Absorption characteristics of multi-layered material anechoic coating on frustum-of-a-cone cavities

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1 MAEC Wb of Confrnc 77, 0800 (06 DOI: 0.05/ matcconf/ ICMMR 06 Abortion charactritic of multi-layrd matrial anchoic coating on frutum-of-a-con caviti Liu Guo-qiang,, Lou Jing-jun,, Li Hai-tao, Collg of Powr Enginring, Naval Univ. Of Enginring, Wuhan 00, China National Ky Laboratory on Shi Vibration &Noi; Wuhan 00, China Abtract. Imrov th low-frquncy acoutic rformanc of ound abortion coating of ubmarin i a hot iu. Bad on th thory of ound wav normally iminging on th abortion layr of D,th D haft mod of frutum-of-a-con caviti i tablihd by finit lmnt COMSOL, which i tt to analyz th abortion charactritic combind tructural aramtr. h calculation rult indicat that undr th condition of th am rforation rat,th abortion rformanc of multi-layrd matrial anchoic coating i bttr than that of ingl-layrd matrial anchoic coating, cially to th rformanc of low-frquncy; th abortion rformanc of frutum-of-a-con caviti i bttr than that of cylindrical and llioidal tructur. With th rforation rat i incraing,th abortion rformanc of anchoic coating in low-frquncy imrov..chooing th aroriat cavity tructur i imortant. And th futur acoutic otimization of th multi-layrd frutum-of-a-con caviti anchoic coating i guidd by th tudy. Introduction Undrwatr anchoic coating i an imortant art of th talth of undrwatr vhicl. With th dvlomnt of activ onar tchnology, th frquncy of dtcting acoutic i gtting lowr and lowr, o imrov th low-frquncy acoutic rformanc of ound abortion coating of ubmarin i a hot iu, and continuou otimization of th cavity tructur could mak th anchoic coating in low-frquncy rform mor xcllnt []. Mainly from th two act of th tructur and matrial otimization to incra th abortion rformanc of anchoic coating in low-frquncy. In trm of tructur, Shang Chao [] hld that th abortion rorty of frutum-of-a-con caviti which mak air a backing by uing finit lmnt mthod, according to otimizing th dign, th anchoic coating rformanc of th whol frquncy band, cially low-frquncy, i furthr imrovd; ao Mng [] analyzd th abortion rorty of anchoic coating of th combind cavity ty by uing wavguid finit lmnt mthod, th abortion rformanc of anchoic coating in low-frquncy gratly imrov with th diffrnt mbdding ratio of combind cavity ty; ang Wilin [] ut forward that uing th boundary condition of th front and back boundari th xrion of ronanc frqunci and rflction cofficint of coating ar givn. In trm of matrial, Lü Linmi [5] gav th otimization mthod of how to imrov th abortion ffct in low-frquncy, according to mbddd vicolatic abortion of diffrnt ha of th cattring layr. h abov litratur i th otimization of th tructur and matrial of ingl-layrd matrial anchoic coating. hi ar focu on th analyi of abortion rformanc of multilayr matrial of frutum-of-a-con caviti tructur. Rult how that th abortion rformanc of multi-layrd matrial anchoic coating i bttr than that of ingl-layrd matrial of frutum-of-a-con caviti tructur and ingl cavity tructur of multi-layr matrial. Ecially, th abortion ffct in low-frquncy i imrovd and obtain th rul about th influnc of othr tructural aramtr on th covring layr.. hortical modl Auming that th fluid i an idal fluid,it ha th charactritic of non vicou, uniform, incomribl flow and zro flow rat. In addition, th dnity and rur ar aumd to b contant too. Fluid finit lmnt quation: 0 M K R whr: ρ 0 dnity of fluid mdium acoutic rur [K ] global tiffn matrix [M ] ma matrix [R] global couling matrix ( h Author, ublihd by EDP Scinc. hi i an on acc articl ditributd undr th trm of th Crativ Common Attribution Licn.0 (htt://crativcommon.org/licn/by/.0/.

2 MAEC Wb of Confrnc 77, 0800 (06 DOI: 0.05/ matcconf/ ICMMR 06 {Ф} th influnc of outr urfac acoutic fild in an unboundd fluid domin xrtd by ound fild within a finit domin. h finit lmnt vibration quation of th gnral olid tructur can b xrd by th following formula [6]: VI K VI m F m M VI K F F ( whr [M ] globa ma matrix [K ] global tiffn matrix M B D B dv VII K N N dv VII whr ρ dnity of tructural matrial [N δ ] dilacmnt introlation function matrix [D] contitutiv rlation matrix[σ]=[d][ε] combin with th boundary condition,gt: K ( m M K R F ( According to th finit lmnt quation of fluid and olid, th fluid and olid couling finit lmnt quation of th whol ytm ar rwrittn a follow: m R K M F K C M R C 0 0 S ( ( ( ( ( ( ( ( X X X X X X X X ( ( ( ( ( ( ( ( S X X X X X X X X ( ( ( ( ( ( ( ( X X X X X X X X 0 C ( ( ( ( ( ( ( ( X X X X X X X X Z In ( ( ( ( ( ( ( ( Z X X X X X X X X S ( ( ( ( Z ( ( ( ( X X X X X X X X Z ( ( ( ( ( ( ( ( X X X X S X X X X ( ( ( ( ( ( ( ( X X X X C X X X X In h ound rur P of fluid nod and th dilacmnt of tructural nod ar in accordanc with th riodic boundary condition a follow: S S S S C C C C C C j x j( j x dx j( dx j( y y x dx y (5 (6 (7 In th quation of fluid tructur, according to th corronding nod of th lmnt, ach matrix i dividd into block. And thn combind with th boundary condition, th couling quation can b changd into th following form: X rrnt dlta or P dilacmnt vctor of tructur articl By olving (7, th dilacmnt and ound rur of ach nod in th unit can b obtaind. h ound rur i xrd in um of ri rctivly. whr x y R E R ( x, y E M M x y j( knxxi kmy yi knmz ( i r( i, i nm r N nm N nmx nmy M M x y j( knxxi kmy yi knmz ( i N x y ( i,,,, N i i i nm t nm N n M n M ( ( i jk nx x i k my y i k nm z Er ( ( i jk nx x i k my y i k nm z Et ( nm :: M ; mm :: M x x y y From th oint of viw of th calculation of acoutic nrgy, h rflction or tranmiion cofficint can b xrd a follow: R Rnm N n m nm N n m So xrion of ound abortion cofficint i dfind a follow:, (8 (9 R (0. Comutational modl Finit lmnt imulation COMSOL modl i hown in Fig.. Conidr that th arrangmnt of th abortion rformanc of frutum-of-a-con caviti ha a riodic, lct a unit of anchoic coating a th rarch objct in ordr to facilitat th calculation. h anchoic coating i comod of a urfac layr, a rforatd layr, a ba layr and a tl backing layr. Fig. i a cro-ctional viw of a frutum-of-a-con cavity tructur. According to th ymmtry, th modl of th two dimnional axiymmtric modl i ud in thi ar. A hown in Figur, on th boundary condition, uing COMSOL to tranform th riodic boundary of th D modl into th boundary of th two dimnional axiymmtric modl ba on th ound olid couling modul. Du to contact with th vhicl hll, th lowr boundary dilacmnt i zro, and th radial dilacmnt of th modl i zro bcau of ymmtry, o boundary 6, 7 dilacmnt i zro, th modl can only axial dformation; oundary,, for fr dformation

3 MAEC Wb of Confrnc 77, 0800 (06 DOI: 0.05/ matcconf/ ICMMR 06 for imulat th chang of cavity with ound rur. hn, th lan wav i normal incidnt at th boundary, boundary 8, 5 t to th cifid dilacmnt, boundary i t to a fixd contraint. riangular mh that b fr litd ar adotd whn imulation calculation, th maximum iz of th grid i.0mm. h ound abortion cofficint of th modl i calculatd by th ound olid couling modul. Matrial aramtr ar hown in abl. 7 rult of FEM i hown in Fig. 5. In th calculation of th cavity covr con, frutum-of-a-con cavity with cylindrical cavity tructur i vry imilar, o in th finit lmnt analyi, th fr boundary i addd in th cavity, lt ound olid couling boundary and non- rflctiv fluid ound aborbing boundary ar not affctd,o do with th th accuracy of th COMSOL modl [0]. hrough th analyi of th grah, it can b n that th variation trnd and th numrical valu of th two curv ar conitnt within th co of nginring rror, which how th faibility of th COMSOL modl of th frutum-of-a-con cavity Figur. two dimnional axiymmtric modl 8 alha Analytic olution COMSOL f (KHz Figur. Frutum-of-a-con cavity tructur abl Structur and matrial aramtr of anchoic coating Matrial R /mmh /mm /(kg m E /Pa Surfac layr Prforatd layr frutum-of -a-con cavity Ba layr Watr layr Vrification of modl validation and analyi of rult. Vrification of COMSOL modl In ordr to vrify th validity of th finit lmnt modl, th tructur aramtr of th vicolatic modl ar a follow: outid th cylindrical radiu a i0mm, th innr radiu of B i mm, and th thickn of L i 50mm, th thickn of th urfac layr and th ba layr ar mm. h matrial aramtr of th ingl layr ar a follow: th latic modulu i 00MPa, th lo factor i 0., th dnity i 00kg/m, and th Poion' ratio i 90. Comarion of analytical formula for th calculation of th two dimnional thory undr th condition of tl backing of Rf.[7] and Figur. Comarion btwn two dimnional axiymmtric modl and two dimnional thortical modl. Effct of matrial on anchoic coating Fig. 6 how th ffct of diffrnt layr of matrial and th cavity on th ound abortion cofficint or not undr th am rforation ratio. h multi-layrd matrial ar comod of th thr diffrnt matrial :th urfac layr, th rforatd layr, and th ba layr ; a ingl layr of matrial i a covring of a matrial. From th grah, th multi-layrd matrial coatingi bttr than th ingl layrd matrial coating. In low-frquncy rformanc, th ound abortion cofficint of multi-layrd matrial i 0.65, and th ound abortion cofficint of ingl layrd matrial i 0.59 at th firt ound wav crt. With th combination of diffrnt matrial, th covring layr rform bttr at low-frquncy. With th addition of th cavity, th covr layr i gratly imrovd at low-frquncy ound abortion. hat bcau th rforatd layr i addd to th cavity, which mak th lan longitudinal wav b convrtd to har wav in th roc of ound abortion and har lofactor of abortion layr i much largr than that of longitudinal wav,w hich can incra diating th acoutic nrgy. Bid, th rcnt ublihd articl [8]-[0] how that multi-layr matrial ar mor fficint than th ingl-layr on in trm of tr ditribution. hrfor, uing multi-layrd matrial intad of ingl-layr matrial could b a good choic for nhancing both abortion and tructural rformanc.

4 MAEC Wb of Confrnc 77, 0800 (06 DOI: 0.05/ matcconf/ ICMMR , 6 0 0, A known from Fig. 8, With th rforation rat i incraing, th abortion rformanc of anchoic coating in low-frquncy imrov, th firt ound wav crt to th low frquncy hift. In th middl and high frquncy, th ound abortion ffct of th covring layr of th thr kind of rforation rat tructur i gnrally imilar. With rforation rat incra,h lifting ffct for th mdium- frquncy and high- frquncy ound abortion i vry mall. Figur 6. Comarion of ound abortion curv btwn diffrnt layr of matrial. Effct of diffrnt cavity tructur on anchoic coating h influnc of cavity tructur on ound abortion cofficint undr th am rforation rat i dicud in thi articl. Fig. 7how that omarion of ound abortion curv btwn cylindrical cavity, frutum-of-a-con cavity, hybrid cavity and llioidal cavity. Obviouly, th low- frquncy ound abortion rformanc of th hybrid cavity i bttr than that of th othr cavity tructur,and frutum-of-a-con cavity i cond. frutum-of-a-con cavit in th firt abortion trough much lowr than th cylindrical cavity,llioid cavity, which ound abortion cofficint i 9 and corronding frquncy i 950Hz. In th middl and high frquncy, ound abortion rformanc of th four kind of cavity tructur ar gnrally th am, and ound abortion cofficint i tabl at about 0.8. In nginring alication, two kind of ituation hould b takn into account to choo. Figur 7. Comarion of ound abortion curv btwn diffrnt cavity tructur. Influnc of rforation rat on anchoic coating hi xaml dicu th influnc of th chang of th rforation rat on anchoic coating. In Fig. 8, h rforation rat of ca,ca,ca ar Figur 8. Comarion of ound abortion curv btwn diffrnt rforation rat. 5 Concluion In viw of rlativly oor ituation of th abortion rformanc of anchoic coating in low-frquncy currntly, hi ar, bad on th thory of ound wav normally iminging on th abortion layr of D, build th D haft mod of frutum-of-a-con caviti which i tablihd by finit lmnt COMSOL,and analyz th abortion charactritic combind tructural aramtr, concluion ar a follow: ( Undr th condition of th am rforation rat, th abortion rformanc of multi-layrd matrial anchoic coating i bttr than that of ingl-layrd matrial anchoic coating, cially to th rformanc of low-frquncy; th abortion rformanc of frutum-of-a-con caviti lay an imortant rol in imroving th abortion rformanc in low-frquncy of anchoic coating, which i bttr than that of ingl cavity tructur. ( h rforation rat i ntial for imroving th abortion rformanc in low-frquncy of anchoic coating. With th rforation rat i incraing,th abortion rformanc of anchoic coating in low-frquncy imrov. h rlationhi btwn th abortion rformanc in intrm diat-frquncy/ high-frquncy and th rforation rat i not vry clo ( Chooing th aroriat cavity tructur i imortant.whn comard to combind cavity tructur, frutum-of-a-con caviti tructur rovid littl aitanc to th imrovmnt of th abortion rformanc of anchoic coating in low-frquncy; comard with th cylindrical and llioidal form, th ooit i th ca.

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