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A.2 Houbolt Algorithm This alg~rithm solves n 3rd order oquation, using n backward iitlile dillcrcnu scheme. The dynamic equst;on d motion (neglecling damping) is: ~wa+ [qr. = ~(1). (h.3) . . .z ia exprmed in a backward finile dillerenec schemc <strong>of</strong> 3rd order m: zi = a=i + + 72~2 + 6 2 + X, ~ ~ (A.4 where i is the term step value oi integration and o, 0, 7, 6 N L x ~ am 1110 coefficients to be computed st each lime step. The reeurrenrc process is initiated with the lollowing cxprcariona: and 5. - %+, -2=;+z'-,), ' - All (A.6) it = L (2rw +3ri - 6zcl + z;.~), (A,@) GAL where At is the interval between two coneffutive stops. The inilinl conditions are (when i = 0): z, = 0, r, = 0, W.7) ii = p(d, -herep(r) is the force per unit maaa. Using thcahovccondiliona in qualiou (A.3) yields (when i = 0): ~(7) = -0 +=-,), 21 + 2-1 = p(r)AL1, z-8 = p(vlAlZ -8,. (n.8) 279
Suhrtituting qualion (A.5) in equalion (A.4), the next relationship is: JkkL, the rceurronce relatianship is: Wllen i = 1. the IToubolt's constants are: U. the rccurrcnce relationship are: !hr.&2, the rccurmnce rcl&ionship ia: . . .i = 2, the Hwbolt'e eonslants are:
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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
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Table 7.9 MEM Damping Estimates fro
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7.2.3 Impact Test Results In Chsptc
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(K 01 0 01- OZ- DE- 0,- OBI (KI 09
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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
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 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
Page 317: - M = the total mass of the slructu
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
Page 347: oa m 01 o or- QZ- oe- om Q Z ~ oo a
Page 353: 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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