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Асимптотичні методи в прикладних задачах теорії нелінійних коливань та теорії композиційних матеріалів: Автореф. дис… канд. техн. наук / В.В. Даніше

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I?eaei?i?ianueea aea?aeaaia aeaaeai?y aoae?aieoeoaa oa a?o?oaeoo?e

Aeai?oaanueeee Aeaaeeneaa Aaeaioeiiae/

OAeE 539.3

ANEIIOIOE*I? IAOIAeE A I?EEEAAeIEO CAAeA*AO OAI??? IAE?I?EIEO EIEEAAIUe
OA OAI??? EIIIICEOIEO IAOA??AE?A

Niaoe?aeuei?noue 05.23.17 – Aoae?aaeueia iaoai?ea

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe

Aei?i?iiao?ianuee – 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a I?eaei?i?ianuee?e aea?aeaai?e aeaaeai?? aoae?aieoeoaa
oa a?o?oaeoo?e ia eaoaae?? iii?o iaoa??ae?a, I?iina?oe Oe?a?ie.

Iaoeiaee ea??aiee:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Aiae??aiia ?ai? Aaneeueiae/,

I?eaei?i?ianueea aea?aeaaia aeaaeai?y aoae?aieoeoaa oa a?o?oaeoo?e.

Io?oe?ei? iiiiaioe:

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Iaaeaiei Aiaoie?e
Aaneeueiae/, caa?aeoaa/ eaoaae?e aeui? iaoaiaoeee Aea?aeaaii?
iaoaeo?a?eii? aeaaeai?? Oe?a?ie;

eaiaeeaeao oaoi?/ieo iaoe, aeioeaio Aa?aiia Einoyioei A?oae?eiae/,
aeioeaio eaoaae?e oai?aoe/ii? iaoai?ee Oa?e?anueeiai aea?aeaaiiai
iie?oaoi?/iiai oi?aa?neoaoo.

I?ia?aeia onoaiiaa:

Aei?i?iiao?ianueeee aea?aeaaiee oi?aa?neoao, eaoaae?a iaoaiaoe/iiai
iiaeaethaaiiy, I?iina?oe Oe?a?ie.

Caoeno a?aeaoaeaoueny 19 aa?aciy 1999 ?. i 13.00 ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae08.085.02 i?e I?eaei?i?ianuee?e
aea?aeaai?e aeaaeai?? aoae?aieoeoaa oa a?o?oaeoo?e ca aae?anith: 320600,
i. Aei?i?iiao?ianuee, aoe. *a?ieoaanueeiai, 24-a.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? aeaaeai??.

Aaoi?aoa?ao ?ic?neaiee 18 ethoiai 1999 ?.

A/aiee nae?aoa? niaoe?ae?ciaaii?

a/aii? ?aaee Eaaoa A.I.CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aneiioioe/i? iaoiaee yaeythoue niaith iaeei ?c
iiooaeieo cania?a aeine?aeaeaiiy caaea/ aoae?aaeueii? iaoai?ee.
A?aeiinia i?inoioa oa iiaeeea?noue io?eiaoe ??oaiiy a aiae?oe/i?e oi?i?
?iaeoue ?o iniaeeai c?o/ieie aeey aaciina?aaeiueiai aeei?enoaiiy a
?iaeaia?i?e i?aeoeoe?. A aeai?e ?iaio? a ?aieao aneiioioe/iiai i?aeoiaeo
?ic?iaeaii iia? iaoiaee aeey ?ica’ycaiiy caaea/ oai??? iae?i?eieo
eieeaaiue aeaiaio?a aoae?aaeueieo eiino?oeoe?e oa aeey aecia/aiiy
aoaeoeaieo (ina?aaeiaieo) oa?aeoa?enoee ia??iaee/ii i?e?iiaiaeii??aeieo
eiiiiceoieo iaoa??ae?a.

Oai??y iae?i?eieo eieeaaiue ? iaeiei ?c aaaeeeaeo ?icae?e?a
aoae?aaeueii? iaoai?ee. Nueiaiaei? ?nio? ?yae aiae?oe/ieo i?aeoiae?a
aeey aeine?aeaeaiiy iae?i?eieo eieeaieo i?ioean?a o nenoaiao ?c
cina?aaeaeaieie ia?aiao?aie. Aea c oi/ee ci?o ?iaeaia?ii? i?aeoeee
a?eueoee ?ioa?an noaiiaeyoue i?inoi?iai iaiaaeai? nenoaie ?c
?iciiae?eaieie ia?aiao?aie: aaeee, ieanoeie, iaieiiee oa ?i.
Niinoa?aaeaiiy oa aeina?ae aenieoaoaoe?? nii?oae iieacaee, ui iae?i?ei?
eieeaaiiy a?ae?a?athoue aaaeeeao ?ieue a iinoao, i?aeaaeeiao,
oeee?iae?e/ieo iaieiieao ?aca?aoa??a oa ?ioeo eiino?oeoe?yo, ye?
caciathoue aieea?a a?ae aeeiai?/ieo iaaaioaaeaiue. Iniaeea?noth aeaiiai
eeana caaea/ ? a?eueo neeaaeia caeaaei?noue i?ae /anoioith eieeaaiue ?
aiie?ooaeaie aa?iii?e, ui aeieeathoue a nenoai?. Oea oneeaaeith?
a?aeiaeaeaiiy ??oaiiy ca aeiiiiiaith o?aaeeoe?eieo aiae?oe/ieo iaoiae?a.
Oiio ?ic?iaea iiaeo aiae?oe/ieo i?aeoiae?a aeey aeine?aeaeaiiy caaea/
iae?i?eieo eieeaaiue nenoai ?c ?iciiae?eaieie ia?aiao?aie ?
aeooaeueiith.

Ia??iaee/ii i?e?iiaiaeii??aei? eiiiiceoi? iaoa??aee oe?iei
aeei?enoiaothoueny a aoae?aieoeoa?, iaoeiiaoaeoaaii?, aa?aoe?? oa ?ioeo
aaeocyo oaoi?ee. I?e oeueiio iaei??th c iaeaieiai?oeo caaea/ oai???
eiiiiceoieo iaoa??ae?a ? ciaoiaeaeaiiy ?o aoaeoeaieo oa?aeoa?enoee. Oey
i?iaeaia ia? i?aeoe/ia cia/aiiy ye aeey aecia/aiiy oa?aeoa?enoee
?nioth/eo eiiiiceo?a, oae ? aeey noai?aiiy iiaeo eiino?oeoe?eieo
iaoa??ae?a ?c iaia?aae caaeaieie aeanoeainoyie. Aaaaoi no/anieo iaoiae?a
?ica’ycaiiy aeaii? caaea/? nie?athoueny ia iaai? i?eiouaiiy noiniaii
ni?aa?aeiioaiue i?ae eiioeaio?aoe?yie aai o?ce/ieie oa?aeoa?enoeeaie
neeaaeiaeo eiiiiiaio?a eiiiiceoii? no?oeoo?e. A oeueiio ca’yceo ?
aeooaeueiith ?ic?iaea iiaeo aiae?oe/ieo i?aeoiae?a, ye? a aeicaieeee
io?eioaaoe aiae?oe/i? ae?ace aeey aoaeoeaieo oa?aeoa?enoee eiiiiceoieo
iaoa??ae?a ca aoaeue yeeo eiioeaio?aoe?e oa o?ce/ieo aeanoeainoae
eiiiiiaio?a.

Iaoo oa caaea/? aeine?aeaeaiue noaiiaeyoue:

?ic?iaea aneiioioe/iiai iaoiaeo aeine?aeaeaiue iae?i?eieo eieeaaiue
i?inoi?iai iaiaaeaieo nenoai ?c ?iciiae?eaieie ia?aiao?aie;

canoinoaaiiy aeaiiai iaoiaeo aeey iiaoaeiae aiie?ooaeii-/anoioieo
oa?aeoa?enoee a?eueieo iae?i?eieo eieeaaiue noa?aeiy, aaeie, iaia?aie,
ieanoei, oeee?iae?e/ii? iaiae? oa nooe?eueiiai i?oaeiueiai na?aaeiaeua a
oiiaao ieinei? aeaoi?iaoe??;

?ic?iaea aiae?oe/ii? iaoiaeeee ciaoiaeaeaiiy aoaeoeaieo oa?aeoa?enoee
ia??iaee/ii i?e?iiaiaeii??aeieo eiiiiceoieo iaoa??ae?a;

canoinoaaiiy cai?iiiiiaaii? iaoiaeeee aeey aecia/aiiy aoaeoeaiiai
iiaeoey cnoao, aoaeoeaieo ooieoe?e cnoaieo ?aeaenaoe?? oa iiaco/ino?
eiiiiceoieo iaoa??ae?a ?c aieieienoeie aeth/aiiyie.

Iaoeiaa iiaecia ?iaioe iieyaa? a ?icaeoeo iiaeo aneiioioe/ieo i?aeoiae?a
aeey aeine?aeaeaiiy iae?i?eieo eieeaaiue nenoai ?c ?iciiae?eaieie
ia?aiao?aie oa aeey aecia/aiiy aoaeoeaieo oa?aeoa?enoee eiiiceoieo
iaoa??ae?a. Oea aeicaieeei a?aeiaeoe iaaeeaeai? aiae?oe/i? ?ica’ycee
?yaeo i?eeeaaeieo caaea/, aeine?aeaeaiiy yeeo ?ioeie iaoiaeaie
oneeaaeiaii.

A??ia?aei?noue io?eiaieo ?acoeueoao?a i?aeoaa?aeaeaii:

iiaoaeiaith iine?aeiaieo aneiioioe/ieo i?ioean?a, ui aeicaieythoue
ciaoiaeeoe ??oaiiy ?c aoaeue-yeei nooiaiai oi/iino?;

ii??aiyiiyi ?c aenia?eiaioaeueieie aeaieie oa ?acoeueoaoaie /enaeueieo
?ic?aooie?a ?ioeo aaoi??a.

Oai?aoe/ia oa i?aeoe/ia cia/aiiy ?iaioe. Cai?iiiiiaai? iaoiaee
a?aecia/athoueny aenieith aoaeoeai?noth oa a?aeiiniith i?inoioith.
A?aeiaeaeai? ca ?o aeiiiiiaith ?ica’ycee ?yaeo caaea/ oai??? iae?i?eieo
eieeaaiue oa oai??? eiiiiceoieo iaoa??ae?a /?oei a?aeaeaathoue o?ce/io
i?e?iaeo caaea/? oa caiaeyoueny aei i?inoeo aiae?oe/ieo oi?ioe, ui ?
iniaeeai c?o/iei aeey ?o aaciina?aaeiueiai aeei?enoaiiy a ?iaeaia?i?e
i?aeoeoe?.

Ai?iaaaeaeaiiy ?acoeueoao?a. Iaea?aeai? ?acoeueoaoe aeei?enoiaothoueny
a ?inoeooo? “ Aei?i?iaa?ii?iaeo” i?e ?ic?aooieao ooiaeaiaio?a oa
aoae?aaeueieo eiino?oeoe?e, ye? caciathoue aeeiai?/ieo aieea?a a?ae
oaoiieia?/iiai iaeaaeiaiiy, a /iio aoei neeaaeaii a?aeiia?aeiee aeo.
Ie?ai? iieiaeaiiy oa ?acoeueoaoe ?iaioe aeei?enoiaothoueny i?e
aeeeaaeaii? ??cieo niaoeeo?n?a ani??aioai oa nooaeaioai.

Ai?iaaoe?y. Iaoa??aee aeena?oaoe?eii? ?iaioe aeiiia?aeaeeny ia
I?aeia?iaeiiio aa?ieini?/iiio eiia?an? (Iineaa, 1994); ia I?aeia?iaeiiio
iaoeiaiio eiia?an? nooaeaio?a, ani??aio?a oa iieiaeeo a/aieo
“Iieiaeaaeue e iaoea – o?aouea ouny/aeaoea” (Iineaa, 1996); ia nai?ia??
naeoi?a iie?ia?ieo oa eiiiiceoieo iaoa??ae?a ?inoeoooa o?i?/ii? o?ceee
?in?enueei? aeaaeai?? iaoe i?ae ea??aieoeoaii i?io. E.?.Iaiaae/a
(Iineaa, 1997); ia 5-io oa 6-io Oe?a?inueei-iieuenueeeo nai?ia?ao
“Oai?aoe/i? canaaee aoae?aieoeoaa” (Aei?i?iiao?ianuee, 1997; Aa?oaaa,
Iieueoa, 1997); ia nai?ia?? a?aeae?eo iae?i?eii? iaoai?ee oi?aa?neoaoa
ooaoa ?ee?iien a O?aaia-Oaiiaei i?ae ea??aieoeoaii i?io. A. Aaeae?na
(O?aaia-Oaiiaei, ?ee?iien, NOA, 1997); ia nai?ia?? a?aeae?eo iaoai?ee
nooe?eueiiai na?aaeiaeua ?inoeoooa ooiaeaiaioaeueieo oaoiieia?/ieo
aeine?aeaeaiue Iieuenueei? aeaaeai?? iaoe i?ae ea??aieoeoaii i?io. I.
Iao/einueeiai (Aa?oaaa, Iieueoa, 1997); ia nai?ia?? oaeoeueoaoa
oeea?eueiiai aoae?aieoeoaa Aa?oaanueeiai iie?oaoi?/iiai ?inoeoooa i?ae
ea??aieoeoaii i?io. A. Uaniyea (Aa?oaaa, Iieueoa, 1997); ia X
I?aeia?iaei?e eiioa?aioe?? c iaoai?ee eiiiiceoieo iaoa??ae?a (?eaa,
Eaoa?y, 1998); ia I?aeia?iaeiiio eiia?an? iaoaiaoee?a (Aa?e?i,
I?ia//eia, 1998); ia 32-e Iieuenuee?e eiioa?aioe?? c iaoai?ee oaa?aeiai
o?ea (Caeiiaia, Iieueoa, 1998).

Ioae?eaoe??. Ca ?acoeueoaoaie aeena?oaoe?? iioae?eiaaii 19 iaoeiaeo
?ia?o, a oiio /ene? 5 noaoae, 5 iaoa??ae?a aeiiia?aeae ia eiioa?aioe?yo
? nai?ia?ao, 9 oac aeiiia?aeae ia eiioa?aioe?yo.

No?oeoo?a oa ianya ?iaioe. Aeena?oaoe?y neeaaea?oueny ?c anooio, o?ueio
?icae?e?a, aeniiae?a, aeiaeaoea oa nieneo aeei?enoaieo e?oa?aoo?ieo
aeaea?ae (139 iaeiaioaaiue). Caaaeueiee ianya ?iaioe noaiiaeoue 158
noi??iie, a oiio /ene? 36 ?enoie?a.

Aaoi? aeneiaeth? aeeaieo aaey/i?noue e.o.i., aeioe. E?anianueeiio A.E.
ca aeiiiiiao o i?aeaioiaoe? aeena?oaoe?eii? ?iaioe. Iniaeeaa iiaeyea
ae.o.i., i?io. Iaiaae/o A.?. ca oe?ii? eiinoeueoaoe??, io?eiai? a oiae?
aeeiiaiiy aeine?aeaeaiue.

INIIAIEE CI?NO ?IAIOE

Anooi. Aecia/aii no/aniee noai aiae?oe/ieo iaoiae?a aeine?aeaeaiiy
caaea/ oai??? iae?i?eieo eieeaaiue oa oai??? eiiiiceoieo iaoa??ae?a.
Iaa?oioiaaii aea?? oaie ?iaioe, ?? aeooaeuei?noue. Noi?ioeueiaaii iaoo
oa caaea/? aeine?aeaeaiue. Iaaaaeaii a?aeiiino? uiaei iaoeiai? iiaecie,
oai?aoe/iiai oa i?eeeaaeiiai cia/aiiy ?acoeueoao?a ?iaioe.

A ia?oiio ?icae?e? i?iaiaeeoueny eiiniaeoeaiee iaeyae ?nioth/eo
aiae?oe/ieo iaoiae?a ?ica’ycaiiy caaea/ oai??? iae?i?eieo eieeaaiue.
Oeaio?aeueia i?noea na?aae ieo caeia? iaoiae cao?aiue. Aieiai? ?aea?
oeueiai iaoiaeo aoee cai?iiiiiaai? ua A.Ioaiea?a ? a oiio /e ?ioiio
aeaeyae? neeaee iniiao a?eueoino? no/anieo aneiioioe/ieo i?aeoiae?a.
Aeaiee iaoaiaoe/iee aiia?ao i?ecaiaeeoue aei aeia?eo ?acoeueoao?a i?e
aeine?aeaeaii? nenoai ?c cina?aaeaeaieie ia?aiao?aie. Aea c oi/ee ci?o
aoae?aaeueii? iaoai?ee a?eueoee ?ioa?an noaiiaeyoue i?inoi?iai iaiaaeai?
nenoaie ?c ?iciiae?eaieie ia?aiao?aie: aaeee, ieanoeie, iaieiiee oa ?i.
Iniaeea?noth oeeo caaea/ ? iiaeeea?noue oae caaiiai aioo??oiueiai
?aciiainao i?ae aa?iii?eaie aeanieo eieeaaiue. A oeueiio aeiaaeeo
canoinoaaiiy a?aeiieo aneiioioe/ieo i?aeoiae?a i?ecaiaeeoue aei
iaiao?aeiino? ?ica’ycaiiy iane?i/aii? nenoaie iae?i?eieo aeaaa?a?/ieo /e
aeeoa?aioe?eieo ??aiyiue. Aeey ae??oaiiy oe??? i?iaeaie ?ic?iaeaii iiaee
aneiioioe/iee iaoiae, ui aaco?oueny ia aaaaeaii? ooo/iiai iaeiai
ia?aiao?o.

Cai?iiiiiaaia aneiioioe/ia oaoi?ea aeeeaaea?oueny ia i?inoiio
iiaeaeueiiio i?eeeaae?. ?icaeyaeathoueny a?euei? iiacaeiaaei? eieeaaiiy
noa?aeiy a iae?i?eii-i?oaeiueiio ciai?oiueiio na?aaeiaeu?. E?ioe?
noa?aeiy aei?noei cauaieai?. Aecia/aeueia e?aeiaa caaea/a ia? aeaeyae:

, (1)

, (2)

. ?icooeo?ii ia??iaee/ia ??oaiiy, yea caaeiaieueiy? oiia?
ia??iaee/iino?

, (3)

– iaa?aeiia aeania /anoioa eieeaaiue.

Ci?ith?ii ianooaa /ano:

, (4)

oa ooea?ii ?ica’ycie e?aeiai? caaea/? (1) – (3) ye aneiioioe/i?
?iceeaaee

, (5)

, (6)

, io?eio?ii ?aeo?aioio nenoaio e?i?eieo e?aeiaeo caaea/.

Ioeueiaa iaaeeaeaiiy ciaoiaeeii o aeaeyae?

, (7)

.

Oiiae a?aenooiino? a ?iceeaae? (5) a?eiaeo (c?inoath/eo ?c /anii) /eai?a
i?ecaiaeyoue aei iane?i/aii? nenoaie iae?i?eieo aeaaa?a?/ieo ??aiyiiue

, (8)

iiaa?oa?oueny aei ii/aoeiai? oi?ie. Iaa?aeii? aaee/eie ?icooeothoueny
ye aneiioioe/i? ?iceeaaee

, (9)

. (10)

A?aeiia?aeii aei ni?aa?aeiioaiiy (7), oi?ia eieeaaiue ia? aeaeyae

, (11)

– /anoioe aa?iii?e. A caaaeueiiio aeiaaeeo nenoaia (8) aeiionea?
?ica’ycee ianooiiiai aeaeo:

. (12)

-oa aa?iii?ea, /anoioa yei? aecia/a?oueny ni?aa?aeiioaiiyi

, (13)

.

), ia? i?noea aioo??oi?e ?aciiain i?ae aa?iii?eaie aeanieo eieeaaiue. A
oeueiio aeiaaeeo iaeii/anii ?aae?cothoueny on? iaia?i? aa?iii?ee,
nenoaia (8) ia? ?ica’ycie:

, … ; (14)

.

A*O aecia/a?oueny oi?ioeith

, (15)

.

. Aecia/aeueia ??aiyiiy (1) ia?aieoaii oae:

, (16)

. ?ica’ycie e?aeiai? caaea/? (2), (3), (16) ?icooeo?ii o aeaeyae?
?iceeaae?a

?en.1. Aiie?ooaeii-/anoioia oa?aeoa?enoeea iniiaiiai oiio iae?i?eieo
eieeaaiue noa?aeiy i?e a?aenooiino? aioo??oiueiai ?aciiaino i?ae
aa?iii?eaie.

?en.2. Aiie?ooaeii-/anoioia oa?aeoa?enoeea iniiaiiai oiio eieeaaiue
noa?aeiy o aeiaaeeo aioo??oiueiai ?aciiaino i?ae aa?iii?eaie.

, (17)

/eaie yeeo, a naith /a?ao, i?aaenoaaey?ii aicaoeaie

, (18)

, (19)

. A ?acoeueoao? ciaoiaeeii ianooiia aneiioioe/ia ??oaiiy:

, (20)

, … ;

, … .

(21)

Aeae? a ia?oiio ?icae?e? ca aeiiiiiaith ?icaeiooi? aneiioioe/ii?
oaoi?ee ?ica’ycaii caaea/? caeaieo eieeaaiue aaeee ia iae?i?eii-i?oaei?e
iniia? oa iae?i?eieo eieeaaiue aaeee, yea ?icoyaiooa iicaeiaaeiueith
neeith.

A ae?oaiio ?icae?e? cai?iiiiiaaiee aneiioioe/iee iaoiae canoiniao?oueny
aeey aeine?aeaeaiiy iae?i?eieo eieeaaiue aeaiaei??ieo nenoai. ?icaeyiooi
i?yiieooi? iaia?aio, ieanoeio, iieiao oeee?iae?e/io iaiaeue ia
iae?i?eii-i?oaei?e iniia?; ieanoeio ia iae?i?eii-i?oaei?e iniia?, yea
?icoyaiooa iicaeiaaeieie neeaie; nooe?eueia na?aaeiaeua a oiiaao ieinei?
aeaoi?iaoe??. A?aeiaeaeaii aneiioioe/i? ?ica’ycee oa iaea?aeaii
aiae?oe/i? oi?ioee aeey aeanieo aiie?ooaeii-/anoioieo oa?aeoa?enoee
nenoai.

O?ao?e ?icae?e ?iaioe i?enay/aii aecia/aiith aoaeoeaieo oa?aeoa?enoee
eiiiiceoieo iaoa??ae?a. I?aaenoaaeaii iaeyae e?oa?aoo?ieo aeaea?ae,
i?iaaaeaii e?eoe/iee aiae?c no/anieo iaoiae?a ?ica’ycaiiy aeaii?
i?iaeaie. Aaaaoi ?c ?nioth/eo aiae?oe/ieo i?aeoiae?a nie?athoueny ia
iaai? i?eiouaiiy noiniaii eiioeaio?aoe?? oa o?ce/ieo oa?aeoa?enoee
eiiiiiaio?a eiiiiceoiiai iaoa??aeo. Aaoi?ii ?ic?iaeaii iiao aneiioioe/io
iaoiaeeeo, yea aeicaiey? ciaoiaeeoe iaaeeaeai? aiae?oe/i? ae?ace
aoaeoeaieo oa?aeoa?enoee, i?eaeaoi? aeey aoaeue-yeeo eiioeaio?aoe?e oa
o?ce/ieo aeanoeainoae eiiiiiaio?a.

. Aecia/aeuei? ni?aa?aeiioaiiy caiaeyoueny aei aeaiaei??iiai ??aiyiiy
Eaieana:

, (22)

a?aeiia?aeathoue ??aiino? aeaoi?iaoe?e oa iai?oa:

, (23)

.

(?en. 3). Aaaaeaii a eii??oe? eieaeueio nenoaio eii?aeeiao:

, (24)

?ici?? eii??ee ia??iaee/iino? aei??aith? 2. ?ica’ycie aecia/aeueii?
e?aeiai? caaea/? (22), (23) ?icooeo?ii o aeaeyae? aneiioioe/iiai
?iceeaaeo

?en. 4. Eii??ea ia??iaee/iino?.

?en. 3. Eiiiiceoiee iaoa??ae,

ui ?icaeyaea?oueny.

. (25)

, io?eio?ii ?aeo?aioio nenoaio e?aeiaeo caaea/.

, io?eio?ii:

. (26)

iaaaaeaii ia ?en. 5.

Aeae? ca aeiiiiiaith ?icaeiooi? aneiioioe/ii? iaoiaeeee aecia/aii
aoaeoeaiee iiaeoeue cnoao eiiiiceoiiai iaoa??aeo ?c aieieienoeie
aeeth/aiiyie ?iia?/iiai ia?a??co. Oaeiae ?icaeyiooi a’ycei-i?oaei?
eiiiiceoi? iaoa??aee ?c aieieienoeie aeeth/aiiyie. A?aeiaeaeaii
aoaeoeai? ooieoe?? cnoaii? ?aeaenaoe?? oa iiaco/ino?, aeey ?aaeeio
noaoe?iia?ieo aa?iii?eieo eieeaaiue aecia/aii eiiieaeni? iiaeoe? cnoao
oa oaiaaine ao?ao.

AENIIAEE

Iniiai? iaoeia? oa i?aeoe/i? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
iieyaathoue a ianooiiiio:

?ic?iaeaii iiaee aneiioioe/iee iaoiae aeine?aeaeaiiy iae?i?eieo
eieeaaiue i?inoi?iai iaiaaeaieo nenoai ?c ?iciiae?eaieie ia?aiao?aie.
Iniaeea?noth aeaiiai eeano caaea/ ? neeaaeia caeaaei?noue i?ae /anoioaie
oa aiie?ooaeaie aa?iii?e, ye? aeyaeythoueny ca’ycaieie iane?i/aieie
nenoaiaie iae?i?eieo aeaaa?a?/ieo ??aiyiue. ?ica’ycie inoaii?o
aaea?oueny a?aeiaeoe oeyoii aaaaeaiiy ooo/iiai iaeiai ia?aiao?o.

Ia iniia? cai?iiiiiaaiiai iaoiaeo iaea?aeaii aeani? aiie?ooaeii-/anoioi?
oa?aeoa?enoeee iae?i?eieo eieeaaiue noa?aeiy, aaeie, iaia?aie, ieanoei,
oeee?iae?e/ii? iaiae? oa nooe?eueiiai i?oaeiueiai na?aaeiaeua a oiiaao
ieinei? aeaoi?iaoe??.

?ic?iaeaii iiaee aneiioioe/iee i?aeo?ae aeey aecia/aiiy aoaeoeaieo
oa?aeoa?enoee i?e?iiaiaeii??aeieo aeaioacieo eiiiiceoieo iaoa??ae?a ?c
ia??iaee/ii ?icoaoiaaieie aeeth/aiiyie. Aeey oeueiai aeei?enoiao?oueny
iaoiae aiiiaai?caoe??, iaaeeaeaiiy o?eoacii? iiaeae?, iaoiae cao?aiiy
oi?ie iaae?, aeaioi/eia? ai?ieneiaoe?? Iaaea oa eaac??aoe?iiaeuei?
ai?ieneiaoe??.

Ca aeiiiiiaith ?ic?iaeaii? iaoiaeeee a?aeiaeaeaii aoaeoeai? iiaeoe?
cnoao i?oaeieo eiiiiceoieo iaoa??ae?a ?c aieieienoeie aeeth/aiiyie;
aoaeoeai? ooieoe?? cnoaii? ?aeaenaoe?? oa iiaco/ino?, eiiieaeni? iiaeoe?
cnoao oa oaiaaine ao?ao a’ycei-i?oaeieo eiiiiceoieo iaoa??ae?a.

NIENIE IIOAE?EIAAIEO I?AOeUe CAeIAOAA*A

Ca ?acoeueoaoaie aeena?oaoe?? iioae?eiaaii 19 ?ia?o, a naia:

a) noaoo?:

Aiae??aiia ?. A., Aeai?oaanueeee A. A. Aecia/aiiy aoaeoeaiiai
eiao?oe??ioo oaieii?ia?aeiino? ?cio?iiiiai na?aaeiaeua ca aeiiiiiaith
aeaiooi/eiaeo ai?ieneiaoe?e Iaaea // Ca??iee iaoeiaeo i?aoeue
Aei?i?iiao?ianueeiai ?iaeaia?ii-aoae?aaeueiiai ?inoeoooa
“?ioaineo?eaoe?y aoae?aieoeoaa”. – E.: ?inoeooo nenoaiieo
aeine?aeaeaiiue II Oe?a?ie, 1994. – N. 20-25. (50% aaoi?nueei? o/ano?,
iinoaiiaea iaoiaeo oa aiae?c ?acoeueoao?a).

Andrianov I. V., Danishevs’kyy V V. Asymptotic investigation of the
nonlinear dynamic boundary value problem for rods // Technische
Mechanik. – 1995. – V. 15, No. 1. – P. 53-55. (50% a. o., canoinoaaiiy
iaoiaeeee oa i?iaaaeaiiy ?ic?aooie?a).

Andrianov I., Danishevs’kyy V., Tokarzewski S. Two – point
quasifractional approximants for effective conductivity of a simple
cubic lattice of spheres // Int. J. Heat Mass Transfer. – 1996. – V. 39.
– P. 2349-2352. (30% a. o., io?eiaiiy aiae?oe/iiai ?ica’yceo).

Aiae?eaiia E. A., Noa?ooaiei A. A., Aeaieoaaneee A. A. Aneiioioe/aneia
i?aaenoaaeaiea yooaeoeaiiai eiyooeoeeaioa oaieii?iaiaeiinoe eiiiiceoiiai
iaoa?eaea n aieieienouie aeeth/aieyie ?iiaiaeaeiie oi?iu aieueoiai
?acia?a // Ca??iee iaoeiaeo i?aoeue Aei?i?iiao?ianeiai aea?aeaaiiai
oi?aa?neoaoo “Aeeoa?aioe?aeuei? ??aiyiiy oa ?o canoinoaaiiy”.
-Aei?i?iiao?ianuee: aeaeaaieoeoai Aei?i?iiao?ianeiai aea?aeaaiiai
oi?aa?neoaoo. –1998. -N.46-52. (40% a. o., a?aeiaeaeaiiy aiae?oe/iiai
?ica’yceo).

Aeaieoaaneee A. Yooaeoeaiue iiaeoeue naeaeaa eiiiiceoiiai iaoa?eaea n
aieieienouie aeeth/aieyie ?iiaiaeaeiiai iiia?a/iiai na/aiey:
aneiioioe/aneee iiaeoiae // Nai?iee iao/iuo o?oaeia I?eaeiai?ianeie
ainoaea?noaaiiie aeaaeaiee no?ieoaeuenoaa e a?oeoaeoo?u. Auione 2.
*anoue 2. – Aeiai?iiao?iane: IAANeA. -1997. – N. 68-71.

a) iaoa??aee aeiiia?aeae ia eiioa?aioe?yo oa nai?ia?ao:

Andrianov I., Danishevsky V., Tokarzewski S. Quasifractional
approximants in the theory of composite materials // Proceedings of the
International Aerospace Congress. –Vol.2. –Moscow (Russia). -1994. –P.
592-594. (40% a. o., io?eiaiiy aiae?oe/iiai ?ica’yceo).

Aeaieoaaneee A. A. Aneiioioe/aneia enneaaeiaaiea eaaceeeiaeiuo eieaaaiee
iai?a?uaiuo nenoai eiia/iuo ?acia?ia // Proceedings of the 5th
Ukrainian-Polish seminar “Theoretical Foundations of Civil Engineering”.
-Dnepropetrovsk-Warsaw. –1997. P. 47-52.

Tokarzewski S., Andrianov I., Danishevs’kyy V. The investigation of a
complex conductivity of regular arrays of spheres // Proceedings of the
5th Ukrainian-Polish seminar “Theoretical Foundations of Civil
Engineering”. -Dnepropetrovsk-Warsaw. –1997. P. 414-425. (30% a. o.,
aiae?c ?acoeueoao?a).

Aiae?eaiia E. A., Aeaieoaaneee A. A., Oieaaeaaneee N. Aneiioioe/aneia
i?aaenoaaeaiea yooaeoeaiuo ayceioi?oaeo naeaeaiauo oa?aeoa?enoee
ia?eiaee/anee iee?iiaiaeii?iaeiiai eiiiiceoiiai iaoa?eaea n aieieienouie
aeeth/aieyie ?iiaiaeaeiie oi?iu // Proceedings of the 6th
Polish-Ukrainian seminar “Theoretical Foundations of Civil Engineering”.
– Warsaw (Poland). – 1998. – P. 386-392. (40% a. o., ?ic?iaea iaoiaeo,
io?eiaiiy aiae?oe/ieo ?ica’yce?a).

Tokarzewski S., Andrianov I., Danishevs’kyy V. Dynamiczne moduly skretne
pretow sprezystych porami wypelnionymi ciecza lepka // Proceedings of
the 6th Polish-Ukrainian seminar “Theoretical Foundations of Civil
Engineering”. – Warsaw (Poland). – 1998. – P.393-398. (30% a. o., aiae?c
?acoeueoao?a)

a) oace aeiiia?aeae ia eiioa?aioe?yo:

Aiae?eaiia E. A., Aeaieoaaneee A. A., Naciiaoe I. Aneiioioe/aneia
enneaaeiaaiea iaeeiaeiie aeeiaieee noa?aeiy // O?oaeu oeieu-naieia?a
“Iaeeiaeiua e?aaaua caaea/e iaoaiaoe/aneie oeceee”. –Eeaa. –1994. -N. 5.
(30% a. o., i?iaaaeaiiy ?ic?aooie?a).

Andrianov I., Danishevs’kyy V. Asymptotic investigation of the nonlinear
longitudinal oscillations of rod // Abstracts of the XXI Yugoslav
Congress of the Theoretical and Applied Mechanics. – NIS (Yugoslavia).
–1995. -P. 268. (50% a.o., ?ic?iaea iaoiaeo oa i?iaaaeaiiy ?ic?aooie?a).

Andrianov I., Danishevs’kyy V. Quasifractional approximants in the
theory of dispersed media // Abstracts of the XXII Yugoslav Congress of
the Theoretical and Applied Mechanics. – Vrnjacka Banja (Yugoslavia). –
1997. – P. 3. (50% a. o., canoinoaaiiy iaoiaeo, io?eiaiiy aiae?oe/iiai
?ica’yceo).

Andrianov I., Danishevs’kyy V., Starushenko G., Tokarzewski S.
Asymptotic approach, multi-point Pade and quasifractional approximants
in the theory of composite materials // Abstracts of the 3rd EUROMECH
Solid Mechanics Conference. – Stockholm (Sweden). – 1997. – P. 27. (30%
a. o., canoinoaaiiy iaoiaeo, io?eiaiiy aiae?oe/iiai ?ica’yceo).

Aiae?eaiia E. A., Aeaieoaaneee A. A. Ii?aaeaeaiea yooaeoeaiuo
oa?aeoa?enoee eiiiiceoiuo iaoa?eaeia i?e iiiiue aneiioioe/aneeo iaoiaeia
e aeaoooi/a/iuo oi?ioe // O?oaeu Iaaeaeoia?iaeiiai eiia?anna nooaeaioia,
anie?aioia e iieiaeuo o/aiuo “Iieiaeaaeue e iaoea – o?aouea ouny/aeaoea”
(YSTM’96). – O.2. – Iineaa: IOA “Aeooaeueiua i?iaeaiu ooiaeaiaioaeueiuo
iaoe”. – 1997. – N.50. (50% a. o., ?ic?iaea iaoiaeeee).

Andrianov I., Starushenko G., Danishevs’kyy V. Asymptotic approximation
of effective heat conductivity of composite materials with large diamond
fiber inclusions // Abstracts of the X International Conference on
Mechanics of Composite Materials. – Riga (Latvia). – 1998. – P. 19. (40%
a. o., canoinoaaiiy iaoiaeo, aiae?c ?acoeueoao?a).

Danishevs’kyy V., Andrianov I. A new asymptotic technique for non-linear
dynamic boundary value problems // Abstracts of the International
Congress of Mathematicians. – Berlin (Germany). – 1998. – P. 231. (50%
a. o., iinoaiiaea iaoiaeo, i?iaaaeaiiy ?ic?aooie?a)

Danishevs’kyy V. An asymptotic technique for non-linear oscillations of
finite sizes systems // Abstracts of the 32nd Polish Solid Mechanics
Conference (SolMec’98). – Zakopane (Poland). – 1998. – P. 115-116.

Tokarzewski S., Andrianov I., Danishevs’kyy V. Continued fraction
approach to the torsionally oscillating viscoelastic beams reinforced
with viscoelastic fibres // Abstracts of the 32nd Polish Solid Mechanics
Conference (SolMec’98). – Zakopane (Poland). – 1998. – P. 377-378. (30 %
a. o., aiae?c ?acoeueoao?a).

AIIOAOe?ss

Aeai?oaanueeee A.A. Aneiioioe/i? iaoiaee a i?eeeaaeieo caaea/ao oai???
iae?i?eieo eieeaaiue oa oai??? eiiiiceoieo iaoa??ae?a. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 05.23.17 – aoae?aaeueia iaoai?ea. – I?eaei?i?ianueea
aea?aeaaia aeaaeai?y aoae?aieoeoaa oa a?o?oaeoo?e, Aei?i?iiao?ianuee,
1999.

A aeena?oaoe?? ?icaeiooi aneiioioe/i? iaoiaee aeey aeine?aeaeaiiy
iae?i?eieo eieeaaiue nenoai ?c ?iciiae?eaieie ia?aiao?aie oa aecia/aiiy
aoaeoeaieo oa?aeoa?enoee i?e?iiaiaeii??aeieo eiiiiceoieo iaoa??ae?a. Ca
aeiiiiiaith cai?iiiiiaaieo iaoiae?a ?ica’ycaii ?yae i?eeeaaeieo caaea/
aoae?aaeueii? iaoai?ee. Iaea?aeaii aiie?ooaeii-/anoioi? oa?aeoa?enoeee
a?eueieo iae?i?eieo eieeaaiue noa?aeiy, aaeie, iaia?aie, ieanoei,
oeee?iae?e/ii? iaiae? oa nooe?eueiiai i?oaeiueiai na?aaeiaeua a oiiaao
ieinei? aeaoi?iaoe??. A?aeiaeaeaii aoaeoeai? iiaeoe? cnoao, aoaeoeai?
ooieoe?? cnoaii? ?aeaenaoe?? oa iiaco/ino?, eiiieaeni? iiaeoe? cnoao ?
oaiaaine ao?ao aeaioacieo eiiiiceoieo iaoa??ae?a ?c aieieienoeie
aeeth/aiiyie.

Eeth/ia? neiaa: aneiioioe/i? iaoiaee, iae?i?ei? eieeaaiiy, eiiiiceoi?
iaoa??aee, ina?aaeiaiiy, aoaeoeai? oa?aeoa?enoeee.

SUMMARY

Danishevs’kyy V.V. Asymptotic methods for applied problems of the
theories of nonlinear oscillations and composite materials. –
Manuscript.

Thesis for a Ph.D. degree by speciality 05.23.17 – Structural
Mechanics. – Prydniprovska State Academy of Civil Engineering and
Architecture, Dnipropetrovsk, 1999.

The thesis is devoted to the development of asymptotic methods in
nonlinear oscillations problems of continuous systems and in problems of
determining effective properties of periodically inhomogeneous composite
materials. Some applied problems of Structural Mechanics are solved by
means of proposed methods. Amplitude-frequency dependencies for free
nonlinear oscillations of a rod, beams, a membrane, plates, a shell and
a continuous elastic medium are obtained. The effective shear modulus,
effective shear relaxation and creep functions, effective complex shear
modulus and loss tangent are evaluated.

Key words: asymptotic methods, nonlinear oscillations, composite
materials, homogenization, effective properties.

AIIIOAOeEss

Aeaieoaaneee A.A. Aneiioioe/aneea iaoiaeu a i?eeeaaeiuo caaea/ao oai?ee
iaeeiaeiuo eieaaaiee e oai?ee eiiiiceoiuo iaoa?eaeia. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05.23.17 – no?ieoaeueiay iaoaieea. – I?eaeiai?ianeay
ainoaea?noaaiiay aeaaeaiey no?ieoaeuenoaa e a?oeoaeoo?u,
Aeiai?iiao?iane, 1999.

Aeenna?oaoeey iinayuaia ?acaeoeth aneiioioe/aneeo iaoiaeia aeey
enneaaeiaaiey iaeeiaeiuo eieaaaiee nenoai n ?ani?aaeaeaiiuie ia?aiao?aie
e ii?aaeaeaiey yooaeoeaiuo oa?aeoa?enoee iee?iiaiaeii?iaeiuo eiiiiceoiuo
iaoa?eaeia. N iiiiuueth i?aaeeiaeaiiuo iaoiaeia ?aoai ?yae i?eeeaaeiuo
caaea/ no?ieoaeueiie iaoaieee.

Aeenna?oaoeeiiiay ?aaioa ninoieo ec aaaaeaiey, o?ao ?acaeaeia,
caeeth/aiey, nienea eeoa?aoo?u e i?eeiaeaiey, niaea?aeeo 158 no?aieoe
iaoeiiieniiai oaenoa, 36 ?enoieia, aeaeeia?aoeth ec 139 iaeiaiiaaiee.

Ai aaaaeaiee iainiiauaaaony auai? oaiu ?aaiou e aa aeooaeueiinoue.
Noi?ioee?iaaiu oeaee e caaea/e enneaaeiaaiee. I?eaaaeaiu naaaeaiey i
iao/iie iiaecia e i?aeoe/aneii cia/aiee iieo/aiiuo ?acoeueoaoia.

A ia?aii ?acaeaea auiieiai iaci? nia?aiaiiuo aiaeeoe/aneeo iaoiaeia
?aoaiey caaea/ oai?ee iaeeiaeiuo eieaaaiee. ?ac?aaioai aneiioioe/aneee
iiaeoiae aeey enneaaeiaaiey iaeeiaeiuo eieaaaiee i?ino?ainoaaiii
ia?aie/aiiuo nenoai n ?ani?aaeaeaiiuie ia?aiao?aie. Aeaiiue iaoiae
i?eiaiyaony e iino?iaieth nianoaaiiuo aiieeooaeii-/anoioiuo
oa?aeoa?enoee noa?aeiy a iaeeiaeii-oi?oaie aiaoiae n?aaea e aaeie ia
iaeeiaeii-oi?oaii iniiaaiee.

Ai aoi?ii ?acaeaea n iiiiuueth ?acaeoiai aneiioioe/aneiai iiaeoiaea
enneaaeothony iaeeiaeiua eieaaaiey aeaoia?iuo nenoai. Iieo/aiu
aiieeooaeii-/anoioiua oa?aeoa?enoeee iaeeiaeiuo eieaaaiee iaia?aiu,
ieanoei, oeeeeiae?e/aneie iaiaee e nieioiie oi?oaie n?aaeu, iaoiaeyuaeny
a oneiaeyo ieineie aeaoi?iaoeee

A o?aoueai ?acaeaea i?eaaaeai iaci? nia?aiaiiuo iaoiaeia ii?aaeaeaiey
yooaeoeaiuo oa?aeoa?enoee eiiiiceoiuo iaoa?eaeia. ?ac?aaioaia
aneiioioe/aneay iaoiaeeea ?aoaiey aeaiiie caaea/e, i?e iiiiue eioi?ie
iaeaeaiu yooaeoeaiua iiaeoee naeaeaa, yooaeoeaiua ooieoeee naeaeaiaie
?aeaenaoeee e iieco/anoe, eiiieaeniua iiaeoee naeaeaa e oaiaainu iioa?ue
aeaoooaciuo eiiiiceoiuo iaoa?eaeia n aieieienouie aeeth/aieyie.

A i?eeiaeaiee i?eaaaeai aeo aiaae?aiey, iiaeoaa?aeaeathuee i?aeoe/aneia
eniieueciaaiea ?acoeueoaoia aeenna?oaoeeiiiie ?aaiou.

Iao/iay iiaecia ?aaiou caeeth/aaony a ?acaeoee iiauo aneiioioe/aneeo
iiaeoiaeia aeey enneaaeiaaiey iaeeiaeiuo eieaaaiee i?ino?ainoaaiii
ia?aie/aiiuo nenoai e ii?aaeaeaiey yooaeoeaiuo oa?aeoa?enoee eiiiiceoiuo
iaoa?eaeia. Yoi iicaieeei iieo/eoue i?eaeeaeaiiua aiaeeoe/aneea ?aoaiey
?yaea caaea/ oai?ee iaeeiaeiuo eieaaaiee e oai?ee eiiiiceoiuo
iaoa?eaeia, enneaaeiaaiea eioi?uo ae?oaeie i?eaiaie cao?oaeieoaeueii.

Aeinoiaa?iinoue iieo/aiiuo ?acoeueoaoia iiaeoaa?aeaeaia:

iino?iaieai iineaaeiaaoaeueiuo aneiioioe/aneeo i?ioeannia, iicaieythueo
iaoiaeeoue ?aoaiea n ethaie noaiaiueth oi/iinoe;

n?aaiaieai n iaeioi?uie ecaanoiuie yenia?eiaioaeueiuie aeaiiuie e
?acoeueoaoaie /eneaiiuo ?an/aoia ae?oaeo aaoi?ia.

Oai?aoe/aneia e i?eeeaaeiia cia/aiea ?aaiou ninoieo a oii, /oi
i?aaeeiaeaiiua e ?acaeoua iaoiaeu ioee/athony aunieie yooaeoeaiinoueth e
ioiineoaeueiie i?inoioie. Iieo/aiiua n eo iiiiuueth ?aoaiey ?yaea caaea/
oai?ee iaeeiaeiuo eieaaaiee no?ieoaeueiuo eiino?oeoeee e oai?ee
eiiiiceoiuo iaoa?eaeia /aoei io?aaeatho oece/aneoth i?e?iaeo caaea/e e
naiaeyony e i?inoui aiaeeoe/aneei au?aaeaieyi.

Iniiaiia niaea?aeaiea aeenna?oaoeee iioaeeeiaaii a aeaayoiaaeoeaoe
ia/aoiuo ?aaioao.

Eeth/aaua neiaa: aneiioioe/aneea iaoiaeu, iaeeiaeiua eieaaaiey,
eiiiiceoiua iaoa?eaeu, in?aaeiaiea, yooaeoeaiua oa?aeoa?enoeee.

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