4 - Memorial University of Newfoundland DAI

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Chapter 3 Theoretical Modelling Tlli. cl~aptcr prcscnts the mathematical modelling of the problem. The the orctical formulations b d on wave and structural mechanics, applicable to the investigation, are given. In addition, s description of the computer im- plcmcntalion (to obtain thmrelieal estimates of the dynamic behavior of the stnncture) i. presen:ed. 3.1 Wave Forces Wave forecs on olfshom structures are commonly mmputed using linearized wave thmry. Gonerally, thm diiTerenl method. are used: 1) Morrison- O'Brien's theory, 2) Fmudc-Krylov Hypothesis and 3) Linear Diffraction tbcory. The Morrison-O'Brien's theory considers the force as being eom- pmod al an inertia and drag component linearly added. This method is ~ ~ t ~ spplieable ~ l i y to smaller abject. (i.r, smaller compared with the wave length). If the iuerlin forces predominate, but the object is still not very small, the Roude-Krylov approach (P-K theory), uaing praure-area methd on tho eurinee ai the object, is used. However, a force coefficient dependent 083 experimental data is mquiled to include the eLctr of added mw and
wave diffraction. For larser objecte (i.e., larger compared wit13 tho wnvc length) linear diffraction thcory, using numerical lechniquea, is ad. Iicrc. the Laplace's equation is solved with appropriate boandsry eonditiona in terms of a total potential which is the sum of an incident and reflcdnl p h tentiai. This methal may be marhematieally more sncl dcairni)lc, but, the fimt two methods, mentioned prwiously, are morc rcndiiy aaed. In thia treatise, the wave forces on the atcueture arc cnlndatcrl the Martiron-O'Brien's equation. The inertia term includea m inertin ro- cffieient, CM; the drag term invoivea n drag coefficient, CD. Morriwu rl ol. 1741 first used the equation to calculate tbe forces on n vrrticnl cyliscler subjected Lo wavea. Since then it lras been applied to other oricntdious el n cylinder baides other aubmorged shapes. Usudly, tllc expronsiorn ia applic
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NOTICE The quallty of this microfor
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I*I Et"" :lbL="*"" k.. bpilmsa7d Di
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Acknowledgements I should like lo t
Page 11 and 12: Abstract As a result of the increas
Page 13 and 14: Contents List of Figures xii List o
Page 15 and 16: 4.6.3 Fnbrieatiox of tllc Rcduced M
Page 17 and 18: A Selected Algoilthma 278 A.1 Diago
Page 19 and 20: 4.5 Member Configuration at level #
Page 21 and 22: 7.21 Dynamic Mode # 6 (Intact Model
Page 23 and 24: 7.49 Typical Measured lnput Wnve Sp
Page 25 and 26: 7.66 hulls fmm Accelerometer A2 due
Page 27 and 28: D.ll DynamicMode # I (Intact Model)
Page 29 and 30: List of Tables 4.1 Symbols, Units a
Page 31 and 32: 8.9 Pacent Changes in Resonant Frrq
Page 33 and 34: List of Symbols d(k) .i(k) A A(L1 1
Page 35 and 36: autosp~trni density of r(t) cms-spe
Page 37 and 38: 0,1,2
Page 39 and 40: [@I a Pu. P. P:,," P.. o2(k) instan
Page 41 and 42: een recorded, then it is beneficial
Page 43: Associated with every vibration mod
Page 46 and 47: Such s model is called a dynamicall
Page 48 and 49: presenlcd. Chapter 3 contains the t
Page 50 and 51: al frequcncic. occurred when member
Page 52 and 53: detwM from the data roeorded (later
Page 54 and 55: y Duggan d a!. [a]. This study inve
Page 56 and 57: ~~lidity of the results war rompsro
Page 58 and 59: nic~~~aan:immcdiateiyuseful, they a
Page 60 and 61: tlncayatem hehavior oftrusswork pla
Page 64 and 65: 3.2 Wave Theories Works by earlier
Page 66 and 67: F;-RY% WAVE THEORY) 1/20 I "w/Lw DE
Page 68 and 69: DIRECTION OF WAVE PROPAGATION FIG.
Page 70 and 71: liero, d and ita wlocity component
Page 72 and 73: and and a+ "=-. OY = wA~inl~IW(1+ s
Page 74 and 75: FIG.3.4 ARBITRARILY ORIENTED CYLIND
Page 76 and 77: ~i n long c mtd wave is being conai
Page 78 and 79: inrther. Ultimately, the resulting
Page 80 and 81: equcncia and mode shapes, equalion
Page 82 and 83: Toestablish tho relationship betwee
Page 84 and 85: Furthermore, from equation (3.56),
Page 86 and 87: lG.3.6 SIMULATED 3-D AND STICK MODE
Page 88: 1. priam&tic heam members, 5. sir d
Page 92 and 93: The equation of motion for each ele
Page 94: From tho ~tatic dispiaeemont muita,
Page 97 and 98: instance, the non-dimensional equal
Page 99 and 100: functional relationship relating th
Page 101 and 102: whcre F, 't iinstantanmua force at
Page 103 and 104: Table 4.1 Symbols, Unit. and Dimens
Page 105 and 106: thc Buckinghm r-Thmrem (i.c., I2 te
Page 107 and 108: That is, equations (4.28) and (4.29
Page 109 and 110: C. Ilence, if the dynamic amplifica
Page 111 and 112: where (2) is the general gmmdric or
Page 113 and 114:
the prolotype. Damping is dcfincd b
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2 LEVEL # 7 1 28956DO NOTE: ALL DIM
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Mataial= Structural Steel, E = 206.
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LEVEL C6 NOTE: ALL DlMENStONS IN m
Page 124 and 125:
Table 4.5 Relevant Materiel Propert
Page 128 and 129:
FlG.4.9 COMPLETED STRUCTURE. 89
Page 132 and 133:
Since the de& sertioo of the struct
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% FINITE ELEMENT ANALYSIS (COMPUTER
Page 136 and 137:
3 53 I CONTROL RM SECTION A-D. MEZZ
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I I SERVO CONTROLLER MODEL 408.1% j
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LEGEND FI B F2 FREE VlBllTlDN INITI
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5.1.4 Response Circuit Data acquisi
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I ~T.UG~U~E LEGEND: DYIIYT I., 10 A
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the basis upon which the irregular
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then manipulated by the computer ro
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,.. G STRUCTURE IN STILL WATER STRU
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dter every set of hen wave excitati
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To gather spectral information fmm
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is the timelag between silrnplev~l~
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ics, with a lew notable exceptions,
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If bath aides of the dove cguntion
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Conversely, r(1) can be estimated b
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quires ahout N(M + 1) + 9Y1 arithme
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So equation (6.18) become: I, i = C
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At each resonant frequency, the hdl
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6.5 Impact Testing Impact testa wer
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Chapter 7 Theoretical and Experimen
Page 181 and 182:
Table 7.1 Natural Wequeney Comparis
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Therefore, with the natural freluen
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Pi7 Be: kD! SF:& iid id . -5 i#@ Ba
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(i.o., at noder 6, 12, 18, 22 and 2
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tirne dntn;lis reprcsez~lnlioti of
Page 214:
-CUI~IW~~~ anstmr 9~1sn-mmu3n DL um
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the posilivc and nogntivr peaks. Re
Page 224 and 225:
Table 7.7 X-Direction Results From
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2 GEhEnnlEO FRDM TdE WrllTE hOISE l
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FIG. 7.53 MEASURED INPUT WRVE FROM
Page 236:
'IUnU133dS 3SIR1 31IHI 9NISn--91 30
Page 244 and 245:
Table 7.9 MEM Damping Estimates fro
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7.2.3 Impact Test Results In Chsptc
Page 252 and 253:
(K 01 0 01- OZ- DE- 0,- OBI (KI 09
Page 257 and 258:
Chapter 8 Discussion of Results In
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of rnemhcr removal can he visually
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emoved is a cancellation offecl, an
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Force Variation Along the Jacket. P
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fi~t on the lower rrequency end of
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pond approximately to thasc which c
Page 273 and 274:
'Ikble 8.1 Measured Resonant Rsquen
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Table 8.6 Measured Resonant Wequenc
Page 277 and 278:
After a close look at the measured
Page 279 and 280:
Table 8.11 Percent Changes in Reson
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Table 8.16 Percent Changes in Reson
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apprmiably. Since the tmnsa of the
Page 286 and 287:
'*~+12 \5 \8 h4 h7 $0 FREOUENCY IHz
Page 288 and 289:
8.2.4 Impact Test Results 'l'incobj
Page 293 and 294:
I able 8.20 Comparison of the Reson
Page 295 and 296:
'Phc invalidity of thc lumped mass
Page 297 and 298:
Chapter 9 Concluding Remarks and Re
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general agreement. 5. An investigat
Page 301 and 302:
mode, br example, might have been e
Page 303 and 304:
References K I'o,lnt~n~. 'A Sludy o
Page 305 and 306:
[21] .I.K. Vandiver, "Structo~ral D
Page 307 and 308:
1431 D.J. Kartewcg and G. d-Vria "O
Page 309 and 310:
1671 I..S. Marplo, "A NCW Autorepes
Page 311 and 312:
(111 J. Zhou "Ocean Wave Simulation
Page 313 and 314:
[Ill M.C. Ilallsm, N.J. Hcaf and L.
Page 315 and 316:
Appendix A Selected Algorithms Tllr
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- M = the total mass of the slructu
Page 319 and 320:
Suhrtituting qualion (A.5) in equal
Page 321 and 322:
..3 Longuet-Higgins and Cokelet Smo
Page 323 and 324:
Appendix B Sample Calculations Typi
Page 325 and 326:
The dcnsity of ABS plsstic (p.,,) i
Page 327:
C.l Calibration and Instrumentation
Page 330:
D.l Mode Shape (Members 70 and 68 R
Page 340 and 341:
D.2 Results for an Impact Initiated
Page 343:
i W 4 P Li I 2: 5: E B '5 2- d :" i
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oa m 01 o or- QZ- oe- om Q Z ~ oo a
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D.3 MEM Damping Estimates for the D
Page 357:
Table D.4 MEM Damping Estimate. fro
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4 - Memorial University of Newfoundland DAI

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