JJMIE Jordan Journal of Mechanical and Industrial Engineering

Transcription

1 JJME Joda Joal o Meaal ad dsal Egeeg Volme Nmbe Sep. 007 SSN Pages 3 - A Nolea Tosoal Dyam Model o Ml-Mes Gea Tas avg Flexble Sas Amad Al-Syab a * Ame Kaama b a Depame o Meaal Egeeg aseme Uvesy P.O. Box 3307 Zaqa 333 Jodo b Depame o Meaal Egeeg Te Oo Sae Uvesy 650 Akema Road Colmbs O 30 USA Absa A o-lea me-vayg dyam model s developed o sdy osoal dyam beavo o a ypal ml-mes gea a. Te pysal sysem osss o M sas M opled o ea oe by M gea pas. Te dsee dyam model ldes e gea baklas leaae gea mes sess laos ad osoal lexbles o e sas. addo e gea oo modaos ad ypal maag eos ae lded e om o peodally me-vayg dsplaeme os appled a gea meses. A ml-em amo Balae omlao s sed ojo w dsee Foe Tasoms ad a Paame Coao eqe o oba e seady-sae peod- moos. De meal egao esls ae sed o demosae e aay o e amo balae pedos. Ees o key sysem paamees ae also sded. 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved Keywods: Gea ;BM; Ml-mes; Tme-vayg; Dsee Foe; Tosoal; Nomelae Ls o Symbols: b al leg o baklas dampg oee e gea asmsso eo exeal oe g dsoos dsplaeme o BM amo Balae Meod pola mass mome o ea J Jaoba max k gea mes sess M Moodomy max m mass eqey mlple p elave gea mes dsplaeme mbe o dsee me pos q dsee me eval R mbe o amo ompoes osdeed e solo base ads S max om o o-lea algeba eqao se T oqe me dsplaeme amo amplde U dsplaeme veo Z mbe o gea ee δ koeke dela dmesoless eqey dmesoless mes sess θ oaoal dsplaeme eqey Ω omal agla veloy dampg ao Sbsps: aaes qay eq eqvale gea o sa dex aal mode m mes s sa Spesps: ms oo-mea-sqae vale T max aspose * Coespodg ao. e-mal: alsyyab@.ed.jo

2 3 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN odo Gea sysem dyams as bee a majo esea op o e las wo deades se bo age le ad ose beavo o a gea se ae mpaed by s dyam beavo. Te dyam espose o e gea sysem sow Fge wll be sded s pape. Te sysem s omed by M paallel sas opled o ea oe by M gea meses omed by M geas. p ad op sas ae oeed o gd eas epeseg pme move p ad op eas espevely. Ts ogao a be od a wde age o aomove maal aoma ad oosly vaable asmssos aeospae ooa dve as mae wd be ad dsal applaos. Fge : A M-sa gea a ogao osdeed s sdy A mbe o dyam models wee poposed e pas o desbe e dyam beavo o ml-sa gea sysem. Mos o ese models wee lea me-vaa ype as e gea baklas ad mes sess laos wee bo goed -0]. S smplaos allowed a lage mbe o degees o eedom o be lded e models se Ege Vale ad Modal Smmao omlaos wee sable. Sa ad beag lexbles ad ombed asvese-osoal moos o geas wee all lded ese models o sdy lage sale geasa-beag sysems. some ases e ase deleos wee also lded e om o a ase sess max 0]. Wle ese models oeed gdeles owads e desg o gea sysems w avoable sa ad beag aagemes ey bog lmed sg o e beavo a e gea mes. Aoe gop o models -] lded e mes sess laos e om o a paame exao wle sll assmg o oo sepaaos. Tese sdes osed o e sables ased by paame exaos ad peded pmay ad paame esoaes eslg egos o sable moos w ely lage ampldes. Tese models as well wee o apable o desbg e o-lea beavo obseved ee expemeal daa 95-] de o baklas-ded oo sepaaos. Models o Kaama ad Blakesp 67] lded bo e gea baklas ad mes sess laos o a sgle sp gea pa ad exbed a soeg ype olea beavo o a sgle gea pa de o appae oo sepaaos. Tey also demosaed a e sgle gea pa model oelaes well w expemeal daa. Mos eely ese aos 90] poposed a olea me-vayg dyam model o e sysem sow Fge o a ase o ee sas ad wo gea pas. Te sysem was eded o a wo degee o eedom dee model by sg e elave gea mes dsplaemes as e oodaes ad assmg gd sas. Dmesoless eqaos o moo wee solved o e seady sae peod- moos 9] ad peod- sb-amo moos 0] by sg a ml-em amo Balae meod BM ojo w dsee Foe asoms ad a paame oao seme. Tese solos wee sow o ompae well w e de meal egao solos. Floqe eoy was appled o deeme e sably o e seady sae solos. A example gea a was sed o vesgae e lee o key sysem paamees ldg aleag mes sess ampldes gea mes dampg ad oqe asmed. Tese eale models 90] wee lmed seveal aspes: ey osdeed oly a 3-sa -gea pa ogao e osoal lexbles o e sas wee o lded e model eslg same vbao ampldes o wo geas moed o e same sa ad e p ad op eas wee o lded. Ts pape ams a geealzg ese pevos models 90] by osdeg ay mbe o sas ad ldg bo e osoal sa lexbles ad p/op eas. Te model wll lde N ea elemes N degees o eedom wee N M w ad N epeseg p ad op eas espevely. Te ml-em BM a was sed sesslly o e eesa sysem 90] wll be exeded ee as well as o e seady sae peod solos o s M-sa sysem ldg bo peod- ad peod- sb-amo moos.. Dyam Model Fomlao A dyam model o a segme o e M-sa gea a o Fge s sow Fge. Eqaos o moo o e oveall sysem ae gve as: & θ k p T a && θ k p k g 0 b M && θ N N N N k N pn N N N N k N g N 0 & N θ N N N k N pn TN d

3 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN wee N M a ovedo deoes deeao w espe o me ad θ θ odd p θ θ e eve. p p p b : odd : eve e e b ab ad a dmesoless me dmesoless om o eqaos a be we as Fge : Tosoal dyam model o a segme o e e gea a sow Fge && p p g && p && p && p p g p g p e&& g p g 35 L N 3 p && e 6 K N 3 5a 5b 5 5d ee p w odd epeses osoal sa deleos bewee wo geas o a gea ad a gd dsk ad p w eve epeses elave dsplaemes a a gea mes omed by gea eas ad alog e le o ao. ad ae e base le ad o e gea pa omed by geas ad. Tosoal sa lexbles ae epeseed by e osoal sess ad dampg oees k ad odd as sow Fge. Te lexbly o a gea mes s modeled by a peodally me-vayg mes sess k eve a s sbjeed o a olea dsplaeme o g epeseg e gea baklas leaae p b g 0 p b p > b p b p < b eve. 3 addo ad b ae e gea mes dampg oee ad amo o baklas a e gea mes omed by gea eas ad eve espevely. Fally e Fge ad eqao epeses e so-alled sa asmsso eo exao a e mes o geas ad a aos o eoal gea oo pole modaos ad maag eos. Te sysem sow Fge s sem-dee w a zeo-valed aal eqey. Ts gd body mode a be elmaed by sg p as e oodaes. Also deg a aaes leg b ad a aaes eqey s a && pn N N N N N NN NN N N N N g N NN pn N. 5e ee dmesoless mes sess os ae deed as kˆ k eve wee k ad kˆ ae e mea ad aleag ompoes espevely. A ovedo deoes devave w espe o. Te oe dmesoless paamees ae deed as: T / N TN / N 6ab g odd g 6 g b eve k b odd k eve b k odd k eve k b k b odd eve 6de

4 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN eve b odd b 6g eve odd. eve b odd b 6 3. Ml-em amo Balae Solo Te ml-em amo Balae meod s based o e assmpo a e exeal exaos ad e me-vayg oees e seady-sae solos p ad olea os g ae all peod. Tese os ae gve Foe sees om as: K m m ] s os eve 7a s os m E m E E e Γ eve 7b L ] s os l l l l l N K 7 N p R s os K 7d s os v v v g R eve 7e ee Z Ω / s e dameal dmesoless eqey o e sess oo pass eqey o a ose gea mes wee Z ad Ω ae e mbe o ee ad oaoal eqey o oe o e geas omg e mes ad e ege mlples m eve ae deed o lde ommesae sess eqey aos o e vaos gea meses. eqao 7d T N N N ] L L ae kow oees o e assmed solo ad s e sb-amo dex eqed o d sb-amo moos. Deg θ sbsg eqaos 7 o eqao 6 ad eog amo balae e ollowg se o R N o-lea opled olea algeba eqaos ae obaed: 0 v S wee veos v ad S ave dmeso R N. Fo odd e elemes o S veo ae gve as ] R ] ] v v S ϕ ϕ 9a ] ] / Φ Φ S 9b ]. 3 ] 3 Φ Φ S 9 Fo eve e elemes o S ae gve as ] R ] ϕ v S 9d ] / Φ m E S 9e ]. 3 / Φ m E S 9 eqaos o S ad N S R e ems avg des less a oe o lage a N espevely ms be omed. addo paamees ϕ ad Φ eqaos 9 ae deed below

5 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN v v v m m m v v v m m m 3 v v v m m m v v v m m m v / v m / m v v / m v v / m 0a 0b 0 0d ϕ 0e Φ Φ 0g lae seps e seleo o as a ool paamee o solve o e elemes o sg Newo-Rapso eao meod poses dles Te deema o e Jaoba max also appoaes zeo ea e bao pos. Ts a be avoded by swg o aoe kow as e ool paamee leavg e dmesoless eqey ad e oe elemes o e solo veo as kows o be deemed. ode T N T o mpleme s s expaded o U ] N R wee R. Aodgly e ollowg dmmy eqao s added o eqao 9 N * SR j wee N j R o e vales o e des j R ] ad N] dee w eleme s ose as a ool paamee ad * s a meal vale pesbed o e ool paamee. πq gq s q 0 v 3a- Tese v vales ad e Newo-Rapso eee omla m m m m U U J ] S ae sed o solve eqaos 9 o U wee m U ad m U ae e pevos ad e e eao vales o e veo U espevely ad ] m J s e vese o e Jaoba max o e veo S esmaed a e pevos po m. Elemes o e Jaoba max J o s model ae deed Appedx A. Te Floqe eoy s sed o deeme e sably o e seady-sae moos as desbe eeee 9].. Resls A ee-sa gea a 6-DOF sem-dee model s osdeed as e example sysem. osss o wo gea pas o deal dmesoless paamees oeed o ea oe ad o e pme move ad load eas va osoally lexble sas. Te dmesoless paamees ae allaed by sg eqaos 6 ad e dmesoal paamees lsed Table. Table. Dmesoal paamees o e example gea pa Te oees o e olea dsplaeme N os v ae epeseed ems o ad R N] R ] by sg Dsee Foe asoms. Te vales o e p ad g a e dsee me qρ q 0 ] ae gve as R πq πq pq os s ] pq b gq 0 pq b pq > b pq b pq < b eve. a b ee ρ π/ wee s e oal mbe o e dsee pos. Te oees o g ae deemed by sg e vese Foe asoms s a R] v gq q 0 πq v gq os q 0 ode o lm e sze o e paamee sdy mosly amo mes sess os w amplde 0.3 ae osdeed K eqao 7. Ts oespods o a sp gea pa w a vole oa ao vale o.7. A osa exeal p oqe o T 50 N-m L 0 eqao 7 oespodg o 000 ad 5 5 s osdeed. All geas ae assmed o be ee o pole eos so a all e 0. A aaes leg o b 30 μm s osdeed a epeses al magde o e gea baklas so a b b.0. A aaes eqey 970 ad/s s sed. addo e dameal mes eqees o bo gea pas ae osdeed eqal m m less speed. Te vales o e mes dampg oees Table ae s a

6 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN ey oespod o a dampg ao o m 0.05 gve m k mm wee m. Smlaly e vales o sa dampg oee 3 5 oespod o a sa dampg ao o s 0.0. Te esls e ollowg seos wll be peseed e om o ms p ad ms p vess e dmesoless eqey. ee ms p s e oo-mea-sqae ms amplde o p deed as ms R / p { A ] } wee / A { ] ] } s e - amo amplde. ms p ad ms p ae o pmay ees ee se ese paamees epese gea mes dsplaemes a ae dely popooal o dyam gea mes oes... Ml-em amo Balae vess Nmeal egao Fge 3 sows peod- eqao 7 BM solo ms p ad ms p as a o o o a sysem avg ad k 3.00 N- m/ad. Te k ad sold les deoe e sable ad sable amo balae moos o R 6. Fge 3 also sows e sable ad sable BM solos o e oespodg lea me-vayg sysem b b 0 as k ad dased les espevely. addo e de meal egao esls o bo olea ad lea sysems ae epeseed by sqae symbols. As sow Fge 3 e 6-em BM solos ma well w e meal egao solos o bo e olea ad lea ases. Te age o ldes pmay esoaes a a ad b. 6 as well as a spe-amo esoae a / 0. wee ad a ae wo o e aal eqees. b Bo e olea ad e oespodg lea models esl e same vbao ampldes a eqees wee oo oa s maaed all e me ad ee e gea baklas oleay s o a ao. As appoaes aal eqees ad a b.6 pmay esoaes w aaes soeg-ype olea ves ae obaed. Ts s solely bease e ee loose oa dg a poo o e mesg yle 90]. Te soeg ppe ba o e pmay esoae a a also exbs a adeg ype ve sloped o e g. Ts oespods o e bak ollsos oa a e loaded oo lak addo o oo sepaaos w s moe lea o ms p. s also oed Fge 3 s a ee s a age o w o sable peod- moos ae od. Ts oespods o e paame esoae a a. As wll be llsaed lae s age s daed by peod- sb-amo moos. Fge 3: Compaso o peod- ml-em BM R 6 ad meal egao esls o K ad k 3 0 N-m/ad. Sable ad sable solos o e olea model sable ad sable solos o e oespodg lea model ad ms ms meal egao solos. a p ad b p.. lee o Tosoal Sa Flexbly ms Fge ee o k 3 o peod- p s llsaed. ode o desad s ge bee e vaao o e aal eqees o e oespodg lea me-vaa sysem ae ploed Fge 5 agas e osoal sess k 3 o e sa oeg e gea pas o ea oe. Fge : lee o e sa sess k 3 o peod- BM ms solos o K 0. 3 ad 000 ; a p ms ad b p. Sable ad sable BM solos

7 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN ae evde Fge we k 3 0 N-m/ad. Fo e 5 oe wo vales k 3 50 ad 6 0 N-m/ad e pmay esoaes ae obseved a a b ad ms. Te p esoaes ae moe sga a a ad ms wle p exbs a lage soeg-ype esoae ea b. Spe-amo peaks a oe-al o e aal eqees ae also pese. addo e peod- solos ae sable ea ages mos o w oespod o e paame sables de e gea mes sess laos. Fge 5: Vaao o aal eqees a b K e o e oespodg lea me-vaa sysem w k 3 Two o e aal eqees ae d e egadless o e vale o k 3. Fo e sysem deed Table ese modes ae domaed by e deleos o e sas oeg e pme move ad load eas o e espeve geas ad d k / ad e k5 / 6 wee k ad k 5 ae osoal sesses o ese sas ad ad 6 ae e eas o e pme move ad e load. Fo smalle vales o k 3 5 say k 3 < 0 N-m/ad e wo gea pas ae dyamally opled ad ea gea pa as depedely as sgle gea pas. s ase a 0 b k / m3 ad k / m wee m ad m 3 ae eqvale masses o e s ad seod gea pas ad k ad k ae e aveage mes sess vales. Se bo gea pas o e example sysem ave e same dmesoless paamees b. 6 o small vales o k 3. O e oe ad o k 3 > 0 N-m/ad e wo gea pas ae oeed almos gdly ad a ad b.6 wle s lealy osde a eqey age o ees 03]. Fally a emedae sa 5 sess vales say k 3 50 all ee aal eqees a b ad ae o-zeo ad w e eqey age osdeed. Teeoe esoae peaks sold be expeed a ese eqees. Fge osdes o dee k 3 vales 0 N-m/ad vey 5 so 5 0 ad 6 0 N-m/ad emedae ad 0 N- m/ad. vey s. We k 3 0 N-m/ad e wo gea pas ae dyamally opled ad se bo gea pas o e example sysem ave deal dmesoless ms ms paamees p p bo avg pmay esoae peaks a b. 6. O e oe ad a sess vale o k 3 0 N-m/ad s lage eog o povde a almos gd oeo bewee geas ad 3 s a θ 3 θ. Aodg o Fge e s gea mes aal eqey s appoxmaely we e seod aal eqey b a. 6. As a esl wo pmay esoaes a a ad b. 6 as well as a spe-amo esoae / 0. a.3. lee o Oe Sysem Paamees lee o e mea oe asmed by e gea a o e seady sae peod- espose s sow Fge 6. Te vales o e osa dmesoless oes 5 wee ad 3700 oespod o p oqe vales o T ad 50 N-m espevely. Te espose ves ae ageeme w pevos obsevaos o sgle gea pas 567] ad ee-sa sysem esls 90]. easg e osa oqe appled does o peve oo sepaaos 5 om og. Lage ad vales esl ms ms ge ampldes o p ad p. Te pmay esoa peak a a exbs oly a soeg ype beavo o wle e ampldes ae sgaly lage o e oe wo oqe vales o ae bak ollsos ad a adeg ype ve ollowg e ypal soeg beavo. Fge 6: lee o mea load asmed o peod- BM solos o K 0. 3 ad k 3 0 N-m/ad; ms Sable ad sable BM solos. a p ad b ms p Lkewse e spe-amo esoae ampldes a a / 0. Fge 6b ad a b / Fge 6a ae eased sgaly we e oqe

8 3 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN s eased. Te paame sably egos ea a ad e jmp-p eqees ae o leed 5 by e vales o ad vales. Fge 7 llsaes e lee o e gea mes sess ampldes o peod- moos. Te mes sess amo ampldes o a sp gea pa deped pmaly o e vole oa ao a paamee epeseg e aveage mbe o egaged oo pas. Fo vales o amo mes sess ampldes ad 0. ae osdeed Fge 7 oespodg o vole oa aos o.5.7. ad.9 espevely. s ge e mes sess ampldes appea o lee e peod- espose seveal ways. eased vales esl eased espose ampldes as well. Ts lee s moe sga a e oe sow Fge 6 as o oly e ampldes b also e degee o olea beavo s leed. We vales ae low say 0. a mo soeg ype esoae peak s obseved ea a 0.96 Fge 7a wle e pmay esoae peak ea b. 6 s lea. Fo 0. bo pmay esoae peaks beome o-lea oo sepaaos. Fo 0. 3 bak ollsos ae also aed ea a Te spe-amo esoaes a a / 0. Fge 7b ad a b / 0.93 Fge 7a beome sgaly lage we s eased. Lage ampldes ae obseved o eae e paame esoaes as well. Wle ee s o sable ego o peod- moos o 0. a wde bad o sable moos s obseved o 0. w.65.5]. Fge 7: lee o amo mes sess amplde o peod- BM solos o k 3 0 N-m/ad ad 000 ; ms Sable ad sable BM solos. a p ad b ms p Nex ge amo ampldes o e peod mes sess os eqao 7a ae also osdeed o llsae e lee o e seady-sae peod- moos. Fg. e ve Foe amos o e mes sess os & ae osdeed o epese a vole oa ao o.5. was sow eeee ] a a mes sess o old be appoxmaed o a eagla waveom w beomes a sqae wave o a vole oa ao o.5. s ase eve amo ampldes ae zeo ad e s ee o-zeo amos ae & K 5 eqao 7. s ase e ms espose ves exb o oly e pmay esoaes ea a ad b ad spe-amo esoae ea a / ad b / as dsssed eale b also addoal esoae peaks a a 3 3 b 5 a ad 5 b de o e ge amo ems o e mes sess ad lee o gea mes dampg ao m s vesgaed ex Fge.9. Te seady-sae peod- solos ae sow o m ad 0.0. Te vale o e gea mes dampg s obseved o ae e espose ampldes level o olea9] beavo exbed ad e wd o paame sably eqey bads. Te sysem w low dampg vales demosaes lage ampldes doma pmay & spe-amo esoaes as well as wde eqey ages o sably.

9 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN e eqees a / m a / m 0. b / m.6 ad b / m As wo o e pmay esoae eqees ode a / m b / m e peod- espose ves ea s eqey lde seveal jmp dsoes. addo bak ollsos ae evde a e s wo esoae eqees. As e seod example osde a sysem avg m 3 ad m wose espose s sow Fge. s ase e pmay esoae eqees ae a a / m 0. 3 a / m 0. b / m 0.65 ad b / m Se ese o esoae peaks ae spaed losely w aow eqey age e espose ves beome ae omplex w seveal baos ad sable ad sable egos. Fge : Peod- BM solos o peod K 5 mes sess ampldes ad o 000 ad k 3 0 N-m/ad; Sable ad sable ms ms BM solos. a p ad b p Fge 0: Peod- BM solos de amo K mes sess ampldes 0. 3 o m m 000 ad k 3 0 N-m/ad; sable ad sable ms ms BM solos. a p ad b p Fge 9: lee o mes dampg ao o peod- BM m solos o k 3 0 N-m/ad ad 000 ; Sable ad sable BM solos. a m b m ad m 0. 0 Te dmesoless mes oo pass eqey was deed eqao 7a as m wee m s a mlple oded o adle e ases we e mes eqees o dvdal gea pas ae o eqal. Te esls sow p o s po osdeed m m dag a e gea mes eqees o bo gea pas ae deal. Ts mples geas ad 3 a ae oeed by e sa o sess k 3 ave e same mbe o ee b dee modles. geeal oweve s may o be e ase. Two dee saos ae llsaed Fges 0 ad o demosae e ages seady sae espose we m m. Fge.0 e espose s sow o e ase we m ad m wee e pmay esoaes ae ea.. Sb-amo Resoaes ad Peod- Moos Seveal o e oed espose ves sow eale lded egos o sable peod- moos a e paame esoae eqey a. 9. Alog was o sow ese ges e same s e o b 3. 9 as well. eeee 0] peod- moos wee sow o lose e sably a e bodaes o ese egos o sably o yeld sable peod- moos. Fge. sable ad sable peod- moos ae sow ea a ad b. Tese moos ae obaed by seg eqao 7de ad 9.

10 0 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN Fge : Peod- BM solos de o amo K mes sess ampldes 0. 3 o m 3 m 000 ad k 3 0 N-m/ad; sable ad ms ms sable BM solos. a p ad b p Fge 3: Peod-3 sb-amo BM solos de o amo K mes sess ampldes 0. 3 o 000 ad k 3 0 N-m/ad; sable ad sable ms ms BM solos. a p ad b p 5. Colsos Fge : N ad Peod- sb-amo BM solos de o amo K mes sess ampldes 0. 3 o 000 ad k 3 0 N-m/ad; sable ad sable ms ms BM solos N solo. a p ad b p Te ampldes o e moos ae vey lage s a bak ollsos ae also obaed e om o peod- moos. As ese sable peod- moos ove e ee ages o sable peod- moos ay aasop eases o ampldes ese ages ae peveed solely de o e gea baklas oleay. Smlaly Fge.3 peod-3 sb-amo moos ae od o exs ea e paame esoae eqey 3 a by seg 3. Tese moos oexs w sable peod- moos. oweve ey om solaed slads w ae o oeed o e peod- moos sggesg a e sysem may o exb s moos less dsbed dasally. A o-lea me-vayg osoal dyam model o ml-mes gea a omed by M sas opled o ea oe by M gea pas. Te dyam model lded e gea baklas oleay allowg oo sepaaos ad bak ollsos e gea mes sess laos ad osoal lexbles o e sas. A ml-em amo Balae omlao ojo w dsee Foe Tasoms ad a Paame Coao eqe wee poposed o oba e peod- seadysae moos. Te aay o solo meod was demosaed og a ompaso o e de meal egao esls. A ee-sa wo gea-pa example gea a was sed o sdy e lee o e key sysem paamees. Te osoal sess o e sa oeg e gea pas was sow o lee o oly modal aaess o e sysem b also e olea espose. was also sow a e gea mes sess amplde gea mes dampg ao e oqe asmed ad e ao o e gea mes eqees all leed e oed espose sgaly. addo o pmay ad spe-amo esoaes o peod- moos e sb-amo esoaes o peod- ad peod-3 moos wee also sow o exs oe e example sysem osdeed. Akowledgemes Te aos ak aseme Uvesy Jodo o sppog e aos dg s sdy.

11 007 Joda Joal o Meaal ad dsal Egeeg. All gs eseved - Volme Nmbe SSN Reeees ]. Vayak R. Sg ad C. Padmaaba Lea dyam aalyss o ml-mes asmssos oag exeal gd geas Joal o Sod ad Vbao Vol ] S.. Co J. Gleke D. C. a ad K. Uls Dyam gea load de o opled laeal osoal ad axal vbaos a elal geaed sysem Joal o Vbao ad Aoss Vol ] T. C. Lm ad J. L Dyam aalyss o ml-mes oe-sa asmsso Joal o Sod ad Vbaos Vol ] A. Kaama Dyam aalyss o a ml-mes elal gea a Joal o Meaal Desg Vol ]. da A. Tama K. Kk ad. Agaa Copled osoal-lexal vbao o a sa a geaed sysem o oos s epo Blle o e JSME Vol ]. da A. Tama ad M. Oos Copled osoallexal vbao o a sa a geaed sysem 3 d epo Blle o e JSME Vol ]. da A. Tama ad. Yamamoo Dyam aaess o a gea a sysem w soly sppoed sas Blle o e JSME Vol ] T. wasbo S. A ad R. Kawa Copled laeal-osoal vbao o oo sysem aed by geas Blle o e JSME Vol ] K. Umezawa T. Ajma ad. ojo Vbao o ee axs gea sysem. Blle o JSME Vol ] M. Kb A. Kaama D. Z ad K. Kezle Dyam aalyss o ml-mes elal gea ses by e elemes pess Joal o Vbao ad Aoss 00. ] M. Beo M. ad A. Seeg Smlao o esposes ad sably odos a po-gea sysem Joal o Meaal Desg Vol ] M. Beo ad A. Seeg Faos leg sably ad esoaes geaed sysems Joal o Meaal Desg Vol ] W. Molles Paameeeege Swgge esge Zyldeadgeebe P.D. Dsseao Res- Wesalse Tese osle Aae 9. ] T. Nakada ad M. Uagawa Te dyam loads o geas ased by e vayg elasy o e mag ee Po. o e 6 Japa Naoal Cogess o Appled Meas ] A. Kaama ad G. W. Blakesp Expemes o olea dyam beavo o a osllao w leaae ad peodally me-vayg paamees Joal o Appled Meas Vol ] G. W. Blakesp ad A. Kaama Seady sae oed espose o a meaal osllao w ombed paame exao ad leaae ype o-leay Joal o Sod ad Vbao Vol ] A. Kaama ad G. W. Blakesp eaos bewee ommesae paame ad og exaos a sysem w leaae Joal o Sod ad Vbao Vol ] A. Kaama ad G. W. Blakesp Ee o vole oa ao o sp gea dyams Joal o Meaal Desg Vol ] A. Al-syyab ad A. Kaama No No-Lea Dyam Aalyss o a Ml-Mes Gea Ta sg Ml-em amo Balae Meod: Peod-oe Moos pess Joal o Sod ad Vbao00. 0] A. Al-syyab ad A. Kaama No-lea dyam aalyss o a ml-mes gea a sg ml-em amo balae meod: sb-amo moos pess Joal o Sod ad Vbao00.

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