4 - Memorial University of Newfoundland DAI

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In all cases, tbe diserelmncics bctsvcen lllc oxpcrit~,estnl and ~ltmmlicsl (FEM) results arc m>nll. These diacrepntlcies (which ix~clttdr (a) tlw rrroltilnl frequencies preenled in Tables 8.17-8.20, and (b) lhr pcrrenlage xhifl in tlmr resonant Ireqlxeneier resulling fmm dnmagcgecl nnembera) n9.c n rmalt of tllc. many approximations incorporated in the BEM compalcr ~n>oor very rigid or ircrl~vlly Ilrxil~lr. 11, 1.l~~ oxperimenlnl hydro-clnstic model tlle cnn~~e~tios~r 1hrlw~r.1, tllc I ~~~u~IM.~ are noither rigid nor porfeclly flexi1,le. . Structural masses are c.lirnnted md honlpccl at the noQc!* to rosrc~vc. boll, aloragc and compulorsolulion time. 9'l~is can rrpn:awl. Ll~r glc,I,a~l behaviour of slructure "cry well, bul climinbnlrs all tho ittrlivi~lt~;d IVI- ber vibrations. (More details will be give13 Inter.) The response of lho structure is reprcscstsd RV limo lir~vi~r sum of ihdc. pendent, unmupled modal responses. Thauglt this Is n good nppnnx- imation in thc lower modes, higher orcller modc~ rnny no1 I,.: ~:sl.in,ly independent, for lhcy may he coc~plnl hy nnn-pmporliosnl ,lun~ir~g tams. Subject to thne limilationr, the Iollowing statements mn bc ntudc mgrrding the computer generated Rnilc elomcnl results.
'Phc invalidity of thc lumped mass idealization of the structure can be explained as bliows: For any dynamicnystom, the analyaia isgmatly mmpli- crled lmausc the inortia farces rcsuil from structural displacements which, is turn, are slfcctml by themagnitudeof tho inertia forces. This closed cycle of cause and ellecl can be approached directly only by formulating the pmb- Icm in lcrms of dillcrontial equations. However, because tho mass of each struclarral membcr ia distribuld continuously along its length, the dirplace- ments and arcolerations must be deflned for each point along the length of the mcnmbcr if tho incrtis forces arc to be mmpleteiy understood. In such n ~itaation, tho analysis must be formuiald in terms of partial differential cclantions, since the position .long the span ofeach member besides the time ~ n bc ~ t~kon ~ M t inclopcndent va~inblcs. On thcother hand, when the lumped mass idealization is uscd (as io the con>pulcr analysa), the wry mmpiicated motion of the structure is greatly .educed, lor lhe incrtia force. can only be developed at the nodal points in the linite element model of lhe structure. Tl~c discrcpnncia bclwcen the experimental results and theoretical re- ~~xlts arc larger for the damaged structural configuration. This may have mulled bcenuse, in tho camputcr model, the rigidity of the connections at lho joint was rnainlnined even after the member(s) were removed. In reality, llle removd of onc or mom members would reauit in an increase in the stress of the remaining members which, in turn, would be transmitted to the joints (nodcs). The cxcoss stress would haven weakening effect on the jointa (par- tiealacly the ncighbouring joints); Lhe extent of which is proportional to the mngniltndo of thc cxeess stress tmnsfemd. This weakening of the joints is nd prcrnt in tllc theoretical model, because the change in flexibility results
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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
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the posilivc and nogntivr peaks. Re
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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
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'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 and 266: Force Variation Along the Jacket. P
Page 267: fi~t on the lower rrequency end of
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: I able 8.20 Comparison of the Reson
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
Page 317 and 318: - 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
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Table D.4 MEM Damping Estimate. fro
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