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Combined Direct-Adjoint Approximations for Large-
‘Scale Design-Oriented Structural-Acousties Finite-
Flement Analysis
‘Levent Coskoner
BIST RUTION STATS
Aphroved for Pubilic Fel
‘Distribution Linkimited,
A thesis submitted in partial falliment of th requirements forthe degree of
Master of Siencs in Asronaulics und Astronates
University of Washington
aw
rogram. Authoriaed to Otfbr Degree:
‘The Department af Asronautios md Astuorautie
20050218 028
Univessity of Washington
radiate Schaol
This ep cory that Theve examined dis copy of master’s thesis by
event Cosiamer
snd have found that it is complete and suis tony inal respects,
‘aid ist any and all roisious required hy he il
‘examining committee have been made
Committee Meer
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degree at us University of Washington, } agree thatthe Library shal make its
copies ticely available for inspectin. [Turher agree ha extensive copying of
"his thesis is allowable ony for scholarly purposes, consstent with “air use” as
presodbed in the U.S, Copyright Law, Any other reproduction for ay purposes or
by an nteans shall nat be allowed without my weitan permission.
Signacare
Date
University of Washington
Abwtraet
(Combined Ditest-Adjoint Approxiaation for Large-Scale Desig Oriented
‘Steuotnal-Aaoustics Fink-Blemene Analysis
Leven Coskunee
(Chair uC the Supervisory Comumittes
Dr. ElLivue
Depantnant of Aeronnutics and Astronautics
| second-order combine apposite dnetapproximate-odjln method
for acura and oficintredused onder atelaon of Fraqueney response fo a
strucual acoustic enelowure mauled using finite elements x presented. A
<esigmorinted approach was oped: not only does the method account for
responses itself (uch as displacement, sonics and prowarsleveh) ita
‘counts for sensitivities af the respenaes with respect to design variables.
Approsinats fst order onus ware obttined using made dinplacerent
der reduction, eud-ender juin soutioms busted on Rite xetrs, ond fist
onder Taylor series. A contbined socand-ordr approinaton incomporting toss
fist-ondr sprcximations wasn ceated for made with madd design
‘arabes, ond was compared [ofl onder results oF a are Finite,
picblem. Accivacy ofthe coun ardee method sas yuandfed
‘Table of Contents,
ENTROPUCTION..
CIAPTER 1: ORDER REDUCTION OF THE COUPLED STRUCTURAL.
ACOUSTIC PROBLEM. 4
1.4 Coupled sisuctoralacoust probe. 4
1.2 Fulhorder sractural-avoustic rade, io 5
1.3 Reduced-onder simetural-scoustic model 6
14 Selostion of reduced ander basis mies. a
CHAPTER 2: A SRCOND-ORDER APPROXIMATION USING COMBINED.
DIRECT AND ADJOINT SOLUTIONS ssn onernnrn 10
2.1 Sevund-ordee approxuinstion of salar responses td
22 Second order approximation of sonsitivitss nem aenesnie LD
‘28 Seunnd ander approximations foe the senettal-accusie prablem
(CHAPTER 3; THE DESIGN-ORIENTED STRUCTURAL-ACOOSTIC 20
FINITE EURMENT MODEL... 16
3.1 Fino-oleret frrafation 6
3.2 Deseription ofthe Fite element model. ”
3.2.1 Geunetry ofthe fnte-etament mode) an senna
3.2.3 Material properties ofthe reference mods. at
3.24 Maer! pruperties ofthe modified wadets 20
3.2 Validation of the finite clement model ue anarne nee est
(CAAPTER 4; NUMERICAL 180 26
4,1 Anmodstion tn the tel 2585. cy
442 Dynamic results ofthe second ord approximation, sual seale mde vn 9
4.2.1 Adjotat based on Ritz Veclors, Direct Desed on Modes ven 38
2.2. Adjeint hasod on meades, direct based oa Ritz weeks 33
412.3 Adicint and dec based on original solution. 34
4.24 Adjcint hase im modes, direct based on original sol =
42.5 Aajoint and dinaot haved on Taylo-sries approximation 38
43 Dynatnic reso ofthe seonnd-order approximation, large seafe model 39
4.3.1 Adjnint based on modes, direct based on Ritz vectors 39
43.1 Adjpint based on Ritz vectors, dieet based on modes
44 Convergenoe study ofthe sevomi-otdet approximation when using a a
‘es-onter approximation
CHAPTER 5: CONCLUSIONS
REFERENCES, smn 94
APPENDIX A: DERIVATION OF ACOUSTIC EQUATIONS 98
APPENDIX Ws VFI} TRIANGULAR ACOUSTIC FINITE ELEMENT jessnve 107
APPENDIX €: THE STRUCTURAL-ACOUSTIC COUPLING TERMS 00114
APPENDIX i: YH SECOND ORDER APPROXIMATION ia
List of Figures
Figive 1: 2D Swuctural Acoustic Systen: vm 23
Figure 2: Large-scale 2D Strubiural Acoustic Syst enon 28
Figure 3: Snend pressure frequency response compurizon wena 35
igure 4: Cra (2) 5a Bending Moment eppraximativn
igure 5: Ertor (4) ia Presture approximation ann
Figore 6: Eror 0
Figure 7: Ervor (4) ia dA approsimatine.
igure Bevor (4) in dP approximation
gure 9: Error (8) in PISA approximation vend
in 6M opproxima‘on.
gure 10; ror (8) in Hering appsexdtat.on 9
igure 11: Pra (0) in Pressure appvoxiunation. sl
[Figure 12: Pressure responce approximation. 82
‘gus 13: Pressure response approximation. 38
igure [4s Error (2) i Pressuéapprenimation. a 54
igure 15: Hor (16 in AMAA appeoxitation. 3
igure 16: Eee (24) in PA pproxioticn on 56
Figur 17: Pressure response voomed uy area uF iteest,
Figure 18: Tar in Pressure appsoxiuations.
Figure 18: Ente in 4N4L approxioatfons. 3”
Figure 20; Error in dM3A upproximarions.. ~%
Figure 21: Ettae in 4P/4 apprenimations. 61
igure 22: ror in UPALA opproxizaations @
Figute 25: Pressure response appreximelios 83
igure 24: Prewure eegponse appresimatin, n 6
Figure 25: Emor in pressure cespanse apprexitustions 65
Fignee 26. Euro ia bending moutent response approximations 66
igore 27: Pressure response approxiMaQOMM AHO nnnnnneinennnnenne SP
Figure 28: Bundling sceponse appresimation zoomed to area of ater. onun 68
Figure 20: Erorin GMT appeoxiniatons. %
Figure 3:
Figure 31:
Figure 32:
Figure 33
Figure 3:
Figure 3s:
Figure 36
Figure 37
igure 38
Figure 3:
Figure a:
Figured
igure a2:
Piyuee 43:
Higuro 4:
igure 45:
igure 46
Figure 47:
Figure #8:
Figure 1:
Figure 50:
Tar in dM approximations
Evtar in dP approximations
Exar in dPAA approximations... se P2
Ear ia Pressure approximations nz)
Ear ie Pressue approximations 7
Enver in Pressure appronionations %
mura Pressure approximations sn
Etror in abd appenximations: 0
vor i PI appcoxentions ns . vse
[Erotin dP approximations p
[Bot in PL approximations seamen 80
[Enoe in dP approximations snnaninnamnscen BL
ess erm aproxinton, Lasse (1543 DOF) made
“Zonmed in area oiler 82
Er (4) Bending Moment apoio, Lage (1544
DOF) mods! a
Bor tn EGA appreioaos epee (383 or)
model
Ee) dBA arenas Taree 188 ba)
Modelo
as
Fre (JPA apcoaatos Large (1843 DOF) model 5
nor (%) in P/4A spproximations. Large-scale (1543 DOF) model. 87
Eor (9) i dP/AT eppeoxituatons, Large-scale (1543 DOF) model. 88
Reduction in err of the teem order heruing moment
%9
approximation
Reduction in ertr of the second order presure approximation
