Optimization of Passive Constrained Layer Damping Treatments for Vibration Control of Cylindrical Shells

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1 Oao of Pae Coae aye Dag eae fo bao Cool of Cylal Sell H. Zeg. S. H. Pa a. R. Aba ae ee e layo oao of ae oae laye ag PCD eae fo bao ool of ylal ell e a boaba foe eao. e eao goeg e bao eoe ae ee g e eegy aoa a ae-oe eo. ee eao oe elao bewee e egae laee eoe oe e wole al ole.e. e al ole laee SD of a ylal ell o al aaee of bae e a lle PCD ae ee algo A bae ealy fo eo eloye o f e oal layo of eagla PCD ae w e e a laee eoe of PCD-eae ylal ell. Oao olo of PCD ae loao a ae ae obae e e oa of oal ao of PCD e of eeage ae weg o e bae e. aao of e oal layo eeal a e ae e o eae e oeage e aal eo a be oe e wole fae of e ylal ell fo oal ool of e al ole laee. Ie e bao aaly olea oao ylal ell oae laye ag. C I. INRODCION oae laye ag CD eae a bee egae a a effee way o e bao of a o aao fo ao e. eae ey ow a e oee wok e y of CD eae ol be ae bak o 95 we Daao [] a Mea a Mak [] eeloe e eoeal oel eeely fo e aal a beg bao of aw bea w oela oe. Afe a ay eeae ae eoe ffee folao a ee fel e.g. Dogla a Yag [3] a Rao [4] Ya a Dowell [5] a Rao a He [6]. e oble of og ae aal feee a lo fao elly Ma eee Oobe 3.. R. w e Deae of Meaal geeg of Naoal ey of Sgaoe e Rge Cee Sgaoe 96. He SMA Fellow e-al: elg@.e.g. H. Zeg w e Ie of Hg Pefoae Cog #- e Cao See Pak II Sgaoe 758. e-al: eg@.aa.e.g.. S. H. Pa e SMA gaae HPCS. He ely w Mooola leo Pe Sgaoe. e-al: a@ooola.o. ole [78] fo bo bea a lae we ly o e oo ae ae. Aalyal-eal oee ae ooe o ole e oble we ffee boay oo ae ae [9]. e fe elee oee a alo bee aoe o e ba of eg oeao [~]. Mo of ee ealy wok eal w fll oeage CD eae a ae eely o aal alao. I aally oee oelaally ae aw bea o lae w oae ye of eae oly a oo of e bae e oee w CD. Noke a Nelo [3] wee aog e eale egao o oe e olo o e oble of a aally oee aw bea. A a oe oog aalyal y wa ae o by all e al. Wo ole by g Rayleg-R aoa e egeale oble fo a bea [4] a fo a lae [5] w a gle ag a. g Sg [6] eee a efe eo fo aalyg e oal ag of bea w lle oae-laye oela ae. I ao o all aboe-ebe wok o PCD eae fo bao eo of bea a lae e y of bao a ag ell w ae ag eae a alo bee of ee o ay eeae. Pa [7] e e ayeal bao of a fe leg ylal ell w a oela oe. Joe Saleo [8] egae e effe of ag o e foe ayeal bao of ylal ell w a oela oe. Ala Aa [9] ae o e bao a ag aaly of a geeal llayee ylal ell og of a abay be of ela a oela laye w ly oe e oo. Rae aea [] e a fe elee eo o ole fo a yle-abobe ye w aal w boe o e yle w a oela laye. e al [] eee a fe elee eo fo bao ool lao of laae ooe e w egae eoeleo. H a Hag [] eeloe a gee eoy fo e CD eae ell w fll oeage. Reely Ce a Hag egae e ag effe of CD eae of ye alog logal eo [3] a alog feee [4] eeely o e foe eoe of a ylal ell. A ell eoy ojo w e Doell-Ma-lao ao eloye o

2 yel e aeaal oel. loyg e ae-oe eo e ee eao of oo e of ell aee oal ooae ae ee. e aae e owe a ke o ffe C waa bee ag a ke M oe o alway ge bee ag a e oe we C eee a ea ke. ee eoeal wok a aae e o PCD eae fo bao a oe eo eally a eg eo. Howee e bae o e oao ae ey few alaly e o eg of aal PCD eae of ylal ell ee a bee o eg leae o e ao' be kowlege. Mael e al [5] oee bo aal oeg a oao w eg aable beg e eo a e loao of all e oela laye. Seal bea fe elee wee e o eee e beao of e aw a of e bea. Bo eoy a eee [6] ow a fo ff oela laye e lo fao geae fo aal oeage a fo fll oeage. Ce Hag [7] eee a y o oal laee of PCD eae fo bao eo of lae. I e oao e al ag lay e a efoae e a e feee f a CD ke lay a ealy fo. oogaal a ole oal olo ee wee eloye eag fo e oal ale of CD eae. e y eee ae ae o ae a a o eg of aal PCD eae of ylal ell by fg a oal layo of lle eagla PCD ae of fe ke a aeal oee o e e foe bao eoe e a boaba aee eao. e eao elag e egae laee eoe oe e wole al ole.e. e al ole laee SD of a ylal ell o al aaee of bae e a lle PCD ae ae ee g eegy bae aoa a ae-oe eo. ee algo A bae ealy fo eo [89] eloye o f e oal layo of eagla PCD ae w a o e e SD of PCD-eae ylal ell. Oao olo of PCD ae loao a ae ae obae e e oa of oal ao of PCD e of e eeage of e ae weg o e bae e. ffe of e oal be of ae weg e o PCD eae ae alo e owa a bao aeao g ao of PCD ae. II. ANAYICA MOD OF CYINDR WIH MIP PCD PACHS A. ea Relao A yle eae w lle PCD ae oele a a ooe ylal ell og of 3 laye aely e bae oag a oela laye ea efee o by g e be a eeely. A geeal ofgao fo a ly-oe yle eae w a PCD a ow Fg. w labele eg aaee a eg aable. e laye ae ffee ke eoe by wee o. Slaly Y e ela ol of e laye. e e aeaal oel fo e yle ee bae o laal oee [3]. e e Doell-Ma-lao ao [3] e e-a elao ylal ell a oag laye ae ebe by Fg.. A ly oe yle w oe aal PCD a A e yle aoae by a ell e laee a eo ae ae o ay lealy og e ell ke a e laee e aee eo eee of. e alaee elao ge by Fo e oela laye e e elao ge by [3] 3 a a-laee elao ge by β β e efoao ae of ee laye aal eo ow Fg.. akg o oeao e oe 4

3 lfao e ao of o-l oo bewee laye a wee yel Fg.. e efoao ae of e laye eo fo ylal ell w PCD eae B. egy eo e ke eege of e laye w eglee -lae ea ae 6 wee a e be of PCD ae. e a eege ae ] [ ] [ 7 Ag a eeal aee loa of f ale o e yle fae e wok oe by foe a be eee a w f P 8 C. ao of Moo e ya eoe of e PCD eae yle ee by e eeal aee loa a be allae by bg e ke a a eege o agage eao [3] Q 9 wee eee e geeale ooae a Q e geeale foe a ae eeely e ke a a eegy of e wole ye eee by Fo a yle e laee a be aoae by W W w ζ ζ Hee W a ae e ae laee ae a ζ a I ae e geeale ooae of e lae eoe yle aal aal a feeal eo eeely. D. Solo of Dlaee Reoe I e ae of ly oe e e oe ae fo ae a follow φ φ φ W o o o g aboe ae fo a bg eao 6~8 o agage eao 9 yel e eao of oo of e yle e fo [ ]{ } [ ]{ } { } F M 3 wee [ ] [ ] M M M M e a a a [ ] [ ] e ffe a of e PCDeae yle. eo { } [ ] ζ a ol eo oag e oal oeffe a {F} e eo of geeale foe of w e f elee a be we a

4 { F} f Wj 4... ; j... All oe ae eo e oly a aee loa ale o e yle fae. Fe ag aee loa a e-ao o foe a e loao * * e j oal foe * * jω jω F W e F e 5 j j j wee ω e la feey of e aee foe. e e eao of e-ao foe e ye eao a be we a [ ω M ]{ } { F } 6 Solg ye eao yel e olo of geeale laee a la feey ω. Mllyg e by e ae oe fo e e e yal laee eoe a ay loao of e yle a be allae. III. PCD AYO OPIMIZAION A. Objee Fo A geeal olea oao oble a be efe a follow [3]. F a -eo of eg aable o e a objee fo f f 6 Λ bjee o e ealy a ealy oa j j o g o 7 8 a le bo o e eg aable o 9 l Se o objee o ee e bao eoe of e yle e o-of-lae laee ole ale e aly of ee. Oboly aly loaoeee. A al ole laee SD eefoe efe a e objee fo o be e a D wee w w e ole of o-of-lae laee ole ale a yle fae loao. SD a fo of e layo of e PCD ae a e oal ao of PCD aeal e. Oboly g e SD wol lea o gfa eo of e baoal eegy of wole yle. Feoe a e SD ee o e feey a egal eo oe a aoae feey ee fo e ae of boaba eao. A olo a ee eal ee ω a f D ω ω ω ω ω a Hee ω a ω a a eeely e a a feee of ee. I e oao a follow ee wo aaee ae e H a 3kH B. aable a Coa Ag a oly eagla ae ae e e layo of oe PCD a a be oleely efe by fo eg aable aely e aal loao agla loao aal leg a agla leg a ow Fg. 3. Fo e oeee of fabao alo ae a e of all ae ae ae. Meawle all e PCD ae ae ke ae ke a Yog ol fo oag laye a oela laye eeely. I ae e be of aable of oao fo e oble.e. e eg aaee o be oe ae 4 oe a ae ae e fo e eae. I eal-lfe bao ool eg e ae weg o e bae e owg o CD eae alway ee o a all ao of eeage of e e. e layo oao e oal ao of PCD aeal fe ea oao. e oble e oae o ee yal feably w e ae ae boe w e fae of e yle a o o oela ea oe. C. Oao Saegy Seeal oao algoeo ae aalable o ole e oble efe by eeo 6~9. Mo algo ae ege o fa o f a loal o. Oe eale e eeal aa ogag SQP algo w a ow o be ob a effe fo o oao oble [3]. Howee ay oao oble ae eeal loal oa a ofe of ee o f e be o e wole feable eg oa.e. e global o. Se o aeaal oo fo global oaly e a global o ally oe ffl a e-og o f a a loal o. Soe eo ae eeele bee eeloe o f a aoao of e global o wo ag e wole feable eg oa. e gee algo o oly A a eo a eeloe o ea fo e aoao of global o. e A a bee e eoly by a lo of eeae o ole ao olea oao oble [89]. Hee e A bae ealy fo eo alo eloye fo e PCD layo oao. Fg. 3. e fo aable o be oe: aal loao agla loao aal leg a agla leg

5 W aboe efo of e bo o e eg aable e oao oble lea o a lage eg oa. e alao of gee algo ay o yel goo el. I oe o oba a olo loe o global o e eg ae ae o be fe oae. eefoe ee ffee aoae ae e o e e be of eg aable. I e f aoa e fae of e yle e o ee ege alog aal eo a e ae ae eely be ea ege. e aoa la o aoa ee a e yle e o wo ege. I aoa 3 ee o yle g b e aal leg a agla leg of ea PCD a ae fe. So e aal loao a e agla loao oe wo eg aable of ea PCD a. I. RSS AND DISCSSION e geoe a aeal oee of e yle o be oolle ae ow able. e leg a a of e yle ae eeely.35 a.. e lo fao of oela aeal a alo ea ol ae ae aa w feey. Fo oao oe a all al ag oe e fo of a ole la Mol fo e bae ell a e oag laye: ~ wee e al lo fao. A ale of. e. W e gee algo ale o e oao oble fo ea of e aoae ole. Fo ea e of aaee efe by e oal ao of PCD aeal e be of ae a e aoa e 5 ae eee o ae a e layo w e lowe SD of e yle. able Maeal oee e aaly of ylal ell PROPRIS SH C PZ-5H MARIA la Mol ~ 7 49 Pa.. Dey kg ke... Sea Mol.896 MPa.5 A ao aee foe ale a e le yle.e * a * a e eao feey fo o 3.5kH. Befoe efog e oao e aalyal oel a aoae olo oee ae alae by oag e aal feee of bae yle w e eoeal eo ge [7]. Fo yle w PCD eae e feey eoe a e foe loao oae o el obae a lle y fe elee oe. e yle w gle PCD a eae oee. oo ageee bewee e ale ae obee fo bo ae. A. Coao of ee Aoae Fo ea of aboe-ebe oao aoae e oal layo obae fo a fe be of ae a a fe oal ao of PCD aeal eale o a ae weg of.4%. I ow a aoa e be aoa e e oal layo obae oely ge e lage eo SD. W aoa 3 alog ge a oal layo w lage eo SD g e lea be of ae eglay e eo aee ao be ealy aee. A fo aoa e eo aee oely lowe a aoa 3 a aoa. el ae a a well-beae oble be ably oae o ee e oble eg ae. B e oa oe o ele e aal oal olo. e layo obae g aoa ae ow Fg. 4 fo e ae of a ae fo PCD eae. Neeele ee aoae ow la e e el w e al ole laee eeae w g eo we e be of ae eae. Beyo a ea be of ae fe eo of SD beoe eglgble. e fa a e e o eee o e aoa e le a a oey of e ye. Fg. 4. PCD ae layo obae g a ae g aoa B. Abe of Oal ayo Oal layo w ae obae g ee aoae ae eae o eee e abe of a oal layo. A ow Fg. 5 e layo obae g aoa w ge e lage eo e ae e o eae oeage e aal eo ae a e agla eo. O e oe a aoa w e ae ao ae oeage aal eo e o e oa oe lowe eo SD obee. I ao aoa 3 w e ae' oo ae o oae alo ae a la layo obae g aoa. ow a aao of oeage e aal eo a abe of a oal layo e eee of e aoa e.

6 Feoe all ee layo ow Fg. 5 e ae e o be oe e wole fae of e yle. aoe abe of a oal layo. Aoa Aoa Aoa 3 Fg. 5. Coao of oal layo fo ofgao g ae a eo elg fo e be layo obae bae o aoa. Feey eoe of e wo layo Fg. 7 eoae la eoe. C. ffe of e Pae' Sae o eee e flee of e ae' ae o e SD eo aee a e oly eagla ae ae e a eole aaee ao of aal leg o agla leg efe o aaee e ae. e el a ow Fg. 8 ae a e eo of e SD eeae we e ao eeae. oe w e eo obeao wee we fo a a oal layo e ae e o eae oeage e aal eo ae a e agla eo. ae w lage ao of aal leg o e agla leg ol be e e layo eg. Fg. 6. PCD ae layo aoae by e aally be oe ae layo Fg. 8. aao of SD w e ao of aal leg o agla leg of e ae D. ffe of oal Ao of PCD e Aoa Aoa Fg. 7. Feey eoe of e layo obae g aoao of e aally be oe ae layo a aoa Bae o e aboe obeao a geeal layo ow Fg. 6 ooe fo a ofgao w ae. I eeble e aally be oe ae eo layo eeloe [3]. e eo of SD obae bae o geeal layo. B. eo.4 B oe Fg. 9. ffe of eag e oal ao of PCD ae e e el ow Fg. 9 wee e eeage ow e eeage of ae weg o e bae yle. I a be ee a e egee of bao aeao aee eae a e oal ao of PCD aeal e. e oal be of ae ae ae by e ae le e

7 fge. e el ly a geae al ole laee eo a be aee we e PCD ae ae ea o oe e wole fae of e yle. I alo ae a fo all e ae ee a oal a e of w ay fe eo wll lea o geae ffly obag a bee oal olo.. CONCSION e oao of e layo of PCD ae fo al ole laee SD eo of a lyoe yle ee by a boaba aee foe eee ae. A aalyal oel eeloe g e eegy eo o elae e SD of yle a geoe a yal aaee of bo e bae ylal ell a all PCD ae fo e eae. A-bae ealy fo eo eloye o oe PCD ae loao a ae w e a of g e al laee eoe e ge oa of oal ao of PCD e. e oal aalye ae a fo a fe be of ae a ao of PCD aeal ee ae wo abe of a oal layo. F e ae e o eae e oeage e aal eo; a eo e ae e o be oe e wole fae of e yle. Oe oal aaly fg le a eagla ae w lage ao of aal leg o agla leg oe bee ag effe a e egee of bao aeao of e yle w PCD eae gfaly eae w e eae of e oal ao of PCD aeal. RFRNCS [] R. A. Daao 965 eoy of baoy beg fo ela a oela layee fe-leg bea. ASM Joal of Ale Mea 88-6 [] D. J. Mea S. Mak 969 e foe bao of a ee-laye ae aw bea w abay boay oo. AIAA Joal [3] A. Baa 994 Saw bea eoy a e aaly of oae laye ag. Joal of So a bao [4] D.. Rao 978 Feey a lo fao of aw bea e ao boay oo. Ieaoal Joal of Meaal geeg See 7-78 [5] M.J. Ya.H. Dowell 97 oeg eao of bag oae-laye ag aw lae a bea. ASM Joal of Ale Mea 4-46 [6] M.D. Rao S. He 993 Dya aaly a eg of laae ooe bea w lle ag laye. AIAA Joal [7]. S. Rao B.C. Naka 973 eoy of baoy beg of yeal aw lae. Ae of Mea [8]. Sakyaa H. Maa C. Moa 996 Fee bao aaly of aw bea w ela o oela oe by alyg e ee ee fo. Joal of So a bao [9]. M. Ae 97 Dya aaly of aw bea. Joal of So a bao [] M.. So F.. Boge 98 Fe elee bao aaly of ae e. AIAA Joal 7-77 [] C. D. Joo a D. A. eol 98 Fe elee eo of ag e w oae oela laye. AIAA Joal 84-9 [] X.Q. Peg.Y. a a.r. 998 Ae bao ool of ooe bea w eoelee: A fe elee oel w -oe eoy. Joal of So a bao [3] D.S. Noke F.C. Nelo 968 Coae laye ag w aal oeage. Sok a bao Blle [4] A.. all N.. Aa B.C. Naka 988 Dag aaly of aally oee aw bea. Joal of So a bao [5] A.. all N.. Aa B.C. Naka 988 bao a ag aaly of eagla lae w aally oee oae oela laye. ASM Joal of bao Ao Se a Relably Deg [6] S.W. g R. Sg 998 bao aaly of bea w lle oae laye ag ae. Joal of So a bao [7] H.H. Pa 969 Ayeal bao of a la aw ell w a oela oe laye. Joal of So a bao [8] I.W. Joe.. Saleo 99 Aaly of fee ae bao of laae ooe lae a ell. Ieaoal Joal of Sol a Se [9] N. Ala N.. Aa 984 bao ag aaly of a llayee ylal ell Pa I: eoeal Aaly. AIAA Joal [].C. Rae N. aea 995 bao a ag aaly of ylal ell w oae ag eae a oao of eeeoe. Joal of bao a Ao [].R. X.Q. Peg.Y. a a J. a 999 bao ool lao of laae ooe lae w eoelee. Joal of So a bao [] Y.C. H S.C. Hag e feey eoe a ag effe of ee-laye ell w oela oe. Coe a Se [3].H. Ce S.C. Hag 999 bao of a ylal ell w aally oae laye ag CD eae. Ieaoal Joal of Meaal See [4].H. Ce S.C. Hag bao aeao of a ylal ell w aally oae laye ag eae. Coe a Se [5] J.. Mael P. oee A. Sa 99 Oal oae laye ag w aal oeage. Fe elee Aaly a Deg [6] J.. Mael S. Sake F. Pooy 995 Oal oae laye ag of bea: eeeal eal e. Sok a bao [7] Y.C. Ce S.C. Hag A oal laee of CD eae o bao eo of lae. Ieaoal Joal of Meaal See [8].R. X. Ha a.y. a A obe gee algo a olea lea ae eo fo aeal aaeao g ela wae. Coe eo Al. Me. a g [9] Z.. Yag.R. a.y. a A ee oee fo ak eeo g egal a eae by oal fbe Sa Maeal a Se [3] W. Soeel 993 bao of Plae a Sell e. New Yok: Mael Dekke 993 [3] S.S Rao 996 geeg Oao eoy a Pae. 3 e. New Yok: Wley [3] H.S. Zo J.P. Zog a M. Nao 993 Seo ea of be ell oolg eo ale o fleble g. ASM Joal of bao a Ao