Vibration control of a flexible structure with electromagnetic actuators

Transcription

1 Dowloe ro or.. o: J 7, 9 Vro orol o lexle rre wh eleroge or rz, Mrío; So, Ilr Plhe : Jorl o he Brzl Soey o Mehl See Egeerg o rle, DOI:.7/ x Plo e: 6 Doe Vero Peer revewe vero o DT Or Co APA: rz, M., & So, I. 6. Vro orol o lexle rre wh eleroge or. Jorl o he Brzl Soey o Mehl See Egeerg, 84, -4. DOI:.7/ x eerl rgh Copyrgh orl rgh or he plo e ele he pl porl re ree y he hor /or oher opyrgh ower oo o eg plo h er reoge e y he legl reqree oe wh hee rgh. er y owlo pr oe opy o y plo ro he pl porl or he prpoe o prve y or reerh. Yo y o rher re he erl or e or y pro-g vy or oerl g Yo y reely re he R eyg he plo he pl porl I yo eleve h h oe rehe opyrgh plee o provg el, we wll reove e o he wor eely vege yor l.

2 Vro orol o lexle rre wh eleroge or Mrío rz Depre o Mehl Merl Egeerg Mlry Ie o Egeerg, IME Prç eerl Túro 8, r, Ro e Jero-RJ CEP 9-7 Brzl e-l: grz@e.e.r Tel.: Ilr Ferrer So Depre o Mehl Egeerg Tehl very o Der, DT Koge ygy, 8 Der Ar Th wor pree he oel o her re ype rre opoe o x lexle e hree rg e. Fxe o he gro, oe he rre, wo volge orolle eleroge or re e or vro orol. To oel he lexle e, eol e elee were e. o-ler eqo or he or eleroge ore, oe he poo eor, e ely or he orol gl pe volge ro were lo oere he oel. For orollg prpoe ree ler qr reglor oe wh preve ll-orer ree ler oerver w eploye. Rel o erl lo, where he rre e o plve re ore o hro ore, how h he ollo e gly ree wh he e o he eleroge or. Keywor Srre. Vro Corol. Eleroge or. Dree ler qr reglor. o yol A e rx o he oo e-pe eqo r gp ro eo B p rx o he oo e-pe eqo C op rx o he e-pe eqo orol veor ore veor e rx o he ree e-pe eqo H p rx o he ree e-pe eqo I ey rx ol eler rre oe or ol eler rre or ol eler rre or K e elee e rx l legh o he lexle e ewee he gro l legh o he lexle e ewee l legh o he lexle e ewee l legh o e elee M e elee rx er o r o he eleroge or ol P olo rx o he lger R eqo q veor o e vrle veor o ee e vrle qˆ r or eler ree e ewee he or re he erroge re e ewee or re le re e ewee or re rgh re oo e

3 ol volge or ol volge or v Iroo rre plee veor rre veloy veor Whe y ore re pple rre, ere ollo y or. There re y wy o ze hoe ollo. Pve, e-ve ve eho re exevely ere lerre. A oo pve eho o o g y vro orer, lo ow e per, ore wh prg or, prg vo per, ere,, 6, 4, 7, 4]. Depe eevee whe pero ore re pple, hey re le o oe reqey rge. I orer o llow eeve opero wer ore reqey rge, 4] propoe he e o lple egree o reeo vro orer. Oher ype o pve olo e heve wh he e o reo r he pezoeler,, 7, ], e o voel erl ] or hpe eory lloy 9]. Alerve ehqe, he e o pve eleroge per, e o ]. Se-ve eho oe rg eer vro reo who he power opo reqre y he ve eho. The georheologl per, ere el y 9, ], re ooly eoe lerre. Exple o hoe per wh ere oroller e o,, ], where pel eo gve or orol o rrl vro e y erhqe. Aoher ype o e-ve ehqe e o ], where ol e eleroge vro orol eve h ee e. The o eeve l o vro orol eve re o he ve ype. They e e o ree he ollo e o pero re wer reqey rge well ollo e y plve re. Dere ve eho or vro orol e e. A wely e eho o eployg pezoeler or, how,, 7, 8], where hey re e oo wh ere oroller. I ] ve-pve pezoeler ewor preee. Aoher ve ehqe o g reo e, preee, ]. I ] opro ewee he perore o ve oroller h e reo e pve oroller preee. Reely, eleroge or, ele xe oe he rre, hve ee e o orol vro o lexle e. I, 8, ] gle or eploye. I 7] wo or re e, llowg eleroge ore oppoe reo. I 9] wo or re e o orol he vro o ovg he o rg r h roe wh repe o he gro. The e o eleroge or very ee hey re ele oe who y phyl o wh he rre whoe ollo ee o e orolle. Th e her e ereg olo whe or o e ele rely he rre. Bee, whe ollo h were o expee rg he eg ge ee o e ree, he e o hoe exerl or y e heper h oyg rre h h lrey ee ore. Depe he eoe vge o he eleroge or hey hve rw, he relve oo ewee he or re he e pr o he rre ee o e very ll 6, 8], lly le h oe lleer. B h oo e ep ll, he e o eleroge or ele oe he rre vle. I h wor eleroge or wll e eploye o orol he vro o rre e o plve ore. For h, oel o he rre, or he oroller wll e evelope lo rel wll e preee o how he eevee o h vro orol ehqe. Srre, or poo eor Aorg o he hee ellow, he her re ype rre oere h wor opoe o hree rg e,, oee o eh oher wh lexle elee, 4, 6. The r rg lo oee o he gro wh lexle elee. To orol he vro, wo eleroge or re xe o he gro h wy o exer ore. I orer o hve ge ore g he rre, hol o o erroge erl or hol hve erroge erl re g he or. To ere plee poo eor p ele er oe o lerl re. For orollg prpoe, wll e oere h gl oper e. Coerg h he he o he lexle rre re h ller h wh oerg h el prllel o, h el prllel o 4,, h

4 el prllel o 6, e e h he e wll oly ove prllel o he gro xe X x. Thereore ll he ly wll e e oerg ore pple h reo, org o he gre elow, where re ore,, pple how.. Srre oel Fg. Sher re rre I he legh o eh lexle elee gly lrger h wh he, eol e elee e e or oelg prpoe. Coerg h he rg e wll ove oly reo prllel o X x, e elee wh wo o or egree o reeo e eploye or he rezo o he lexle elee he rre,,, 4, 6. The egree o reeo o e elee re repreee ellow. Fg. Be elee wh wo o or egree o reeo The e rx he oe rx o lexle e elee wh o pe, o ro eo re A, o re oe o er I, o ely ol E wh legh l re repevely gve y ]: / l 6/ l EI / l 6/ l 6/ l 4/ l 6/ l / l / l 6/ l / l 6/ l 6/ l / l 6/ l 4/ l K

5 4 6l A l 4 4l l l 4 l l l 4l l 6l l l l l 4l M For lexle e wh o ro eo re o wh w he h: A hw I hw / 4 I wo e elee wh he e legh re e or he rezo o eh lexle e he rre, oel wh e elee egree o reeo oe. The rp e o e h he egree o reeo re reerre o he whole rre glol egree o reeo. The rre lo o hree rg elee,. Fg. Dreze rre The glol e rx, K, he oe rx, M, repreee wh Eq. 6, e oe ro he e re o eh e elee org o he eho e ]:,, K,,,, M 6,, The elee o he re ove re gve he Appex. Se, ere, repevely, he plee o,, hoe e were e he opoe,,,, o he glol oe rx. Coerg h he rre h proporol pg, he, org o, 4], he vo pg rx, D, e lle wh Eq. 7.

6 K M D 7 I he r wo ol pg or,, he r wo rl glr reqee o he rre re ow, he oee e lle g wh he ollowg ye o eqo ]: 8 Whh olve or : / 9. Aor oel A eleroge or oly exer rve ore erroge erl. Aorg o 6, 8], he ge o h ore e oele : 4 Where, he ge el o o he v Coerg h he wo or,, re el, wh pllg o he le pllg o he rgh, he ore exere y he or re repevely gve y: ] 4 4 ] 4 4 Where, he r gp ewee eh or re he erroge re o he rg whe he rre eqlr poo, how Fg. 4.

7 6 Fg. 4 Dplee o wh repe o eqlr poo I volge orol e, he rre eh or e lle wh he ollowg erel eqo ellow 6]: r 4 r To hve ore rel oel, vrle e vrle volge-veloy oee wll e oere. The e epe o he gp ewee he or re he erroge erl re. The volge-veloy oee epe o h gp he or rre. Thereore, eqo 4 e re-wre : r, 6 r, A eprl orl or he e o o he r gp gve 4]: / 7 x Where, o he e whe he erroge elee o pree, x he e whe he erroge erl ohg he or preer. I he e whe he erroge erl oe e ro he or re ow.e. he preer e lle: / 8 x x 9 Thereore, Eq. 7, pple o or or, eoe:

8 7 ] x x x x ] x x x x I 6] eoe h whe he eleroge ore lerze ro eqlr gp,, rre,, he volge-veloy oee,, eql o he ore-rre or,, gve y Eq.. For ere gp,, rre,, he oee e pproxe y:, Thereore, or he or rre eqo he oee wll e pproxe y Eq. 4 or he or wll e pproxe y Eq.. ], 4 ], The ol volge prove or eh or wll e opoe o he volge,, he orol volge,, org o he eqo ellow: 6 7 The e o volge eery o e rre he or,, whh eery o llow he lerzo o he rel or ore, e 6, 8]. Wh lerze expreo or he o ore pole o eg ler oroller. The orol volge wll e oe y he oroller, e el rher. Sg Eq., 4 6 Eq. g Eq., 7 Eq. 6, ore re repreeo o he erel eqo or he rre he or re oe: ] ] x x r 8

9 8 ] ] x x r 9 Power pler e rel ye prove volge l peror l, p. Th o-ler ere repreee Fg. wll e oere he lo progr. Fg. Volge ro I he oel e h wor, hyere ge ro he or wll e regre. I rel ye hee pheoe oly e voe he lx ey, B, he or re ep elow lg vle, B l, o he el e ore. Eq. rele he lx ey wh he or rre,, he r gp 6]: B I B ller h B l, he or wll e worg wh he hyere ro l. Thereore, rg he lo por o very h oo o gree he ly o he oel e. Th e oe he oo ellow hee every lo e ep: B B l l A here re wo or, he oo hol e hee or eh o he: B l B l. Seor oel There oly oe eor he ye h ere poo. To re h rel eor oel e oe wll e le he lo progr. The op o he eor, y, wh oe,, gve y: y 4 The oe wll e oele ro o h e y vle ewee lower l,, pper l, p.

10 9 Coroller A ye where he orol oe wh gl oper oele h wor. The e o gl oper or orollg prpoe llow he pplo o ore ophe orol ehqe, roe e ely he ye. Thereore, he oel e he lo eery o oer hoe e ely. Te ely e o gl oroller e h he orol gl pple oe lle wh he oro prove y he eor prevo e -. Ag o e ely, T, he relohp ewee wo oeve ple e gve y: T Alervely, he expreo ove e wre : T 6 Bee, zero orer hol ] wll e oere, whh e h he orol gl wll re o he lle vle l ew vle prove y he gl oper, er T eo. The prpoe o he oroller o rg he rre o eqlr poo.e., = er oe re ore pple. A ler qr reglor QR, ere, ], wll e e or h. A h e-pe reglor, eery o prove he ye e or he llo o he orol gl. Ag h oly oe eor vlle, oerver wll e e o ee he e. I h wor ll orer oerver wll e eploye,, ]. Bee, he QR ler reglor, whh e h ege e ler oel o he ye. Thereore eery o evelop ler oel o he ye. De o he e ely, reoee o e ree QR wh preve oerver. For h, ler ree oel o he ye eery. To vo he eo o oo y e, he oroller he oerver wll e ege e ple hree egree o reeo lexle rre, e ex. Thereore, oo ler oel o he ye wll e r evelope. Fro h oel, ree ler oel o he ye wll e oe, whh llow he eg o ree QR preve ree ler oerver.. Coo ple oel For he oroller oerver eg ple hree egree o reeo oel o he rre wll e e. Wh he ple oel, el prg lg he oe re oere e o he lexle e, org o he hee how he gre ellow. Fg. 6 Sple oel The e o or prg h repree wo prllel lexle e o legh l oeg elee h ove prllel o he gro gve y 4]: EI / l 7 4

11 Thereore, eh o he eqvle prg wll hve he ollowg e: / 4 l EI 8 / 4 l EI 9 / 4 l EI 4 Eh or exer rve oler ore. B ll plee o or ro he eqlr poo where he r gp eql o or oh or, how Fg. 4 he or rre olle ro rre,, o rel ler ore, r, e pproxe y, 4] ]: x r 4 Where, x he erel rre. The ore-rre or,, gve y Eq. he oreplee or,, gve y Eq. 4, how 6, 8]: 4 I por o re h, he or re orolle y volge, he rre,, h o e e y provg volge,. r / 4 Thereore, he o e wre : / r 44 / r 4 Aorg o 6, 8], he erel rre, x, e lle wh Eq. 46: r x vg x 46 Where, vg verge e vle, eql o, ow gve y Eq. 44, he orol volge. Se he wll olle ro, he verge vle or he e e oe y oerg = Eq. 7. I he proporol pg oee o he rre re ow, proporol pg e le h ple oel. The e o eqo ellow, ogeher wh Eq. 46, e e o repree he ple rre wh proporol pg. ] x r 47 ] 48

12 ] 49 Mg he ollowg vrle o: q, q, q, q 4, q, q q x 6 The ye, lly, e wre he oo e-pe or, 4]: 7. q Aq B Where: q q q q q q q q q q q q q q q q T vg B / 4 A A A,, 7, A A A,, 7, A A A,7,7 7,7 A The elee o he rx A re how he Appex.. Dree ple oel The ree e-pe eqo o ler e vr ye re gve y Eq. 6. I oere h y wo oeve ree e re epre y T eo. q q H 6 Where, 7 The ree oel e oe ro he oo oel. Aer g he erl vle o he preer re A B, he erl vle o re H e lle org o he eqo ellow ]: e AT 8 T T H T e A B 9. Dree QR eg The QR e pe reglor whoe orol gl gve y: C K q 6

13 Where, K C he oroller g rx here gle le rx wh eve ol. Th g hol ze he qr perore ex, J, elow: T T J q Qq R 6 The orol veor he orol eo, lr. Thereore Eq. 6 e wre : J q T Qq R 6 The wegh re Q R h l oe lr hol e hoe wy where he e o eepg plee ll o vo rhe ewee he or re oere o rl. Thereore, he ollowg re re gog o e e: Q R= The oroller g rx K C h ze J gve y ]: K C T T R H PH H P 6 Where P e lle ro he R eqo, ]: T T H PH H P T T P Q P P R 64.4 Preve ree ler oerver eg I pe-e oroller or reglor, he QR, ll e re reqre or he llo o he orol gl, how Eq. 6. However, here oly oe eor he ye h ere he plee o ely, oerver h o e e o ee he e. The orol gl oe wh he ee e gve y: K C qˆ 6 Bee, e o he e ely T, he oerver wll prove he e eve oe wh he oro vlle he -, ely he prevo e eve, q, he ˆ oe y he poo eor, y. I h wor preve ll orer oerver ] wll e eploye. Th oerver ee he e or wh he ollowg eqo: K C HK q ˆ K y ˆ e C e q 66 The rx C rele he oro prove y he eor, y, wh he e vrle. A he eor ere he plee o ely, he:

14 C 67 The rx K e he oerver g rx hol e hoe h wy o gree h he error y er h he ye y. The ye y, repreee y he ler Eq. 6, e lo wre : q q H q H KC]q ] HK C] q 68 The error y gve y ]: e KeC] e e 69 Where, he error veor, e, he eree ewee he e veor he ee e veor: q qˆ 7 Aer K C oe, he eve pole,,..., lle wh Eq. 7 ploe he z-ple. y y y 7 o he rx HK ] C, e HK ] 7 yi C A ler qr reglor w e, he ye y hol e le. Th e h ll pole wll e loe e he rle o r eql o oe. Wh he loo o he pole he z-ple, rle ohg he pole h loer o he org o he z-ple e rw. Th rle h he r r x. Fg. 7 Crle ohg he loe ler ree ye pole o he org o he z-ple The vle o he eve oerver pole,,..., hol e hoe e he rle o o o o 7 r r x. Th gree h he ree oerver y wll e er h he ler ree ye y. Aer hoog he oerver pole, he oerver g, K e, e lle g, or exple, he Aer Forl ] he rx how Eq. 69, ely - K e C]. 4 Slo 4. Slo progr overvew A oper progr w evelope or he lo o he rre wh he or, poo eor gl oroller. I he r lo plve ore pple reo prllel o X x, how Fg.. The plve ore wll e oele hl eo, wh ple F, rg eo eg eo. I he ollowg lo hro ore wh ple F H glr reqey, wh vle l r/, wll e pple. Eve hogh he oroller oerver hve ee ege oerg he ple ler ree oel o he rre or, he oo o-ler oel or he ee egree o reeo

15 4 rre wh he wo or, repreee wh Eq. 7, e he progr. There e o eveee erel eqo or he o-ler oel o he ere ye, ee eo orer erel eqo or he rre, repreee wh Eq. 7, oe r orer erel eqo or he eler rre or, repreee wh Eq. 8, oe r orer erel eqo or he eler rre or, repreee wh Eq. 9. K D M 7 Where: T ] 7 T ] 74 The opoe o he veor re he plee o he rre o, how Fg.. A orh orer Rge-K eho, 6], wh o e ep o. eo wll e eploye he lo progr. For h, eery o ree he orer o Eq. 7. Th e oe wh he ollowg vrle o: v 7 Thereore, Eq. 7 e wre : K v C v M 76 The oplee e o erel eqo or he o-ler oel e wre wh Eq , oe ro eqo 8, ] ] K C v M v 77 ] ] x x r 78 ] ] x x r 79 Where he ore veor,, gve y Eq. 7 he or ore re gve y Eq.. The orol gl,, pe every T eo re o l he ex pe zero orer hol. A oe T he orol gl, gve y Eq. 6, pe wh vle lle wh he e eve T eo he oro prove y he poo eor T eo, org o Eq. 66. The eor op gve y Eq. 8. y 8

16 I orer o vo volge elow zero ove he ro l rg he lo he ollowg roe re e he progr: I p he I he I p he I he 4. Preer e lo p p Rg e: =.7 g = =.48 g Flexle e: E=77p, =786g/, w=., h=., l =.4, l =.4 l =.9. Aor: =.76, B l =.T, r=9., =6, =.77H, x =H, =.88H =.. Power pler: p =4V Srre: = =.7, =9.6r/ =8.8r/. Coroller: T=. =V. Poo eor oe: =-. p =.. 4.9r 7, =., Oerver pole: o o o o4 o o6 o7 x Iplve re ore ple: F =. Iplve re ore rg eg : = =.. Hro ore ple: F H =.. Hro ore reqee e or he lo o he rre wh he or: =,, 7,,.,, 7.,,.,,., 6, 6., 7., 8,,.,, 4, 4,, 6, 7, 8, 9,, r/. 4. Slo rel A Fg. 8 lo rel o he y repoe whe he plve ore pple rg., egg =, he ye who he eleroge or h le wh he or h le re preee. The grph o, plee eer wh repe o e eo re how.

17 6 Fg. 8 Slo rel or plve re ore I e ee h, eve wh oy poo eor, he plee o ll he hree e re e o he eqlr poo h er whe he or re e. ex, rel o he y repoe whe he hro ore wh ple o. pple re preee. A Fg. 9, plee ple eer logrh le he ey e re how or ere hro re ore glr reqee r/ logrh le. The o orrepo o he ye wh he eleroge or he oo le orrepo o he ye who he or.

18 7 Fg. 9 Slo rel or hro re ore I e ee h, eve wh oy poo eor, he ollo ple re ree whe er he r rl glr reqee o he rre. Drg ll he lo, he x lx ey w.7t, r elow he ro l o he or ore erl, B l. Th e h he oel or he or who hyere ro e e who rher oer. Colo Th wor preee he oelg o lexle rre, wh hree rg e wo volge orolle eleroge or xe he gro. The or, whoe ojeve o ree he ollo e y exerl re, were ele orer o e he lower wo oller reo. To rg he rre o eqlr poo, volge where prove o he or y gl ler qr reglor. Se oly oe poo eor w e o e vlle, ll orer oerver w eploye. For he lo, o-ler or oel were oere, lhogh ler ree oroller wh ler ll orer preve ree oerver w e. oe he poo eor w le well. Whe plve ore w pple he op o he rre, he ree oroller prove eqe volge o he eleroge or orer o rg he ye o he eqlr poo. Whe hro ore w pple he oroller w le o ree he ple o ollo whe he ore glr reqey w er he

19 8 rl glr reqee o he rre. The eevee o he regy or reg vro wh eleroge or pe-e reglor were ore y he lo rel, where opro o he ye wh orol who orol w how. The rel preee re eorgg, g h he ehqe eploye e eeve or vro orol o rre he eleroge or re ele rego where he rre ollo re ll or e ep ll y he or o. Appex: Mre elee Bellow, ll he er h re ere o zero ro he glol e rx K, he glol rx M lg, he e rx A re gve.,, 9 EI / l ;,,,, 96 EI / l ; 6EI / l, 4,4 ;,, 4,,4 4 EI / l ; 9 / 9 /, EI l EI l ;,6,8 6, 6, 8, 8,,6,8 96 EI / l ;,7,9 7, 9, 4 EI / l ; 6,6 8,8 9 EI / l ; 6EI / l 7,7 9,9 ; 7,,7 9,,9 4 EI / l ; 9 / 9 /, EI l EI l ;,,,,,,,, 96EI / l ;,,4, 4, 4EI / l ; 6EI / ;, 4,4 l,,, 9EI / l ;, 4,,,4 4EI / l. 6Al / 4 ; 7Al / 4,,,,,, Al / 4 ;.Al / 4 ;, 4,4, 4,,,4, 6 Al / 4 6Al / 4 ; 7Al / 4 ;,6,8 6, 6, 8, 8,,6,8.Al / 4 ; 6Al / 4,7,9 7, 9, ; 6,6 8,8 Al / 4 ;.Al / 4 ; 7,7 9,9 7, 9,,7,9, 6 Al / 4 6Al / 4 ; 7Al,,,,,,,, / 4 ;.Al / 4 ; 6Al / 4,,4, 4, ;,, Al / 4 ;.Al / 4, 4,4, 6 Al / 4. ;, 4,,,4 A,4 A, A,6 ; A4, / ; A4, / ; A 4,4 ] / ; A4, / ; A4,7 / ; A, / ; A, / ; A, / ; A,4 / A, ] / A,6 / ; A6, / ; A6, / ; A6, / ; A ] A / A r /. 6,6 / ; 7,4 vg Reeree ; ; ;,7 vg 7

20 9. Are CM, Coeção SM, ope Jr V, Bre MJ, Alve MTS Sye Ieo Ave Vro Corol o Flexle Srre. Jorl o he Brzl Soey o Mehl See & Egeerg, Spel Ie, 4:86-9. Are CM, Melo P, ope Jr. V, Bre MJ Ave ol pg orol o r r rre g el-orgzg zzy oroller. Jorl o he Brzl Soey o Mehl See & Egeerg 7:44-4. Aly AM Vro Corol o Blg g Mgeorheologl Dper: A ew Corol Algorh. Jorl o Egeerg :- 4. Bole AR Hgh Spee Mrooor o Three Ax Ave Mge Berg. The. Éole Polyehqe Féérle e e. Boe A, TW, Shelley S Mol Fler erl ewor or Apve Vro Corol. Jorl o Vro Corol 6: Bher JC 8 erl Meho or Orry Derel Eqo, e. Joh Wley & So, We Sex 7. Crvlhl R, Slv S, ope Jr V 4 Mol Corol Applo Iellge Tr Srre. I: ABCM Sypo Sere Mehro Vole, pp 4-8. Crvlhl R, ope Jr V, Bre MJ 7 A ee ol orol regy or he ve vro orol o r rre. Sho Vro 4: Dole M, Croe D, Mreo R Ipleeo eg o pve orol eve e o eory lloy. Erhqe Egeerg Srrl Dy 9: Erhpor A, S R A revew o vro ervely rer or loor rre. Coper & Srre 8: Fg RF, YT, Wg CC Dy oel o eleroge or or vro orol o lever e wh p. Jorl o So Vro 88: H QP, gye MT, J, Kwo M Sr Srre Wh Crre-Drve MR Dper: Moelg Seo-Orer Slg Moe Corol. IEEE/ASME Tro o Mehro 8:7-7. Hg M, Mrry TM, Prere K Corollg Floor Vro wh Ave Pve Deve. The Sho Vro Dge : Hrr AF Ave Vro Aorer or Corol o Srrl Vro. Dero, Fly o he Vrg Poleh Ie Se very. I DJ Egeerg Vro, e. Pree Hll, ew Jerey 6. Jg J 984 Opl Deg o Pve Vro Aorer or Tr Be. Jorl o e, Corol Dy 76: Mho J, Hgop JD Fzzy Ave Corol o Flexle Srre y g Eleroge Aor. Jorl o Aerope Egeerg 4: A, eogy S, Irreer H 9 Vro Corol o Srre Roor g Oe-e Mge Aor Dgl Proporol-ervve Corol. Jorl o Vro Corol : Ohzz A, Spzzoo M Experel ly o georheologl per or rrl orol. Sr Merl Srre :7-7. Og K 99 Dree-Te Corol Sye, e. Pree-Hll, ew Jerey. Og K Moer Corol Egeerg, h e. Pree-Hll, ew Jerey. Ploer-Ar R Pve Eleroge Dpg Deve or Moo Corol o Blg Srre. The. Mhe Ie o Tehology. Preo A Vro Corol o Ave Srre, A Iroo, r e. Sprger, Berl 4. Ro SS Mehl Vro, h e. Pree Hll, ew Jerey. So HF, Tre MA Srrl Vro Corol g Exeo Sher Ave- Pve Pezoeler ewor Ilg Sevy o Elerl ere. Jorl o he Brzl Soey o Mehl See & Egeerg : Shwezer, Bleler H, Trxler A 994 Ave Mge Berg. v Hohhlverlg, Zürh 7. See Jr. V, Re DA, I DJ g Pve Tehqe or Vro Dpg Mehl Sye. Jorl o he Brzl Soey o Mehl See & Egeerg : Seph RM, Po FC, oe ACD, Se JA, Slzr AO M Mgéo: Merô e Aro. Eor Cê Moer, Ro e Jero 9. Tool A, A, Slvg M Eleroehl Dper or Vro Corol o Srre Roor. I: Vro Corol, pp -

21 . Trph PK, ghr KV Col Be Eleroge Se-Ave Vro Corol or Flexle Srre. Al o Fly Egeerg Heor Ierol Jorl o Egeerg :8-9. V FAC, See Jr. V 6 Mlol vro pg hrogh pezoeler phe opl reo h r. Jorl o he Brzl Soey o Mehl See & Egeerg 8:9-. Wg, Che HH, He XD Ave H orol o he vro o xlly ovg lever e y ge ore. Mehl Sye Sgl Proeg : Wlo CMD, Allh MM Srrl vro reo g el-g zzy orol o georheologl per. Blle o Erhqe Egeerg 8: Zvov S, Pv A, Reyol P Vro ervely o oorge er he exo: lerre revew. Jorl o So Vro 79:-74