( i IMPACT OF LONGITUDINAL AND TRANSVERSE WAVES BY CYLINDRICAL LAYERS WERE LIQUID 2 ~ t (1)

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1 Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - IPT OF ONGITUIN N TRNSVRS WVS INRI RS WR IQUI I.I.Safaov Z.I olav.sh hmdov haa Tchologcal- Is of gg Rpblc of Uzbsa s. K. azayv 5 safaov5@mal W sdy h fld of dyamc ssss ad dsplacms asg a h cyldcal lay lqd a vscolasc mdm dg h passag of a pla wav. I s show ha h clso of h vs pops of h maal vom h calclao of h aco of hamoc wavs dcs sss ad dsplacm o -6%. Kywods: dsplacm poals ssssa wh dsac logdal ad asvs wavs hamoc wavs Gass mhod. Iodco. Impac of logdal ad asvs wavs o a cyldcal body was vsgad by may ahos [ ]. Whl dd axally symmc ad o axally symmc ass sd dff modls fo fld ad lays o shlls. Pvos wos cyldcal body dd as a cyldcal shll ad h qao of moo s obad basd o h hypohss Kchhoff - ov [ ]. lso vom has b vwd as a lasc.. Rlaoshp of sss ad sa sa obys oo's law [9]. Ths wo dffs fom pvos os ha h cyldcal shll amb possssg vs pops.. sss ad sa d obys olzma gal lao - Vola []. Impac modl-s of logdal ad asvs wavs o cyldcal lays ad lqd basd o h chqs dvlopd h dyamcs of bods acg wh a dfomabl mdm fo xampl []. Sam of h poblm. fly log homogos soopc-dfomabl cyld wh a dal compssbl lqd a f vscolasc mdm falls hamoc pla wav xpaso o shf Fg.. Th wav fo s paalll o h cyld axs. Ths h poblm of pla sa. R ad o R - ad of h cyldcal lay. Th ma am of h wo s o dm h sss - sa sa of cyldcal lay ad h vom d h flc of h logdal o asvs hamoc wavs. Ud h assmpo of galzd pla sa sa of h qao of moo ms of dsplacms s gv by [] ~ ~ ~ gad dv oo b wh ad - la o h vom - o lay opao modls of lascy ~ f ~ f f f R R f d f d b vco dsy of volm focs b f som fco ρ dsy maals R τ τ и R τ τ - co laxao o o - saaos lasc modl of vscolasc maal - dsplacm vco. Whch dpds o h. psss p o Pa h fld moo s dscbd sasfacoly by h wav vlocy poal fo h fld pacls []. JSTN5 7

2 Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - С о wh С о ac vlocy of sod h fld. Poal ad h vlocy vco of h fld a lad by V gad. Fld pss R dmd sg h la zd achy agag Р ρ ос - Pss of h fld o h wall of h cyldcal shll ad ρ о -dsy of h lqd. Povdd sppod flow fld omal compo of vlocy ad h lay o h sfac of h coac R ms b qal R R Wh lay of omal movm. h coac of wo bods R h qaly of ssss ad dsplacms gd coac codo. y x-ω R ρ ν x ρ ν Fg.. alclao schm pp wh lqd No ha h cas of h sldg coac sfac of h sol pp by h las qao bcoms []: h cd pla wav popagas h posv dco of h x-axs: p a xω p А d h flc of logdal wavs p o xω p А - wh xposd o sha wavs А ad А - h ampld of h cd wavs ω - ccla fqcy of h cd wavs. xpsso p o p ca b psd pola coodas cyldcal lay ss of А p J Thogh a wh J - ssl fco. w cyldcal JSTN5 7

3 Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - hods of solo. Th poblm s solvd ms of poals movms fo psavs of Whmdsplacm vco h fom: gad o Wh - Th poal of logdal wavs - Th vco poal of h asvs wavs. asc qaos of h hoy of vsco lasc fo hs poblm o a pla dfomao ca b dcd o h followg qao o o o R d o R d ρ ρ ρ o o R d ρ ρ 5 wh dffal opaos cyldcal coodas ad v - Posso's ao []. fy poals of logdal ad asvs wavs w sasfd wh h Somfld adao codo []: lm 6 lm lm к lm к. qao ca b fod h fom: ω ω q q q q q q 7 Wh и complx fco whch s o solv h followg qaos 7 q wh q q q q q q q q 8 o ρω o o o ρω ω o С o a b o a ω b ω a ω b ω ω R τ sωτ dτ ω R τ ωτ dτ. o Th solo of qao wh 8 s xpssd ms of h l fco of h s ad d d -h od: JSTN5 75

4 Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - s 9 s N K J K Wh К и K - Th xpaso coffcs whch a dmd by h appopa boday codos ad - Rspcvly h l fco of h s ad d d -h od N J ± Solo 9 a sasfs a fy h Smmfld adao codo 6 ad s psd as:. s * * п п п С m Н А ω ω Solvg h poblm sasfs h a codo a pow fa [] ad follows ha K w J K Fll poal ca b dmd by applyg a poal cd ad flcd wavs. Ths h bas poal wll b p Ψ Ψ I follows ha h ssss ad dsplacms ca b asly xpssd ms of bas poal [] JSTN5 76

5 Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - splacm ad sss fo h cas of h lay o h compsso wav obad. f sbsg o wh 9 w oba h followg xpsso fo h dsplacms ad ssss: s co co co co wh [ ] [ ] [ ] JSTN5 77

6 [ ] [ ] 6 где J N. Udmd coffcs dmd fom h d Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - sysm of la algbac qaos of h svh od [ ]{ q} [ F] С wh {q}-colm vco coag abay as {F}-colm vco of xal loads []-sqa max lms-whch a xpssd hogh h ssl ad l. qao ca b solvd by Gassa lmao wh h las of h ma lm. wh : z z ± l z l z z l z z z m!! z z т / ± zπ / т z πz * Th sls of calclaos ad coclsos aa fallg ox ssss ad dsplacms a dfd ows bg dscbd by h xpssos 9 - h cas of had coac. alclaos w pfomd by N comp pogam complx «a lab» ss calclad wh a accacy p o -8. ll xpssos fo h ssss ad dsplacms a of h fom: w wγ R Im R Im / π π { } π l asympoc fomla sd s ad d d []. I hs pap dsplacm ad sss s dcd dmsolss foms * * * s yo ca s h solo of h poblm s xpssd ms of spcal f of ssl ad l f of h s ad d d. Wh h casg mb of h agm 9 - covgs. Thfo o h bass of mcal xpms showd ha h accacy of 5-6 mmbs of h as of h accacy achvd s laxao l a a h-paam vscolasc co R Rzhasa- Kolova [] has a wa sglay wh - maals paams []. W s h followg paams: ρ с кг С JSTN5 78

7 Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - н Е 95 н Е кг ρ ρ 786 R R кг axmm volag a lay of lqd o h aco of logdal ad asvs hamoc wavs s h adal sss. Thy chag alog wh h -vda Tabl ad wh o who a lqd mdm. Tabl. Radal sss h lay a mpac wh h mpac of logdal wavs mpy lay lay lqo Tabl. Radal sss a lay of lqd a h mpac of asvs wavs agl: mpy lay lay lqo I h log-wavlgh > sss dsbo lay ad h lqd who lqd dffs o % ad h sho-wav som fqcy vals hy dff p o %. ccog fo h vs pops of h maal a amb basd JSTN5 79

8 Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - o logdal ad asvs ffcs of hamoc wavs ad dcs h ssss ad dsplacms a -6%. Th maxmm adal sss wh xposd o logdal wavs s achvd 9 ad 7 I shold b od ha h maxmm adal sss a h mpac of h asvs wavs s achvd 5 ad 5 as wll as h dsbo of sss a R 99 almos h sam as h sac cas whl a hgh wav R 5 mbs of h sss dsbo s sgfcaly dff fom h sac. Th ao of h dss η / has a ga flc o h volag ad h bas lay. Wh h casg dsy of h lay maxmm volag ad bas lay cass. Ths mhods ad algohms fo solvg ass allow s o fd h sss-sa sa of cyldcal bods d h flc of hamoc wavs. Rfcs. N Gz Kbo V... hvo ffaco of lasc wavs. "Scc" p.. Pao.. ow.. dffaco of lasc wavs ad dyamc sss cocao. Nmb Ga Rssa p.. KOTUNOV.. p ad laxao. - oscow: gh School p.. aa S.K. Tsoal wavs a f lasc sold coag a py - shapd cac.-z. asw. ah. d Phys. 97 p baa.n. Safaov I.I. O h aco of lasc wavs o a cyldcal shll. Pblsh Tash ss of Tchcal Sccs p Safaov I.I. valao of dgod scs sysmoapyazhogo mhodology wav dyamcs ollco "ssm dyamcs obs ad facls" Tash Scc Flppov I.G. O.. goychv Usady oscllaos ad wavs h dffaco of ac ad lasc mda.. -.: chacal wh. 8. Safaov I.I. Th aco of wavs mllay cyldcal lays posos bodlss lasc mdm. Pocdgs VII vssoyz. ofc 'yamcs h basc fodaos ad dgod scs "popovs 989. p Safaov I.I. zhmav Z.F. O blowp l wh sog movms of h ah. Iaoal cofc o ahqa gg. Pblsh Sa - Pbg p vlyalov N.N. Safaov I.I. od poblms of sacs ad dyamcs of dgod ppls. Tash p.. ozoov.. Safaov I.I. Sho.I. Nmcal smlao of oscllaos of homogos ad homogos dsspav mchacal sysms. Th Novosbs: Pblshg os. S RS wh. JSTN5 8

9 . Rashdov T.R. Safaov I.I. ad ohs abo h wo basc mhods of sdyg h ssmc sss sa of dgod scs d h aco of ssmc wavs. Tash: N. Nmb Pp Safaov I.I. vlyalov N.N. hods o mpov ssmc ssac of dgod plasc pp / / Uzb Ol ad Gas Joal 5 -.S... Gac. ahws G.. ssllya f ad h applcao o physcs ad mchacs.- Pblsh oscow 95-7 p. Joal of ldscplay gg Scc ad Tchology JST ISSN: 59- Vol. Iss Novmb - JSTN5 8