Numerical methods for acoustics and noise control

142 Pages·2010·12.05 MB·English

by  Tuomas Airaksinen

J Y V Ä S K Y L Ä S T U D I E S I N C O M P U T I N G
120
Tuomas Airaksinen
Numerical Methods for
Acoustics and Noise Control
ABSTRACT
Airaksinen,Tuomas
Numericalmethodsforacousticsandnoisecontrol
Jyväskylä: UniversityofJyväskylä,2010,58p.(+includedarticles)
(JyväskyläStudiesinComputing
ISSN1456-5390;120)
ISBN978-951-39-4031-7
Finnishsummary
Diss.
This dissertation considers numerical methods for wave propagation modelling
and noise control. The first part of the dissertation discusses an efficient method
for solving time-harmonic wave equations in acoustic (the Helmholtz equation)
and elastic domains (the Navier equation). The solver is based on precondition-
ingaKrylovsubspacemethod,suchasGMRES,withapproximationsofdamped
variants of the corresponding wave equations. An algebraic multigrid method
is used in approximating the inverse of damped operators. The method can be
used in complex three-dimensional computational domains with varying mate-
rialproperties.
The second part of the dissertation considers noise control problems. Two
different noise control problems are discussed in detail. First, a shape optimiza-
tion of a duct system with respect to sound transmission loss is discussed. The
sound transmission loss is maximized at multiple frequency ranges simultane-
ously, by adjusting the shape of a reactive muffler component. The noise re-
duction problem is formulated as a multiobjective optimization problem for the
NSGA-IIgeneticalgorithm. Thediscussedmethodprovidesanefficientapproach
to design muffler components. Second, a novel method is introduced for assess-
ingtheeffectivenessoftheoptimalanti-noiseforlocalsoundcontrolinastochas-
tic domain. A three-dimensional enclosed acoustic space, for example, a cabin
with acoustic actuators in given locations, is modelled using the finite element
method in the frequency domain. In a model problem, a significant noise reduc-
tionisdemonstratedparticularlyatlowerfrequencies.
Keywords:acoustics, preconditioning, noise control, finite element method, op-
timization,stochasticdomain,geneticalgorithm,shapeoptimization,
duct,reactivemuffler
JYVÄSKYLÄ STUDIES IN COMPUTING 120
Tuomas Airaksinen
Numerical Methods for
Acoustics and Noise Control
Esitetään Jyväskylän yliopiston informaatioteknologian tiedekunnan suostumuksella
julkisesti tarkastettavaksi yliopiston Agora-rakennuksen auditoriossa 2
lokakuun 9. päivänä 2010 kello 12.
Academic dissertation to be publicly discussed, by permission of
the Faculty of Information Technology of the University of Jyväskylä,
in the building Agora, Auditorium 2, on October 9, 2010 at 12 o'clock noon.
UNIVERSITY OF JYVÄSKYLÄ
JYVÄSKYLÄ 2010
Numerical Methods for
Acoustics and Noise Control
JYVÄSKYLÄ STUDIES IN COMPUTING 120
Tuomas Airaksinen
Numerical Methods for
Acoustics and Noise Control
UNIVERSITY OF JYVÄSKYLÄ
JYVÄSKYLÄ 2010
Editor
Timo Männikkö
Department of Mathematical Information Technology, University of Jyväskylä
Pekka Olsbo, Sini Rainivaara
Publishing Unit, University Library of Jyväskylä
Cover picture: BMW Series 3 2005, wikipedia.org
License: http://creativecommons.org/licenses/by-sa/3.0/deed.en
URN:ISBN:978-951-39-4037-9
ISBN 978-951-39-4037-9 (PDF)
ISBN 978-951-39-4031-7 (nid.)
ISSN 1456-5390
Copyright © 2 0 1 0 , by University of Jyväskylä
Jyväskylä University Printing House, Jyväskylä 2010
Author TuomasAiraksinen
[email protected]
DepartmentofMathematicalInformationTechnology,
UniversityofJyväskylä,Finland
Supervisors Dr. JariToivanen
DepartmentofMathematicalInformationTechnology,
UniversityofJyväskylä,Finland
Dr. ErkkiHeikkola
NumerolaLtd
Jyväskylä,Finland
Reviewers Prof. OliverErnst
InstitutfürNumerischeMathematikundOptimierung
TechnischeUniversitätBergakademie
Freiberg,Germany
Dr. RadekTezaur
AeronauticsandAstronautics
StanfordUniversity,USA
Opponent Prof. MartinBerggren
DepartmentofComputingScience
UmeåUniversity,Sweden
ACKNOWLEDGMENTS
IwouldliketoexpressveryspecialthanksandpraisetoGodforhisundisputable
guidance with respect to my studies and personal life and for the promise of
John6:47
eternallife( ). IalsowanttogiveheartfulthankstoDr. JariToivanenand
Dr. Erkki Heikkola for their professional and devoted supervision through my
Ph.D. project. Thanks to my workmate Jukka Räbinä for his good company – I
willmissthelunchbreaksandthepleasantatmosphereinourlab. Thankstomy
parents, Harri and Eeva Airaksinen, for love and support. Finally, thanks to my
friendsforallthefriendship,support,andprayers.
LIST OF FIGURES
FIGURE1 Theone-dimensionalfluidelement......................................... 12
FIGURE2 Finiteelementmeshexamples................................................ 18
FIGURE3 Five-pointstencil. ................................................................. 19
FIGURE4 Thecrosscutofaductsystem................................................. 24
FIGURE5 Selectedcoarselevelnodesinalgebraicmultigridmethod........ 31
FIGURE6 Across-sectionofthesolutionofNavierprobleminacube....... 31
FIGURE7 Solutionofthescatteringproblem. ......................................... 33
FIGURE8 MemoryusagewithrespecttoCPUtime;comparisonbetween
exactcontrollabilityanddampedpreconditionermethod. ........ 34
FIGURE9 TheeigenvaluesofpreconditionedHelmholtzandNavierprob-
lems..................................................................................... 38
FIGURE10 Paretooptimality................................................................... 40
FIGURE11 The diagram of a muffler component and optimal example
solution................................................................................ 43
FIGURE12 The non-dominated fronts of the optimization of the muffler
component........................................................................... 43
FIGURE13 Thetransmissionlossasafunctionoffrequency. ..................... 43
FIGURE14 Athree-dimensionalmodelofthecarcabinofaBMW330i....... 47
FIGURE15 Driver’spostureparameters................................................... 48
FIGURE16 Theexpectedvalueofattenuationandstandarddeviation........ 48
FIGURE17 Exampleplotofthenoisecontrolinacarcabin........................ 49
LIST OF TABLES
TABLE1 FirstrootsofBesselderivativefunction, J b = 0. ....... 14
m(cid:48) j
j
TABLE2 The iteration counts for the cube problem for the Helm-
(cid:0) (cid:1)
holtzandNavierequations. ............................................ 32
TABLE3 Thenumberofmillionsoffloatingpointoperations(MFLOPs)
fortheHelmholtzandNavierequations. ......................... 33
CONTENTS
ABSTRACT
ACKNOWLEDGMENTS
LISTOFFIGURESANDTABLES
CONTENTS
LISTOFINCLUDEDARTICLES
1 INTRODUCTION ............................................................................ 9
2 PHYSICSOFSOUND....................................................................... 11
2.1 Acousticwaveequation............................................................ 11
2.2 Time-harmonicelasticwaveequation(Navierequation) .............. 15
3 NUMERICALMETHODSFORACOUSTICMODELLING.................. 17
3.1 DiscretizationmethodsforPDEs................................................ 17
3.2 SolutionmethodsforPDEs........................................................ 20
3.3 Otheracousticsimulationmethods ........................................... 22
3.4 Ductacousticsmodelling .......................................................... 23
4 DAMPEDPRECONDITIONERMETHOD ......................................... 28
4.1 Problemformulation ................................................................ 29
4.2 Numericalmeasurementsandcomparisonofperformance .......... 31
4.3 Spectralanalysisandnumericalstudyofeigenvalues .................. 34
5 SOUNDCONTROLPROBLEMS....................................................... 39
5.1 Solvinganoptimizationproblem............................................... 40
5.2 Shapeoptimizationofareactivemuffler..................................... 41
5.3 Othershapeoptimizationproblems ........................................... 42
5.4 Activenoisecontrolestimationinastochasticdomain................. 44
6 CONCLUSIONS .............................................................................. 50
YHTEENVETO(FINNISHSUMMARY)..................................................... 52
REFERENCES.......................................................................................... 54
INCLUDEDARTICLES