4 - Memorial University of Newfoundland DAI

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- 1 ZJ = - At2(123 - *1t 4.1 tzd, .. .i = 3, the Houboit's constsnta are: (A.16) .=LR=-S A,2, A12t7=;iij16=~=0. 4 (A.I~) mi the theurrencc rciationship is: 4 = &(lrr -. 5.. t 4r2 tr,). (A.17) .. . i = 4, the Houbolt'r constants am: . = l p = S A,1, 4 - Alfl~ -' = 0. (A.lN) A11'7 = - = - Finally, by substituting equation (A.2) inloeqmnlion (A.1)-wltilc klmw- ing the values d the constants o,R,7 and X-lhcq~tatio~t or motion <strong>of</strong> tLc system is: I [o][M] + [R] ]a = z(r)i -(MI[ Rzc, + 7zi.t t 62.4 + x I. (A.l!l) So irkhe previous timestep vaiuea nrr known, tit= pnscnt timc alep reaponso can be mmputed.
..3 Longuet-Higgins and Cokelet Smooth- ing Algorithm In lhc smoothingalgorithm attributable to Lonyel-Higgins and Cokelet [77], n function /(z) is defined at equally spaced points z,, j = 1, 2. 3, ... , N, and it is assumd that altornato pints lie in a smoolh curve. Thus, f(z) enn bo locally appmximsled by two polynomials: llcm lhe first polynomial represents a, smwth mean curve, while the second roprescnts n quanlity which oacilintcr with period 2 in j. Therelore, the xtnmtl~ eurve can be taken to be the first polynomial: l'hc rocficieatsoo, a,, a2,. . . , a,, md b. bl, h.. . . ,4.t can be defined uniquely from thc condition: h(z,) = /(sj) at (2n + 1) conserutive p:intr (j - n) to (j +a), i~>chaive. When n = 2, the five pint formula lor a. central point hecomcs: 1. - +I - t I - + 0 + 4 - '1, (A.22) wlhcre I f(sj1;fi I I(=,). For j = 1, 2, N- 1 and N, the (2" + 1) mnsecutive points at which h(zj) = J(q) ace to be considered are for the i!ttcrvala: (j) to(j+Zn), (j-I) to(j+2n-I), (j-2n+l) to(j+l)snd (j- 2") to (j), respeclively. Alter carrying out the necessary algebraicoperation., the resulting lorlnulne are: fi = $(ll/f + 12/,+, - GIj+? - 4fj+~ - 3fj+,), lor j = l i, = &3/j-1+ 813 + 6/j+s - fj+.), for j = 2
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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
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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 and 318: - M = the total mass of the slructu
Page 319: Suhrtituting qualion (A.5) in equal
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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