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the rc:xllons* lavela lor thc non-linear annlysc4, noted earlier, were slightly low,:, lllan tllal the ]incar lilmrllter examination 01 lhc fare variations also shows that thc curvature or the rm~-lincnr farces is slightly different from the lorces predicted using linear nnnlyres-i.e., using the linearized form or the Morrison's equation. For inslnnrc. st n time ratio of 0.5 (refer to Figure 1.33), an inflection point exisls R* tho curves changes Imm positive Lo negative values. As seen in Figure 7.31, tilin inflcetion point is not present in the linear analyses. (The it~llcctioc~ point is n result of the non-lincnrity in the forces.) 8.1.3 Response to Irregular Waves Computer sitnulaled studios (using tho measured irregular wave spectra from lhc wave tnnk facility) wnr~arriedout. The results for the white noise input wave spcclrum rcre shown in Figures 7.3C7.39. Tharc for the JONSWAP ilq>ut W ~YC sprrtr~tm svere presented in Figures 7.40-7.42. White Noise Test Simulation. To extract the rcieml modal pa- rilmelors, ll~~ time domain sagnnls (eornpukd at nodes 12, 18, 23 and 18) were 1l.atnrfonned to the frcqucncy domain. These nodal respona~s corm sportclecl lo lhorc mcasured witln accelerometer6 Al, A2, A3 and A4 on the plty~icai lhydro-elastic model. Figure 1.36 shows a typical global x-direction spcctrnl density hxnetion or tbe a~ntput acceleration at node 18. This graph mn obtained using convontionnl FFT procedures. Four resonant peaks are noticenblc. Bornuse or t1.e mlution, it w l d be difficult to locate the ire q~lctncies a1 which resonnncc exist. Figure 1.37 shows the same results using thr MBM neth hod ntontioned presented 'in Chapter 5. Note the difference in rcsoltttiotl and precision. Bned on the free vibration analysis results, the
fi~t on the lower rrequency end of tho spectrum corrclpalldr lo tllr 1st flexural mode (mode 1); the a-nd penk correapo~~ds to lmr 2nd Rrx~rnl mode; the 3rd is umciated with mode T; and the fottrtb puk wrcprcxrntx mode 8. JONSWAP Test Simulation. Compuled nrcclornlion spmlrd dcnri- ties using the JONSWAP input wavo speclrum werc prcscnt~~i is IVigu~rai 7.40-7.42. Similar trends to thc rhilo noisc b ta sirnalationa aro abnc.rvrrl. Damage Simulation Studier Like tl~e fm vibration nnnlyacr rca!nllw presented earlier, Piyres 7.38 and 1.41 shmv thal wlnotl ~naw>l,t,r 70 was severed to simulate damagc of tltnt mcmbor, 1110 mode must nlTa,trd is 111~ 2nd flexural mode, M,. Noticc lhat wlwn n~emi,crs 70 and 68 nrr iu;u.li- vatrd, the 2nd bending mode is morl nficcld-rcfer lo liig!xnr 7.39 aucl 7.42. To mmpaw the cffects of the dnmngnl meml,er(s) on lllr resol>n8ml frequencies visually, the results at node 23 aro ~prcnkccl as an r:xi~trlplc'. Results for the white noire teat pimulalions arc depidcd ill Pigares 8.5 8.6.
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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
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Abstract As a result of the increas
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Contents List of Figures xii List o
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4.6.3 Fnbrieatiox of tllc Rcduced M
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A Selected Algoilthma 278 A.1 Diago
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4.5 Member Configuration at level #
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7.21 Dynamic Mode # 6 (Intact Model
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7.49 Typical Measured lnput Wnve Sp
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7.66 hulls fmm Accelerometer A2 due
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D.ll DynamicMode # I (Intact Model)
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List of Tables 4.1 Symbols, Units a
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8.9 Pacent Changes in Resonant Frrq
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List of Symbols d(k) .i(k) A A(L1 1
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autosp~trni density of r(t) cms-spe
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0,1,2
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[@I a Pu. P. P:,," P.. o2(k) instan
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een recorded, then it is beneficial
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Associated with every vibration mod
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Such s model is called a dynamicall
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presenlcd. Chapter 3 contains the t
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al frequcncic. occurred when member
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detwM from the data roeorded (later
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y Duggan d a!. [a]. This study inve
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~~lidity of the results war rompsro
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nic~~~aan:immcdiateiyuseful, they a
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tlncayatem hehavior oftrusswork pla
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Chapter 3 Theoretical Modelling Tll
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3.2 Wave Theories Works by earlier
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F;-RY% WAVE THEORY) 1/20 I "w/Lw DE
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DIRECTION OF WAVE PROPAGATION FIG.
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liero, d and ita wlocity component
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and and a+ "=-. OY = wA~inl~IW(1+ s
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FIG.3.4 ARBITRARILY ORIENTED CYLIND
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~i n long c mtd wave is being conai
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inrther. Ultimately, the resulting
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equcncia and mode shapes, equalion
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Toestablish tho relationship betwee
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Furthermore, from equation (3.56),
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lG.3.6 SIMULATED 3-D AND STICK MODE
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1. priam&tic heam members, 5. sir d
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The equation of motion for each ele
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From tho ~tatic dispiaeemont muita,
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instance, the non-dimensional equal
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functional relationship relating th
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whcre F, 't iinstantanmua force at
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Table 4.1 Symbols, Unit. and Dimens
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thc Buckinghm r-Thmrem (i.c., I2 te
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That is, equations (4.28) and (4.29
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C. Ilence, if the dynamic amplifica
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where (2) is the general gmmdric or
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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
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Table 4.5 Relevant Materiel Propert
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FlG.4.9 COMPLETED STRUCTURE. 89
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Since the de& sertioo of the struct
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% FINITE ELEMENT ANALYSIS (COMPUTER
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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
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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
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-CUI~IW~~~ anstmr 9~1sn-mmu3n DL um
Page 218: the posilivc and nogntivr peaks. Re
Page 224 and 225: Table 7.7 X-Direction Results From
Page 226: 2 GEhEnnlEO FRDM TdE WrllTE hOISE l
Page 230 and 231: 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
Page 246: 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
Page 260 and 261: of rnemhcr removal can he visually
Page 263 and 264: emoved is a cancellation offecl, an
Page 265: Force Variation Along the Jacket. P
Page 271 and 272: pond approximately to thasc which c
Page 273 and 274: 'Ikble 8.1 Measured Resonant Rsquen
Page 275 and 276: 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
Page 281 and 282: Table 8.16 Percent Changes in Reson
Page 283: 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
Page 299 and 300: 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
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Suhrtituting qualion (A.5) in equal
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..3 Longuet-Higgins and Cokelet Smo
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Appendix B Sample Calculations Typi
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The dcnsity of ABS plsstic (p.,,) i
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C.l Calibration and Instrumentation
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D.l Mode Shape (Members 70 and 68 R
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D.2 Results for an Impact Initiated
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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
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Table D.4 MEM Damping Estimate. fro
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4 - Memorial University of Newfoundland DAI

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