Effect of the bending modes on the radiated sound pressure from a submarine hull

Transcription

1 Poeedgs of ACOUSTICS oembe 9, Adelde, Astl Effet of the bedg modes o the dted sod esse fom sbme hll o Cest, ole Kessssoglo Shool of ehl d ftg Egeeg, The Uesty of e Soth Wles, Sydey, SW 5, Astl ABSTRACT Rotto of the oelle thogh o-fom ke eslts flttg foes tsmtted thogh the olso system to the hll of sbmeged essel. The l omoet of the flttg hmo foes etes the symmet modes of the sbme hle the omoet the dl deto s sho to mly ete the bedg modes of the sbme. The hll s soded by te d s modelled s yldl shell th tel blkheds, g stffees d tted ol ed s. The stte-boe dted sod esse s llted sg the Helmholtz tegl fomlto. Sttl d osts eslts fom both the sem-lytl model d flly oled fte elemet/body elemet model e eseted. ITRODUCTIO Flttg foes de to otto of the oelle ete the lo feqey bto modes of sbmeged essel, esltg hgh leel of dted ose. Udestdg the lo feqey bo-ost esoses of sbme s of get teest ode to eet deteto oblems of defee essels. The Helmholtz tegl fomlto s oefl tool to llte the sod esse dted fom elst sttes. Hoee, oly smll mbe of smle sttes sh s shel shells d ftely eod yldes llo lytl solto (Jge d Fet, 986). y esehes he estgted omte methods to sole the ost dto fom elst sttes. Fte elemet methods ee sed some ely es (Alfedso 973; Alett et l. 968), bt the body tegl eqto fomlto hs beome moe ol. A omehese ee o the eolto of body elemet tehqes s ge by Che et l. (99). Vtol le hs lso bee sed to sole dto oblems (W 989; Che d Gsbeg 993; Bjso et l. 994; Cho et l. 995). Che d Steshe (994) oosed e method bsed o o modl eso to sole fld loded shells. Coled fte elemet/body elemet methods he bee eseted by Jes d thes (99, 993) to stdy the btos of sttes fte ost medm. A ety of tehqes to eme the sod dto fom slede bodes of eolto d sheodl shells he ofte bee deeloed th lto to sbme hlls (Chetok 975; Steshe 997; He-Wg d Steshe 994; Pe-T d Gsbeg 993; Ahebh et l. 99; Cho et l. 996; Pod 966). Reetly, P et l. (8, 8b) stded te otol sttegy to ede the sod dto fom symmetlly btg sbme essel th ol d shel ed s. I ths ok, the esse dted fom sbme hll s eseted. The hll s modelled s fte yldl shell losed t eh ed by tted ol ed s. The otbto fom both the yldl hll d oes e tke to ot eltg the dted sod esse. Imefetos fom the olso system eslt flttg foes both the l d dl detos. The l foe etes the symmet zeoth mfeetl modes of the hll, bt the dl omoet etes ll mfeetl ode modes. The stedy stte esose of the stte s llted by ssemblg the mt of the body d otty odtos. The sod dto s llted solg the Helmholtz tegl the f feld. Fo the = mfeetl bedg modes, the sod esse the l deto beomes sgft se the hll dslemet s mly dl, esltg lge esse lobes oml to the hll. Fo ldty of the eset stdy, lytl eslts e omed th omttol eslts obted fom flly oled fte elemet/body elemet model deeloed sg st d Sysose. STRUCTURAL ODEL OF THE SUBARIE The sbme hll s modelled s yldl shell th tel blkheds d g stffees. The yldl shell s losed by tted ol shells, hh t e losed t eh ed by l ltes, s sho Fg.. The ete stte s sbmeged hey fld medm. Tted oe Blkheds () () (3) (4) (5) Ed ltes Stffees Fge. Shemt dgm of the sbme Usg Flügge th shell theoy, the eqtos of moto d geel soltos fo the fld loded yldl d ol shells d fo the l ltes ee eseted eos by the thos (Cest et l. 8). The yldl shell dslemets e ge by (Less 993) 8 =,, jk, os( θ ) () = = C W e e ω 8 =,, jk, s( θ ) () = = G W e e ω 8 =, jk, os( θ ) (3) = = W e e ω (6) Astl Aostl Soety

2 3-5 oembe 9, Adelde, Astl Poeedgs of ACOUSTICS 9 hee, d e esetely the l, mfeetl d dl omoets of the yldl shell dslemets. The ol shell dslemets be tte s (Tog 993) (, θ, t) = os( θ ) e ω (4),, = (, θ, t) = s( θ ) e ω (5),, = (, θ, t) = os( θ ) e ω (6),, =,, d e the othogol omoets of the ol shell dslemets., s the eto of the eght ko oeffets fo sef mfeetl mode mbe.,, d, e the deedet omoets of the ol shell dslemets eessed tems of oe sees, hee s the deto of the oe log ts geeto (Cest d Kessssoglo 8). Geel soltos fo the bedg d -le motos of th l lte e ge by (Tso d Hse 995) (,, ) = A J ( k ) + A I ( k ) os( θ ) e ω (7) B B = B,J ( k L) J ( k T) jωt = + B, s( θ ) e = (8) J ( k L) B,J ( k T) jωt = B, + os( θ ) e = (9) hee, d mfeetl lte dslemets. embe d e esetely the l, dl d k s the lte bedg B k, k e the embes fo - L T le es the lte (Tso d Hse 995). J d I e esetely Bessel ftos d modfed Bessel ftos of the fst kd. The oeffets A, d B, ( =, ) e detemed fom the body odtos of the l ltes. The dym esose of the ete sbme stte fo eh mfeetl mode mbe s eessed tems of the dl e mltdes W, ( = :8 ) fo eh seto of the hll, the e mltdes A,, B, ( =, ) fo eh l lte, d eght ko oeffets, fo eh ee of fstm of oe. The dym esoses fo the yldl shells, l ltes d ol shells sg the to dffeet tehqes (e oh d oe sees) be oled togethe by otty of the dslemets d sloe, d eqlbm of foes d momets t the oe/lte/ylde jtos. The foes, momets, dslemets d sloe t the jtos d bodes of the oled shells d ltes e ge ode th the sg oeto sho Fge, hee RC s the globl Ctes efeee fme. The membe foes (, θ, θ ), bedg momets (, θ, θ ), tsese sheg Q fo the shells d ltes e ge Less (993). To tke to ot the hge of te betee the ylde d the oe, the follog otto s toded ɶ = osα sα () ɶ = osα + sα () ɶ = osα V sα (),,, Vɶ = V osα + sα (3),,, At the oe/l lte/ylde jtos oesodg to jtos () Fge, the otty odtos e ge by = ɶ = (4) = ɶ = (5) = = (6) φ = φ = φ (7),, ɶ + = (8) θ θ, θ + + θ, + + θ, = (9) + = (),, V + V ɶ + = (),, The Kel-Khhoff she foes V, V, e ge by θ V = Q +, V θ = Q + R( ) θ,, θ, () At the fee eds of the tted oes oesodg to jtos () Fge, sml eessos fo the otty odtos betee the ol shells d l ltes be sed.,, θ, φ, θ, Q,,, θ,, φ Fge. Sg oeto fo the foes, momets d dslemets of the oes, ylde d l ltes. The stedy stte esose of the hll be llted osdeg the foe s t of the body odtos. Wth dl hmo foe, the otty odto of dl foes t the ed lte/oe jto () beomes, φ Q, θ y, θ z RC, θ Q Astl Aostl Soety

3 Poeedgs of ACOUSTICS 9 V ɶ + = ε F os( θ ) (3),, 3-5 oembe 9, Adelde, Astl dl foe F led t the ed lte of the ol shell (jto of Fge. ), s sho Fge 4. hee F = d ε = / π R f = d ε = / π R f.. FAR FIELD SOUD PRESSURE F F D Aost model of the sbme hs bee eseted eosly by the thos (Cest et l. 8). The sod esse t f feld loto s soled by mes of the Helmholtz tegl fomlto. The f feld s loted shel oodtes, s sho Fge 3. Fge 3. Coodte system fo the f feld ot. RESULTS Reslts e eseted fo g stffeed yldl shell of ds = 3.5 m, thkess h =.4 m, legth L = 45 m d th to eely sed blkheds of thkess h =.4 m. A dstbted mss o the ylde m eq = 5 kgm - hs bee osdeed to ot fo the obod eqmet d bllst tks (Tso d Jeks 3). The tel stffees he etgl oss-seto of.8m.5m d e eely sed by b =.5 m. The tted ol shells he smll ds ofr =.5 m, sem-ete gle of α = 8 d thkess h =.4 m. All the sttes e mde of steel, th desty ρ 3 = 78 kgm, Yog s modls E =. m - d Posso s to υ =.3. A omle Yog modls of E E ( jη ) =, hee η =. s the sttl loss fto, s osdeed to ot fo the sttl dmg. The ost eslts e eseted tems of the mmm sod esse defed by P = m ( R, θ ) elted the f feld t θ = m φ π d R = m. ( ) Poelle shft etto Reslts fo the sttl esoses of the sbme hll de etto fom the oelle-shftg system e eseted. The flttg foes t the oelle de to otto of the oelle thogh o-fom ke e tsmtted thogh the olso system, esltg etto of the yldl hll t ts ed lte. The flttg foes the l d dl detos e of sml mgtde (Besl d Adese 994). I ths lyss, the dyms of the oelle-shftg system hs ot bee osdeed d ts flee s smlfed s follos. The l foe s osdeed to be tsmtted detly to the hll etg the symmet modes of the sbme. The dl omoet s omted s ot foe led to the etemty of the ed oe. The totl etto tg o the hll s otbted by symmet dstbted lod D = F / π [m - ] hee F s l foe led t the ed lte of the yldl shell (jto Fge. ), d ot R φ (R,θ,φ ) θ Fge 4. Flttg foes fom the oelle. Sttl esoses Fge 5 esets the feqey esose fto (FRF) of the l dslemet t the oe/ylde jto oesodg to the loto of the dstbted foe. I the se of symmet etto (D ), oly the = odo modes e eted. It be see the fst thee esot feqees o t feqees of od.5, 44.5 d 68.5 Hz. The smll eks t od 9 Hz d 37 Hz e de to the esoes of the blkheds. Ude dl ot foe etto ( F ), the esose s domted by the = bedg modes. FRF db e = [m ] Feqey [Hz] Fge 5. Al dslemet t the ed lte of the yldl shell, = : 3. odeshes t the thd, foth d ffth = esoes eted by the dl foe e sho Fges 6 to 8. The oesodg feqees e 9.5, 6.5 d 33 Hz, esetely. De to the flel moto of the oes, the eds of the hll e sho to be btg hse o ot o hse th eh othe. Ude ot dl foe etto, ese the sttl esose s obseed Fge 5 t od 6 Hz. Ths s de to the ttg-o of the seod lss of es (Clss II). Fge 9 esets the sttl embes k of the yldl shell of the hll fo = modes. The mly el embes eeset tellg es the stte; the smll mgy t s de to both sttl dmg d fld-lodg. Whle the fst lss of es (CL I) ts-o t Hz, t be obseed tht the ttg-o of the seod lss of es (CL II) os t od 6 Hz. The CL II es fll the seso ego of the embe setm ( k < k f ), ths stoge otbto to the sod dto os. At 6 Hz, the oetol defomto she s mly detemed by = bedg modes of the hll d ey stog defomto fo the ed oes s obseed, s sho Fge. D F Astl Aostl Soety 3

4 3-5 oembe 9, Adelde, Astl Poeedgs of ACOUSTICS () Alytl ( o) Comttol (FE) Fge 6. Oetol defomto she t the thd = bedg esot feqey of 9.5 Hz. FRF db e = [m ] Feqey [Hz] 6 4 (b) Alytl (th fld lodg) Comttol (BE) Fge 7. Oetol defomto she t the foth = bedg esot feqey of 6.5 Hz. Fge 8. Oetol defomto she t the ffth = bedg esot feqey of 33. Hz Feqey [Hz] Fge. Al dslemet t the ed lte of the yldl shell de dl etto, () o se, (b) th fld-lodg. 5 el(k ) [d m ] Seso ego Clss I Clss II Aost embe k f Feqey [Hz] Fge 9. Rel t of the sttl embes fo the = bedg modes. Fge. Oetol defomto she t 6 Hz. Fo ldty of the eset stdy, the sttl d ost esoses of the sbme ee omed th eslts fom flly oled omttol model. A fte elemet (FE) model s soled sg st fo stte o d body elemet (BE) model s deeloed sg Sysose fo fld-loded stte. Fges d eset the feqey esose ftos (FRFs) of the l dslemet t the ed lte of the yldl shell de dl etto (Fg. ), d de symmet dstbted lod (Fg. ). Fge esets the FRFs fo both the o d fld loded ses. o dffeee betee the lytl d omttol eslts s obseed fo the o se hle some smll dsees o th fldlodg. These dsees e ttbted to lo feqey omtos fo the fld lodg the lytl model. It be obseed tht fld lodg edes both the le of the tl feqees d the mltde of the FRF. Fge shos tht fo the symmet se, oly smll dffeees betee the lytl d omttol eslts be obseed. The smooth eks t the seod d thd hll esoes e de to the dmg effet of the fld lodg. FRF db e = [m ] 4 3 Alytl (th fld lodg) Comttol (BE) Feqey [Hz] Fge. Al dslemet t the ed lte of the yldl hll de symmet. Aost esoses feld defed by m ( ) φ π Fge 3 esets the mmm sod esse the f P = m ( R, θ ) de to symmet dstbted lod ( D ) d de ot dl etto ( F ). It be see tht the dl foe t the ed lte of the ol shell sgftly otbtes to the sod dto, eselly boe 3 Hz. odes th do ot otbte sgftly to the sod dted to the f feld. At od 6 Hz he the ttg-o of the CLII es os, ese sod dto s obseed. Pesse [ P ] Feqey [ Hz ] Fge 3. mm f feld sod esse, R = m, θ =. F D 4 Astl Aostl Soety

5 Poeedgs of ACOUSTICS 9 Rdto detty ttes Fo the symmet se, the dto detty ttes oesodg to the fst thee l esot feqees e sho Fges 4 to 6 fo θ = d φ 8. Also sho e the ddl otbtos to the dted sod esse fom the yldl d ol shells. The otbto fom the yldl shell s eeseted by the etl lobes the detty ttes, hees the lge sde lobes e de to the otbto fom the ed oes. As the feqey eses, the dto detty ttes ese omlety. Fo the fst thee l esoes, thee e oe, to d thee etl lobes, esetely. De to the hse eltosh betee the esse felds geeted by the yldl d ol shells, the totl sod esse s the getest log the l deto fo the fst to l esot feqees. A tl ellto os the deto oml to the s of the sbme. The detty ttes obted omttolly sg Sysose e lso sho Fge 4 fo the fst l esot feqey d Fge 7 fo the seod d thd l esot feqees. Vey good geemet betee the lytl d omttol eslts s obseed t the fst d thd esot feqees. The dffeee mgtde betee the lytl d omttol eslts s ttbted to the dffeees the mgtde of the sttl esoses s obseed Fg., bt the geel detty she s eseed. Sod esse [P] ± Totl (Alytl) Cylde Coes Totl (Sysose) Fge 4. Rdted sod esse t the fst = l esot feqey of.5 Hz (lytl d omttol eslts) Sod esse [P] ± oembe 9, Adelde, Astl 9 Totl Cylde Coes Fge 6. Rdted sod esse t the thd = l esot feqey of 68.5 Hz (lytl eslt). Sod esse [P] ±8 5 9 d = tl feq. 3 d = tl feq Fge 7. Rdted sod esse t the seod d thd l esot feqees (omttol eslts). Rdto detty ttes fo the thd, foth d ffth = modes of the hll, oesodg to feqees of 9.5, 6.5 d 33 Hz esetely, e sho Fges 8 to. The geel detty shes obted lytlly d omttolly e ey sml, shog eded dted sod esse log the s of the hll d lge lobes oml to the hll. The dffeee mgtde betee the lytl d omttol eslts s ttbted to the dffeees the mgtde of the sttl esoses, s obseed Fge (b). Fo the feqey ge of teest, the mmm dted sod esse s sho to o t od 6 Hz, de to the ttg-o of the CLII es. The detty tte of the dted sod esse t 6 Hz s eseted Fg.. The sod esse s less sgft the l deto se the hll dslemet s mly dl Sod esse [P] ±8 5 Totl Cylde Coes Sod esse [P] ±8 5 Alytl Comttol 3 Fge 5. Rdted sod esse t the seod = l esot feqey of 45.5 Hz (lytl eslt). Fge 8. Rdted sod esse t the thd = bedg esot feqey of 9.5 Hz (lytl d omttol eslts). Astl Aostl Soety 5

6 3-5 oembe 9, Adelde, Astl Poeedgs of ACOUSTICS 9 Sod esse [P] ±8 5 Alytl Comttol Fge 9. Rdted sod esse t the foth = bedg esot feqey of 6.5 Hz (lytl d omttol eslts). Sod esse [P] ±8 5 Alytl Comttol Fge. Rdted sod esse t the ffth = bedg esot feqey of 33 Hz (lytl d omttol eslts). Sod esse [P] ±8 5 Alytl Comttol Fge. Rdted sod esse t 6 Hz (lytl d omttol eslts). COCLUSIOS The bo-ost esoses of sbmeged essel the lo feqey ge he bee eseted sg semlytl model. The sttl esose of the sbme de ot foe etto s obted by ssemblg the body/otty mt. The sfe dslemet d esse ee sed the Helmholtz tegl fomlto to elte the f-feld dted sod esse. Etto fom the oelle s modelled s flttg dl ot foe o the ste sde of the sbme d dstbted symmet lod tg o the yldl hll. It s sho tht etto de to the dl foe eslts gete sod esse dted to the f-feld omed th the sod dto de to symmet etto of the hll. Ths s de to the = mfeetl bedg modes. Fthemoe, the feqey ge of teest, the getest sod dto s fod to o t the feqey oesodg to the ttg-o of the seod lss of es fo the = modes. Ths s ssoted th seso es the stte d ese the globl sttl esose. The mote of the = bedg modes the sod esse dted by sbme de hmo etto fom the olso system s sho. 3 3 REFERECES Ahebh, J.D., Bjso, J. d Igs, T. (99) Effet of btg sbstte o ost dto fom yldl shell. Jol of Vbto d Aosts, Tstos of the ASE, 4, Alfedso, R.J. (973) A ote o the se of the fte dffeee method fo edtg stedy stte sod felds. Aost, 8, Alette, P.L., Bh, A.K. d Zekez, O.C. (968) Alto of FE to solto of Helmholtz's eqto. Po. IEEE, 5, Bjso, J., Igs, T., Cho, S.-H. d Ahebh, J.D. (994) The effet of sbsttes o the ost dto fom symmet shells of fte legth. Jol of the Aostl Soety of Ame, 96, Besl, J.P. d Adese, P. (994) Hydodyms of sh oelles, Cmbdge Uesty Pess. Cest,., Kessssoglo,.J. d Tso, Y.K. (8) Lo feqey sttl d ost esoses of sbme hll, Aosts Astl, 36, Cest,. d Kessssoglo,.J. (8) Vbto of fld loded ol shells. Jol of the Aostl Soety of Ame, 4, Che, H.-W. d Steshe, P. (994) Aost tset dto fom fld-loded shells of eolto sg tme-deedet o egeeto esos. Jol of the Aostl Soety of Ame, 95, 6-6. Che, P.-T. d Gsbeg, J.H. (993) Vtol fomlto of ost dto fom sbmeged sheodl shells. Jol of the Aostl Soety of Ame, 94, -33. Chetok, G. (975) Sod dted by lo-feqey btos of slede bodes. Jol of the Aostl Soety of Ame, 57, 7-6. Che, C.C., Rjyh, H. d Atl, S.. (99) A effete method fo solg the hyesgl tegl eqtos 3-D osts. Jol of the Aostl Soety of Ame, 88, Cho, S.H., Igs, T. d Ahebh, J.D. (995) osymmet bto d ost dto of sbmeged yldl shell of fte legth otg tel sbsttes. Jol of the Aostl Soety of Ame, 98, Cho, S.H., Igs, T. d Ahebh, J.D. (996) Aost dto fom fte-legth shell th osymmet sbsttes sg sfe tol le. Jol of Sod d Vbto, 97, He-Wg, C. d Steshe, P. (994) Aost tset dto fom fld-loded shells of eolto sg tme-deedet o egeeto esos. Jol of the Aostl Soety of Ame, 95, 6-6. Jes, R.A. d thes, I.C. (99) Solto of fldstte teto oblems sg oled fte elemet d tol body elemet tehqe. Jol of the Aostl Soety of Ame, 88, Jes, R.A. d thes, I.C. (993) A qe oled body elemet/fte elemet method fo the elstoost lyss of fld-flled th shells. Jol of the Aostl Soety of Ame, 94, Jge,.C. d Fet, D. (986) Sod, sttes, d the teto, Cmbdge, ss., IT Pess. Less, A.W. (993) Vbto of shells, e Yok, Ame Isttte of Physs. P, X., Tso, Y. d Je, R. (8) Ate otol of lo-feqey hll-dted ose. Jol of Sod d Vbto, 33, Astl Aostl Soety

7 Poeedgs of ACOUSTICS oembe 9, Adelde, Astl P, X., Tso, Y. d Je, R. (8b) Ate otol of dted esse of sbme hll. Jol of Sod d Vbto, 3, 4-4. Pe-T, C. d Gsbeg, J.H. (993) Vtol fomlto of ost dto fom sbmeged sheodl shells. Jol of the Aostl Soety of Ame, 94, -33. Pod, H.L. (966) Lo-feqey sod dto fom slede bodes of eolto. Jol of the Aostl Soety of Ame, 4, 7-7. Steshe, P.R. (997) Aost symmet dto d stteg fom bodes of eolto sg the tel soe desty d Foe methods. Jol of the Aostl Soety of Ame,, Tog, L. (993) Fee bto of othoto ol shells. Itetol Jol of Egeeg See, 3, Tso Y.K. d Hse, C.H. (995) We ogto thogh ylde/lte jtos. Jol of Sod d Vbto, 86, Tso, Y.K. d Jeks, C.J. (3) Lo feqey hll dto ose. Reot o. Dstl/TR566, Defee See d Tehology Ogsto, UK. W, X.-F. (989) Fste lltos of sod dto fom btg yldes sg tol fomltos. Jol of Vbto, Aosts, Stess, d Relblty Desg,, -6. Astl Aostl Soety 7