoustic analysis in an integrated modelling environment,
WCCM V congress in Vienna, 2002.
Paper 6 PeterDavidsson, JonasBrunskog, Per-AndersWernberg, G˜oranSandbergand
Per Hammer, Analysis of sound transmission loss of double-leaf walls in the
low-frequency range using the flnite element method, Submitted to Building
Acoustics, 2004.
Paper 7 JonasBrunskogandPeterDavidsson,Soundtransmissionofstructures;aflnite
element approach with simplifled room description, Accepted for publication
in Acta acustica united with Acustica, 2004.
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V
Summary of papers
Paper 1 The problem in which a (cid:176)exible structure interacts with an acoustic (cid:176)uid is
analysed by use of the flnite element method. With increasing complexity of
the geometry and when increasing the frequency limit is of interest, the num-
ber of degrees of freedom needed to describe the system becomes very large.
To reduce the coupled system, modal analysis is performed in the structural
and in the (cid:176)uid domain separately. The subdomain eigenvectors are then used
to reduce the coupled problem. A method for choosing which of these subdo-
main eigenvectors to include in this operation is derived based on the coupling
betweenthestructuraland(cid:176)uidmodes, furtherreducingthesystem. Thecou-
pling depends on similarity in the natural frequencies and in the shapes of the
subdomain modes.
Paper 2 Theunsymmetricaleigenvalueprobleminvolvedinanalysingstructure-acoustic
problems by use of the flnite element method with a pressure formulation in
the (cid:176)uid domain can be reduced by transforming it into a symmetric standard
eigenvalue problem. The paper shows that when hysteretic damping is intro-
duced in both the structural and the (cid:176)uid domain, the problem can still be
treated as a symmetric standard eigenvalue problem, which becomes complex-
valuedduetothedamping. Thisprovidesasimplemethodforincludingdamp-
ing in the frequency response analysis of structure-acoustic problems.
Paper 3 Astructure-poroelasticsystem,consistingofaporousmaterialdomainbounded
to a (cid:176)exible structural domain, is studied. The porous material is modelled by
Biot’s theory, where both the (cid:176)exible frame material and the (cid:176)uid in the open
pores are described by coupled equations of motion. The component mode
synthesismethodisusedtoderiveareducedsetofbasisvectorsforthesystem.
This is done by dividing the system into three physical domains, the (cid:176)exible
structure, and the (cid:176)uid and structural partitions of the porous material. The
displacementcontinuitybetweenthe(cid:176)exiblestructuraldomainandtheporous
material is fulfllled by interface modes. These modes are derived by study-
ing the two structural subdomains, the (cid:176)exible structure and the structural
partition of the porous material, in vacuo. The interface modes are used to-
gether with a set of basis vectors for each of the uncoupled domains, derived
by modal analysis with the interface degrees of freedom flxed, to reduce the
coupled system.
Paper 4 A reduction method is proposed for the analysis of structure-acoustic and
poroelastic{acoustic problems within the flnite element framework. This in-
cludes systems consisting of an acoustic (cid:176)uid domain in contact with a (cid:176)exible
structural domain and/or a porous sound absorbing material domain. The
problem studied is reduced by dividing the system into a number of physi-
cal domains. A set of basis vectors is derived for each of these domains both
including eigenvectors of the uncoupled domain and interface-dependent vec-
torsincludingthein(cid:176)uencefromconnectingdomains. Theproposedmethodis
compared to solving the total system for both a structure-acoustic eigenvalue
problem and a frequency response analysis of a poroelastic{acoustic system.
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VI
Paper 5 Thispaper, whichisbasedontheresultsreportedinPapers1and2, describes
theimplementationofstructure-acousticflniteelementanalysisinanintegrated
modelling environment, one which has interfaces to programs for meshing and
for flnite element analysis. The aim is to determine the vehicle interior noise
on the basis of the force applied to the structure.. An interface is created to
a code developed for performing structure-acoustic analysis involving coupled
modal analysis and frequency response analysis. The possibilities this mod-
elling environment provides are demonstrated. Use of this approach simplifles
cooperation between researchers and their interaction with industrial groups.
Paper 6 The sound transmission loss of double-leaf walls in the low-frequency range is
evaluated by means of structure-acousticflnite element analysis. A parametric
studyisperformedtoinvestigatethein(cid:176)uenceonthesoundtransmissionlossof
variousmaterialandgeometricpropertiesofthewallandthedimensionsofthe
connecting rooms. It is found that a very detailed description of the system is
neededinordertodescribesoundtransmissionlossinthelow-frequencyrange.
The model conflrms the importance of primary structural resonance and the
sizeofthewallandtheconnectingroomsindeterminingthesoundtransmission
loss in the low-frequency range.
Paper 7 A prediction model within the flnite element framework for the sound insula-
tion of a wall is proposed. The connecting rooms are described as inflnite-long
tubes and the in(cid:176)uence of the rooms becomes loading terms on the wall, re-
ducing the model to the two-dimensional wall. The analysis can thereby be
conducted higher in the frequency range compared to having to include the
modal bases of the connecting rooms. The same method is developed to study
the sound insulation of lightweight double-leaf walls, and the numerical results
are presented.
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