Контактна взаємодія пружних тіл з теплоутворенням від тертя: Автореф. дис… канд. фіз.-мат. наук / Р.В. Юринець, НАН України. Ін-т приклад. пробл. ме

IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO I?EEEAAeIEO I?IAEAI

IAOAI?EE ? IAOAIAOEEE

?i. ss.N. I?AeNO?EAA*A

Ia i?aaao ?oeiieno

TH?eiaoeue ?inoeneaa Aieiaeeie?iae/

OAeE 539.3

EIIOAEOIA ACA?IIAe?ss I?OAEIEO O?E

C OAIEIOOAI?AIIssI A?Ae OA?Oss

01.02.04 — Iaoai?ea aeaoi?i?aiiai oaa?aeiai o?ea

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy a/aiiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

EUeA?A — 1998 ?.

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia ia eaoaae?? iaoai?ee Euea?anueeiai aea?aeaaiiai
oi?aa?neoaoo ?i. ?. O?aiea.

Iaoeia? ea??aieee: aeieoi? oaoi?/ieo iaoe, i?ioani?

A?ee?oeueeee Aeieo?i Aieiaeeie?iae/,

eaoaae?a iaoai?ee EAeO ?i. ?. O?aiea

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?,

A?aae Aaneeue Ieoaeeiae/,

ea??aiee a?aeae?eo iaoai?ee aeaoi?i. oaa?ae. o?ea,

?IIII ?i. ss.N. I?aeno?eaa/a IAI Oe?a?ie;

aeieoi? oaoi?/ieo iaoe, i?ioani?

Nynueeee Aiae??e Ieaen?eiae/,

caa?aeoth/ee eaoaae?ith caaaeueii-oaoi?/ieo

aeenoeeie?i ? iaoiaeeee o?oaeiaiai iaa/aiiy

??aiainueeiai iaaeaaia?/iiai ?inoeoooo.

I?ia?aeia onoaiiaa: O?ceei-iaoai?/iee ?inoeooo ?i. A.A. Ea?iaiea

IAI Oe?a?ie, a?aeae?e o?ce/ieo iniia i?oeiino?

iaoa??ae?a, i. Euea?a.

Caoeno a?aeaoaeaoueny ‘‘28’’ a?oaeiy 1998 ?. i 15 aiae. ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.195.01 i?e ?inoeooo? i?eeeaaeieo
i?iaeai iaoai?ee ? iaoaiaoeee ?i. ss.N. I?aeno?eaa/a IAI Oe?a?ie ca
aae?anith: 290053, i. Euea?a, aoe. Iaoeiaa, 3 a.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? ?IIII (i. Euea?a,
aoe. Iaoeiaa, 3 a).

Aaoi?aoa?ao ?ic?neaiee ‘‘25’’ eenoiiaaea 1998 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe Oaa/oe I.?.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Caaacia/aiiy i?oeiino? ? aeiaaia?/iino? aeaiaio?a
eiino?oeoe?e, ye? i?aeaeathoueny i?ae /an aenieoaoaoe?? aieeao oaieiaeo
? neeiaeo iaaaioaaeaiue, coiiaeei /eneaii? aeine?aeaeaiiy ?o
oa?iiiai?oaeaiiai noaio.

Cia/iee aianie o ?icaeoie oai??? eiioaeoieo caaea/ oa?iii?oaeiino? c
oaieiooai?aiiyi c?iaeaii o i?aoeyo A.I. Ae?enaiae?iaa, A.I. A?aaea,
Ae.A. A?ee?oeueeiai, I.A. Aaia?aeiaa, ?.A. Eiaaeaiea, I.A.
Ei?ia/einueeiai, A.A. Eoae?yaoeaaa, A.I. Eaaeoeueeiai, A.C. Ia?oiia, J.
Barber, F. Ling oa ?i.

O no/anieo ??ciioeiieo oaoi?/ieo eiino?oeoe?yo /anoi aeei?enoiaothoueny
neeaaeia? aeaiaioe, ye? iaae?eai? ai?cio?iiieie ? iaa?oue
iaiaeii??aeieie aeanoeainoyie. Iaiaeii??aei?noue o?ceei-iaoai?/ieo
aeanoeainoae iaoa??ae?a neeaaeiaeo aeaiaio?a eiino?oeoe?e oa ?o
ai?cio?ii?y iiaeooue aooe i?e?iaeieie aai aeieeiooe a i?ioean?
oi?ioaaiiy caaioiaie aiane?aeie oaoiieia?/ieo iia?aoe?e, aai ae
c’yaeoeny a i?ioean? aenieoaoaoe?? i?ae aieeaii ae?? ?aaeoeaieo
na?aaeiaeu. A?aooaaiiy ?aaeueieo aeanoeainoae iaoa??ae?a i?ae /an
i?iaeooaaiiy ? ?ic?aooieo eiie?aoieo eiino?oeoe?e i?ecaiaeeoue aei
cia/iiai oneeaaeiaiiy iaoaiaoe/ieo iiaeaeae oa ?o oi?iae?ciaaiiai iieno.
Oea aeiaaa? ?ic?iaee iiaeo i?aeoiae?a aei aiae?oe/iiai ?ica’ycoaaiiy
oaeiai eeano caaea/ ? ?o /eneiaiai iiaeaethaaiiy ca aeiiiiiaith
ia/enethaaeueii? oaoi?ee. Oaeei aeine?aeaeaiiyi i?enay/ai? iaoeia?
i?aoe? A.I. Aa?aia, Ae.A. A?ee?oeueeiai, A.I. Eeceie, TH.I. Eieyii, N.A.
Eaoi?oeueeiai, O.E. Ia?oeiiae/a, A.I. Naa?ia, A.N. Na?e?nyia, A.I.
Nynueeiai, Ashiba F., Noda N., Singh A. oa aaaaoueio ?i.

Iaoa ?iaioe iieyaa?

— o anoaiiaeaii? aieeao eiioaeoii? aca?iiae?? i?oaeiiai ?cio?iiiiai
oeee?iae?a c aei?noeith iaieiith ia eiai oa?iiiai?oaeaii-aeaoi?iiaaiee
noai;

— o aeaaaeaii? ni?aa?aeiioaiue aeey aecia/aiiy oa?iiiai?oaeaiiai noaio
aeaioa?iaeo i?oaeieo oeee?iae??a c a?aooaaiiyi oaieiooai?aiiy ia iaae?
?icae?eo;

— o ?ic?iaoe? iaoaiaoe/iiai i?aeoiaeo aeey aecia/aiiy
oa?iiiai?oaeaii-aeaoi?iiaaiiai noaio o?ainaa?naeueii-?cio?iiieo
oeee?iae?e/ieo o?e;

— o anoaiiaeaii? aieeao o?ainaa?naeueii? ?cio?ii?? ia iai?oaeaiee noai a
oeee?iae?? i?e eiai iinooiaeueiiio ?on? a aei?noe?e iaiei?;

— o aecia/aii? aieeao oaiea ia ?iciiae?e eiioaeoieo iai?oaeaiue,
ia?ai?uaiue ? oaiia?aoo?ieo iie?a a i?oaei?e i?aieiuei?, ui aeieeathoue
i?e aca?iiae?? aei?noeiai iaoeeaiiai ooaiia ? i?aieiueie c a?aooaaiiyi
/anoeiaiai a?aenoaaaiiy i?aieiueie a?ae ooaiia.

Caaaeueia iaoiaeeea aeeiiaiiy aeine?aeaeaiue. Iiaoaeiaa ?ica’yce?a
e?aeiaeo caaea/ noaoe?iia?ii? oa?iii?oaeiino? aeey ?cio?iiieo ?
o?ainaa?naeueii-?cio?iiieo o?e a?oioo?oueny ia canoinoaaii? ?yae?a
Oo?’?, ?ioaa?aeueiiai ia?aoai?aiiy Oo?’?, iaoiae? caaaeaieo iaa’ycie.

Iaoeiaa iiaecia. Iniiai? ?acoeueoaoe ?iaioe noinothoueny caaea/ i?i
eiioaeo aeaioa?iaeo oeee?iae??a oa ooaiia ? i?ai?inoi?o i?e ?o aca?iiiio
iaa??aaii? a?ae oa?oy. Iaoeiaa iiaecia i?noeoueny a iinoaiiaeao caaea/,
a iaoiaeao ?ica’ycoaaiiy, a io?eiaieo ?acoeueoaoao. O ?iaio?:

— iaea?aeaii ?ica’ycie noaoe/ii? inaneiao?e/ii? caaea/? oa?iii?oaeiino?
aeey ?cio?iiiiai oeee?iae?a, yeee iinooiaeueii ?ooa?oueny a aei?noe?e
iaiei?;

— cai?iiiiiaaii iaoaiaoe/iee i?aeo?ae aeey aecia/aiiy oa?iiiai?oaeaiiai
noaio o?ainaa?naeueii-?cio?iiieo o?e i?e canoinoaaii? ?iceeaaeo ooeaieo
?ica’yce?a aeo?aeieo ??aiyiue a ?yaee Oo?’? ii inueia?e eii?aeeiao?;

— canoiniaaii ?ic?iaeaiee i?aeo?ae aei ?ica’ycaiiy inaneiao?e/ii?
caaea/? oa?iii?oaeiino? aeey o?ainaa?naeueii-?cio?iiiiai oeee?iae?a,
yeee iinooiaeueii ?ooa?oueny a aei?noe?e iaiei?;

— io?eiaii ?ica’ycee inaneiao?e/ii? caaea/? aeey aecia/aiiy
oa?iiiai?oaeaiiai noaio aeaioa?iaeo i?oaeieo oeee?iae??a o aeiaaeeo
oaieiooai?aiiy a?ae oa?oy ia iaae? ?icae?eo;

— ciaeaeaii a?aeaeaeaiiy (caeeaeaiiy) iaoeeaiiai iaa??oiai ooaiia a?ae
i?oaeiiai i?ai?inoi?o oa aeine?aeaeaii eiai aieea ia neeia? ?
oaiia?aoo?i? iiey.

I?aeoe/ia oe?ii?noue. Io?eiai? a aeena?oaoe?ei?e ?iaio? ?acoeueoaoe
iiaeooue ciaeoe canoinoaaiiy i?e ?ic?aooieo ?ooiieo c’?aeiaiue a iaoeiao
? iaoai?ciao i?e ao?iaeo ?iaioao, i?ioyaoaaii? oiui. Iiaeaia a ?iaio?
iaoaiaoe/ia iiaeaeue aea? iiaeeea?noue iienaoe ? iiynieoe oa?iii?oaeio
iiaaae?ieo o?ainaa?naeueii-?cio?iiiiai oeee?iae?a, yeee iinooiaeueii
?ooa?oueny a aei?noe?e iaiei?. Aeeoa?aioe?aeueia ??aiyiiy aeey
aecia/aiiy ocaaaeueiaii? ooieoe?? iai?oaeaiue iiaeia canoinoaaoe aeey
?ica’ycoaaiiy caaea/ oa?iii?oaeiino? aeey o?aiaa?naeueii-?cio?iiieo o?e.

A??ia?aei?noue iaea?aeaieo ?acoeueoao?a caaacia/o?oueny no?ia?noth
iinoaiiaie caaea/ ? ei?aeoi?noth aeei?enoaiiy iaoaiaoe/ieo iaoiae?a ?o
?ica’ycoaaiiy, ciaoiaeaeaiiyi oi/ieo aiae?oe/ieo ?ica’yce?a iniiaieo
aeo?aeieo aeeoa?aioe?aeueieo ??aiyiue, ca?aii ie?aieo ?acoeueoao?a
aeena?oaoe?? c a?aeiieie a e?oa?aoo??.

Iniaenoee aianie caeiaoaa/a. Aaoi?ii ?iaioe i?iaaaeai? aeine?aeaeaiiy c
eiioaeoii? aca?iiae?? i?oaeieo o?e c oaieiooai?aiiyi a?ae oa?oy,
c?iaeai? ocaaaeueiaiiy io?eiaieo ?acoeueoao?a, iaea?aeai? ?ic?aooieia?
caeaaeiino?, ye? i?iaiicothoue iiaaae?ieo o?e i?e eiioaeo?.

?ica’ycaii caaea/? oa?iii?oaeiino? i?i eiioaeoio aca?iiae?th ?cio?iiieo
oeee?iae??a, aei?noeiai ooaiia oa i?oaeiiai i?ai?inoi?o c a?aooaaiiyi
oaieiooai?aiiy a?ae oa?oy, iinoaiiaea yeeo cae?eniaia e.o.-i.i
aeine?aeaeaia eiioaeoia caaea/a aeey
o?ainaa?naeueii-?cio?iiieo oeee?iae?e/ieo o?e i?ae ea??aieoeoaii ae.o.i.
A?ee?oeueeiai Ae.A.

Ai?iaaoe?y ?iaioe. Ie?ai? ?acoeueoaoe aeine?aeaeaiue c oaie
aeena?oaoe?eii? ?iaioe aeiiia?aeaeeny ia IV I?aeia?iaei?e eiioa?aioe?? c
iaoai?ee iaiaeii??aeieo no?oeoo? ( Oa?iii?eue, 1995?.), ia
Anaoe?a?inuee?e iaoeia?e eiioa?aioe?? «?ic?iaea oa canoinoaaiiy
iaoaiaoe/ieo iaoiae?a a iaoeiai-oaoi?/ieo aeine?aeaeaiiyo» ( Euea?a,
1995?.), ia ??? I?aeia?iaeiiio neiiic?oi? «Iaeeane/i? i?iaeaie oai???
oiieino?iieo aeaiaio?a eiino?oeoe?e oa o?ceei-o?i?/ii? iaoai?ee
eiiiiceoe?eieo iaoa??ae?a» ( ?aaii-O?aie?anuee, 1995 ?.), ia ??
I?aeia?iaeiiio neiiic?oi? «Iaoai?ea ? o?ceea ?oeioaaiiy aoae?aaeueieo
iaoa??ae?a oa eiino?oeoe?e» (Euea?a-Aeoaeyie, 1996?.), ia 3-io
I?aeia?iaeiiio neiiic?oi? oe?a?inueeeo ?iaeaia??a-iaoai?e?a o Eueaia?
(Euea?a, 1997?.).

Caaaeii aeena?oaoe?eia ?iaioa iaaiai?thaaeany ia iaoeiaiio nai?ia??
eaoaae?e iaoai?ee Euea?anueeiai aea?aeoi?aa?neoaoo ?i. ?. O?aiea, ia
?icoe?aiiio iaoeiaiio nai?ia?? ?IIII ?i. ss.N. I?aeno?eaa/a IAI Oe?a?ie.

Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?eii? ?iaioe iioae?eiaaii
aeaaiaaeoeyoue iaoeiaeo i?aoeue.

No?oeoo?a ? ianya ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny c anooio,
/ioe?ueio ?icae?e?a, aeniiae?a oa nieneo aeei?enoaieo aeaea?ae (131
iaeiaioaaiue) ? i?noeoue 139 noi??iie oa 22 ?enoiee.

CI?NO ?IAIOE

O anooi? iaa?oioiaaii aaaeeea?noue oa aeooaeuei?noue ieoaiue, ?icaeyaeo
yeeo i?enay/aia aeena?oaoe?y, aeacaia iaoa ?iaioe ? noi?ioeueiaaii
iniiai? iieiaeaiiy, ui aeiinyoueny ia caoeno. Iaaaaeaii iaeyae iaoeiaeo
i?aoeue c eiioaeoieo caaea/ c a?aooaaiiyi oaieiooai?aiiy ?
o?ainaa?naeueii? ?cio?ii?? iaoa??ae?a.

A ia?oiio ?icae?e? iaaaaeaii aeo?aei? ??aiyiiy oa iniiai?
ni?aa?aeiioaiiy, iaiao?aei? aeey iinoaiiaee ? ?ica’ycoaaiiy
inaneiao?e/ieo eiioaeoieo caaea/ oa?iii?oaeiino? aeey ?cio?iiiiai e
o?ainaa?naeueii-?cio?iiiiai o?e oa oi?ioee ?iceeaaeo ooieoe?e a ?yaee
Oo?’?.

Aeeoa?aioe?aeuei? ??aiyiiy inaneiao?e/ii? oa?iii?oaeiino? aeey
?cio?iiiiai o?ea iathoue aeaeyae

, (1)

— ?aae?aeueia ? inueiaa ia?ai?uaiiy, ( — iia?aoi? Eaieana,

( — eiao?oe??io e?i?eiiai oaieiaiai ?icoe?aiiy, ( — eiao?oe??io
Ioanniia.

?ica’ycie iaeii??aeii? nenoaie (1) ooea?oueny aaaaeaiiyi ooieoe?? Eyaa
L(r,z), yea caaeiaieueiy? ??aiyiiy

. (2)

, yeee caaeiaieueiy? ??aiyiiy

EMBED

. (3)

Aeeoa?aioe?aeuei? ??aiyiiy inaneiao?e/ii? oa?iii?oaeiino? aeey
o?ainaa?naeueii-?cio?iiiiai o?ea iathoue aeaeyae

,

. (4)

— iiaeoe? i?oaeiino?.

Aeey ciaoiaeaeaiiy ?ica’yceo iaeii??aeii? nenoaie (4) aaiaeyoueny
ooieoe?? (1(r,z), (2(r,z) ca aeiiiiiaith ni?aa?aeiioaiue:

, (5)

caaeiaieueiythoue ??aiyiiy

(6)

?ica’ycie iaiaeii??aeii? nenoaie (4) ooea?ii oeyoii aaaaeaiiy ooieoe??
((r,z), yea ? ocaaaeueiaiiyi ooieoe?? iai?oaeaiue aeey ?cio?iiiiai
o?ea,

, (7)

aea

, (8)

(9)

— eiao?oe??ioe oaieii?ia?aeiino? o?ainaa?naeueii-?cio?iiiiai o?ea
a?aeiia?aeii a ?aae?aeueiiio oa inueiaiio iai?yiao.

??aiyiiy noaoe?iia?ii? oaieii?ia?aeiino? aeey
o?ainaa?naeueii-?cio?iiiiai na?aaeiaeua ia? aeaeyae

. (10)

. Oeee?iae?e ia?aaoaathoue i?ae ae??th inaneiao?e/iiai noaoe?iia?iiai
oaiia?aoo?iiai iiey iaaeieeoiueiai na?aaeiaeua. Oaieiaee eiioaeo i?ae
o?eaie ia?aeaaeueiee. E??i oiai, a ?acoeueoao? ae?e nee oa?oy ia
iiaa?oi? eiioaeoo aeaio oeee?iae??a ooai?th?ouenyny oaiei, ui
iioe?th?oueny a eiaeia ?c ni?aaeioe/ieo o?e.

Oaieia? e iaoai?/i? e?aeia? oa eiioaeoi? oiiae iathoue aeaeyae

:

, (11)

:

, (12)

, (13)

:

, (14)

— oaiia?aoo?a iaaeieeoiueiai na?aaeiaeua, yea ? ooieoe??th eii?aeeiaoe
z ? iiaea?oueny o aeaeyae? ?yaeo Oo?’? ia naaiaio? [-l,l].

Aeey iiaoaeiae ?ica’yce?a aeo?aeieo ??aiyiue aeei?enoiao?oueny ?iceeaae
ooeaieo aaee/ei a ?yae Oo?’? ca inueiaith eii?aeeiaoith ia naaiaio?
[-l,l]. ?ica’ycie noaoe?iia?iiai ??aiyiiy oaieii?ia?aeiino? aeey
?cio?iiiiai o?ea ia? aeaeyae

(15)

— iaa?aeii? eiao?oe??ioe, ye? aecia/athoueny c e?aeiaeo oiia.

, ui na?ae/eoue i?i ?nioaaiiy ciie a?aenoaaaiiy i?oaeiiai oeee?iae?a
a?ae aei?noei? iaieie a iaeano? eiioaeoo.

Uia aecia/eoe ?ici?? ciie a?aenoaaaiiy, iaiao?aeii aeiaeaoe aei
?ica’yceo caaea/? c e?aeiaeie oiiaaie (11)-(14) ?ica’ycie caaea/? c
oaeeie e?aeiaeie oiiaaie

:

(16)

:

(17)

(18)

(19)

(20)

(21)

:

, (22)

aea [-l1, l1] — aaee/eia ciie a?aenoaaaiiy.

? iiaoi?th?ii ?ica’ycoaaiiy caaea/? c e?aeiaeie oiiaaie (16)-(22).
I?ioean i?iaeiaaeo?oueny aeioe , iiee eiioaeoi? iai?oaeaiiy ia aoaeooue
anthaee a?ae’?iieie.

, aea N aeinoaoiuei aaeeea /enei, SN — noia iaaiiai /enea aeiaeaie?a
a?aeiia?aeiiai ?yaeo. Aeey /eneiaeo ?ic?aooie?a a?aeiny N=27. A?aeiinia
iioeaea ia ia?aaeuoaaea i’yoe a?aenioe?a.

(E)). I?e ca?eueoaii? oaeaeeino? ?ooo aioo??oiueiai oeee?iae?a
eiioaeoi? ?aae?aeuei? iai?oaeaiiy ciaioothoueny. Ia ?en. 2 e?eaa 4
io?eiaia i?e V=0.01 i/n, a e?eaa 1 i?e V=0.02 i/n.

A o?aoueiio ?icae?e? ?icaeyiooi inaneiao?e/i? caaea/? oa?iii?oaeiino?
aeey oeee?iae?e/ieo o?e. A ia?oiio i?ae?icae?e? aecia/athoueny
oaiia?aoo?i? iiey, iai?oaeaiiy ? aeaoi?iaoe?? i?oaeieo oeee?iae??a i?e
?o a?aeiiniiio iinooiaeueiiio ?on?. Oeee?iae?e ia?aaoaathoue i?ae ae??th
ciai?oiueiai inaneiao?e/iiai noaoe?iia?iiai oaiia?aoo?iiai iiey. E??i
oiai, a ?acoeueoao? ae?? nee oa?oy ia iiaa?oi? eiioaeoo ooai?th?oueny
oaiei, ui iioe?th?oueny a eiaeia ?c ni?aaeioe/ieo o?e. Aiane?aeie
?ica’ycoaaiiy a?aeiia?aeii? e?aeiai? caaea/? io?eiaii ni?aa?aeiioaiiy,
ye? aeathoue iiaeeea?noue ia/enethaaoe an? iaiao?aei? aaee/eie
oa?iii?oaeiiai noaio oeee?iae??a. sse /anoeiaee aeiaaeie ?icaeyiooi
caaea/o, eiee a?aenooi? oaieiooai?aiiy ia iiaa?oi? eiioaeoo. Aecia/ai?
oaiia?aoo?i? iiey ? oaieiai iioiee, iai?oaeaiiy ? aeaoi?iaoe??
aeaioa?iaeo i?oaeieo oeee?iae??a.

I?ney iiaeaiiy ?ica’yce?a aeo?aeieo ??aiyiue o aeaeyae? ?yae?a Oo?’?,
caaea/o caaaeaii aei ?ica’ycoaaiiy nenoaie e?i?eieo aeaaa?a?/ieo
??aiyiue aeey ciaoiaeaeaiiy iaa?aeiieo eiao?oe??io?a.

Aeaye? ?acoeueoaoe ?ic?aooie?a i?e cia/aiiyo oaiia?aoo? a?aeiia?aeii
aioo??oiueiai ? ciai?oiueiai iaaeieeoi?o na?aaeiaeu

,

=2 i-1 (e?ea? 2).

Aeae? aeine?aeaeo?oueny oa?iiiai?oaeaiee noai
o?ainaa?naeueii-?cio?iiiiai oeee?iae?a, aeeaaeaiiai a aei?noeo iaieio
i?e o?eeoe?eiiio iaa??aaii?. I?oaeiee oeee?iae? a iaiei? ?ooa?oueny
??aiii??ii c oaeaee?noth V. Oeee?iae?e ia?aaoaathoue i?ae ae??th
inaneiao?e/iiai noaoe?iia?iiai oaiia?aoo?iiai iiey. Aecia/a?oueny
oa?iiiai?oaeaiee noai aioo??oiueiai oeee?iae?a, coiiaeaiiai
noaoe?iia?iei inaneiao?e/iei oaiia?aoo?iei iieai ? aca?iiae??th c
iaieiith. E?aeia? oiiae iathoue aeaeyae (11)-(14).

?ica’ycie ??aiyiiy oaieii?ia?aeiino? (10) ooea?ii o aeaeyae? ?yaeo Oo?’?

(23)

.

io?eio?ii ae?ac

.

. I?e m=0 ?ica’ycie ??aiyiiy (8) iiaea?ii o aeaeyae?

. (24)

Iiooe /anoeiiiai ?ica’yceo iaiaeii??aeii? nenoaie ??aiyiue (4)
caiaeeoueny aei io?eiaiiy /anoeiiiai ?ica’yceo ??aiyiiy (8), yeee
iiaeaii o aeaeyae?:

. (25)

(?=1,2) cae/aei? aeeoa?aioe?aeuei? ??aiyiiy /aoaa?oiai ii?yaeeo,
/anoeiiee ?ica’ycie yeeo ooea?ii iaoiaeii aa??aoe?? noaeeo ? caieoaii o
aeaeyae?

(26)

, ui na?ae/eoue i?i ?nioaaiiy ciie a?aenoaaaiiy i?oaeiiai oeee?iae?a
a?ae aei?noei? iaieie a iaeano? eiioaeoo. Uia aecia/eoe ?ici?? ciie
a?aenoaaaiiy, iaiao?aeii aeiaeaoe aei ?ica’yceo caaea/? c e?aeiaeie
oiiaaie (11)-(14) ?ica’ycie caaea/? c e?aeiaeie oiiaaie (16)-(22), ye
oea c?iaeaii a ae?oaiio ?icae?e?.

=2 i-1- ia a?ae??ceo [-3.42 i; 3.42 i]. Eiao?oe??io oa?i?/ii?
i?ia?aeiino? eiioaeoo h oaeiae aieeaa? ia aaee/eio ae?eyiee
a?aenoaaaiiy. I?e ca?eueoaii? h ?ici?? ciie a?aenoaaaiiy ca?eueoo?oueny.
I?e ca?eueoaii? iiaeoey cnoao G’ aeey ieiueie, ia?iaiaeeeoey?ii? aei
ieiueie ?cio?ii??, ae?eyiea a?ae?eao i?oaeiiai oeee?iae?a a?ae aei?noei?
iaieie ca?eueoo?oueny. I?e ca?eueoaii? E( (iiaeoeue THiaa aeey ?icoyao ?
noeneo a iai?yi?, ia?iaiaeeeoey?iiio aei ieiueie ?cio?ii??)
niinoa??aaeiny ca?eueoaiiy eiioaeoieo ?aae?aeueieo iai?oaeaiue ?
ae?eyiee a?aenoaaaiiy i?oaeiiai oeee?iae?a a?ae iaieie.

ssaeua a?aenoaaaiiy ooaiia a?ae ?cio?iiii? i?aieiueie ?icaeyiooi a
/aoaa?oiio ?icae?e?. Iinoaaeaia ? ?ica’ycaia caaea/a i?i ?oo iaa??oiai
iaoeeaiiai aei?noeiai ooaiia ii i?oaeiiio i?ai?inoi?o i?e ia?aeaaeueiiio
oaieiaiio eiioaeo?.

?icaeyaea?oueny aei?noeee ooaii aenioe H, yeee aoenea?oueny neeith ? a
i?oaeio i?aieiueio ? ?ooa?oueny c? noaeith oaeaee?noth V (?en. 8).
I?aieiueia ia?aaoaa? a oiiaao ieinei? aeaoi?iaoe??. Oaieiaee eiioaeo
i?ae ooaiiii ? i?aieiueiith ia?aeaaeueiee c eiao?oe??ioii
oaieii?iieeeeaino? eiioaeoo h. A?ae ae?? nee oa?oy ia ae?eyioe? eiioaeoo
a?aeaoaa?oueny oaieiooai?aiiy, i?iii?oe?eia ieoii?e ?iaio? nee oa?oy.
Iaiao?aeii aecia/eoe oaiia?aoo?i? iiey, oaieia? iioiee a eiioaeooth/eo
o?eao, a oaeiae iai?oaeaiiy ? ia?ai?uaiiy a i?oaei?e iniia?.

Aeey iiaoaeiae ?ica’yceo caaea/? iaiao?aeii i?i?ioaa?oaaoe ??aiyiiy
oa?iii?oaeiino? aeey i?aieiueie

, (27)

, (32)

i?e oaeeo oaiia?aoo?ieo e?aeiaeo oiiaao:

y=-H

, (33)

a

; (34)

y=0

,

,

, (35)

oa neeiaeo e?aeiaeo oiiaao i?e y=0:

,

, (36)

— oaiia?aoo?a iaaeieeoiueiai na?aaeiaeua.

Aeei?enoiaoth/e ne?i/aii-??cieoeaao ai?ieneiaoe?th ??aiyiiy
oaieii?ia?aeiino? aeey ooaiia ? e?aeiaeo oiia (33), (34) ii eii?aeeiao?
x , ?ica’ycie caaea/? aeey ooaiia aoaeo?ii iaoiaeii i?yieo, a
?acoeueoao? /iai io?eio?ii nenoaio e?i?eieo aeeoa?aioe?aeueieo ??aiyiue
ia?oiai ii?yaeeo, ?ica’ycie yei? aoaeo?ii ca aeiiiiiaith iao?e/ii?
aeniiiaioe.

*anoeiiee ?ica’ycie ??aiyiue (31) oa (32) aeey i?aieiueie ooea?ii o
aeaeyae?:

. (37)

aea

. (38)

I?ney canoinoaaiiy ?ioaa?aeueiiai ia?aoai?aiiy Oo?’? ii eii?aeeiao? x, a
i?inoi?? o?ainoi?iaio ?ica’ycie ??aiyiiy oaieii?ia?aeiino? aeey
i?ai?inoi?o y(0 ia? aeaeyae

.

?ica’ycie iaeii??aeii? nenoaie ??aiyiue (31), (32) ooea?oueny o
aeaeyae?:

, (39)

aea ooieoe?y f ia? aeaeyae:

. (40)

I?ney caaeiaieaiiy e?aeiaeo oiia, caaea/a caaaeaoueny aei ?ica’ycoaaiiy
ia?ieo ?ioaa?aeueieo ??aiyiue, aeey ?ica’ycoaaiiy yeeo aeei?enoaii
?iceeaae iaa?aeiieo ooieoe?e a ?yaee Oo?’?

. (41)

.

*eneia? ?ic?aooiee aoee i?iaaaeai? aeey aeiaaeeo, eiee iaoa??ae ooaiio ?
noaeue, a i?ai?inoi?o — aethi?i?e, i?e oaeeo ia?aiao?ao:

iiaa?oi? eiioaeooth/eo o?e aaaaeathoueny a?eueieie a?ae ciai?oi?o
iaaaioaaeaiue, ? iaiao?aeii caaeiaieueieoe oae? e?aeia? oiiae:

(42)

ia ia?anoaiooue ci?ithaaoe ciae.

O aeniiaeao iaaaaeaii iniiai? ?acoeueoaoe c aeena?oaoe?eii? ?iaioe.

INIIAI? ?ACOEUeOAOE ? AENIIAEE

Iinoaaeaia ? ?ica’ycaia inaneiao?e/ia eiioaeoia caaea/a oa?iii?oaeiino?
aeey aeiaaiai ?cio?iiiiai e?oaiaiai oeee?iae?a, yeee iinooiaeueii
?ooa?oueny a aeiaa?e aei?noe?e oeee?iae?e/i?e iaiei? c a?aooaaiiyi
oaieiooai?aiiy a?ae ae?? nee oa?oy ia ae?eyioe? eiioaeoo. A oiae?
iiaoaeiae ?ica’yce?a aoei io?eiaii ae?eyieo a?aenoaaaiiy i?oaeiiai
oeee?iae?a a?ae aei?noei? iaieie. Oea i?ecaaei aei iaiao?aeiino?
?ica’ycoaaoe caaea/o i?e iiaeo e?aeiaeo oiiaao ia ci?iai?e ae?eyioe?
eiioaeoo. Anoaiiaeaii, ui i?e ca?eueoaii? eiao?oe??ioa oaieiiai?io
aei?noeiai oeee?iae?a c iaaeieeoi?i na?aaeiaeuai ca?eueoo?oueny ae?eyiea
a?aenoaaaiiy. I?e ca?eueoaii? eiao?oe??ioa oa?i?/ii? i?ia?aeiino?
eiioaeoo ?ici?? ciie eiioaeoo ciaioo?oueny. sseui oiaueio i?oaeiiai
oeee?iae?a ca?eueoeoe, oi ae?eyiea a?aenoaaaiiy ciaioo?oueny.

?ic?iaeaii iaoaiaoe/iee i?aeo?ae aeey aecia/aiiy
oa?iiiai?oaeaii-aeaoi?iiaaiiai noaio aeey o?ainaa?naeueii-?cio?iiieo
o?e. Aeey iiaoaeiae ?ica’yceo aeo?aeieo ??aiyiue canoiniaoaaany ?iceeaae
ooeaieo aaee/ei a ?yaee Oo?’?. *anoeiiee ?ica’ycie iaiaeii??aeieo
??aiyiue ooeaany iaoiaeii aa??aoe?? noaeeo.

Ia iniia? ?ic?iaeaiiai iaoaiaoe/iiai i?aeoiaeo ?ica’ycaia caaea/a i?i
oa?iii?oaeiee noai i?e iinooiaeueiiio ?on? aeiaaiai
o?ainaa?naeueii-?cio?iiiiai oeee?iae?a a aeiaa?e aei?noe?e iaiei? c
a?aooaaiiyi oaieiooai?aiiy a?ae ae?? nee oa?oy ia ae?eyioe? eiioaeoo.
sse ? aeey ?cio?iiiiai aeiaaeeo ia? i?noea ae?eyiea a?aenoaaaiiy, ui
i?ecaiaeeoue aei iaiao?aeiino? ?ica’ycoaaiiy eiioaeoii? caaea/? ?c
ci?iaieie e?aeiaeie oiiaaie. Anoaiiaeaii, ui oaieiooai?aiiy nooo?ai
aieeaa? ia oa?aeoa?enoeee eiioaeoii? caaea/?: oaiia?aoo?a ? oaieia?
iioiee a eiioaeooth/eo o?eao c?inoathoue. Iieacaii aieea ai?cio?ii?? ia
oa?iiiai?oaeaiee noai oeee?iae?a. I?e c?inoaii? iiaeoey cnoao G’ ?
iiaeoey THiaa E( ca?eueoothoueny eiioaeoi? ?aae?aeuei? iai?oaeaiiy oa
ae?eyiea a?ae?eao i?oaeiiai oeee?iae?a a?ae aei?noei? iaieie. I?e
ciaioaii? eiao?oe??ioa Ioanciia (( c?inoathoue inueia? ia?ai?uaiiy.

C aeei?enoaiiyi iaoiaeo caaaeaieo iaa’ycie ?ica’ycaii ieineo eiioaeoio
caaea/o oa?iii?oaeiino? iaoeeaiiai ooaiia, ui ?ooa?oueny ii i?oaei?e
i?aieiuei? c a?aooaaiiyi oaieiooai?aiiy a?ae oa?oy ia ae?eyioe?
eiioaeoo. A oiae? iiaoaeiae ?ica’yce?a aoei io?eiaii ae?eyiee
a?aenoaaaiiy ooaiia a?ae iniiae. Oea i?ecaaei aei iaiao?aeiino?
?ica’ycoaaoe caaea/o i?e iiaeo e?aeiaeo oiiaao ia ci?iai?e ae?eyioe?
eiioaeoo. Iieacaii, ui ?c c?inoaiiyi eiao?oe??ioa oaieiiai?io aa?oiueiai
oi?oey ooaiia c iaaeieeoi?i na?aaeiaeuai ciia eiioaeoo ciaioo?oueny. I?e
c?inoaii? eiao?oe??ioa oa?i?/ii? i?ia?aeiino? eiioaeoo ae?eyiea eiioaeoo
ciaioo?oueny. Aa?oeeaeuei? ia?ai?uaiiy e?ath i?aieiueie c?inoathoue a
iai?yieo, i?ioeeaaeiiio aei ae?? neee.

IOAE?EAOe??

A?ee?oeueeee Ae.A., TH?eiaoeue ?.A. Oa?iiiai?oaeaiee noai
o?ainaa?naeueii-?cio?iiiiai oeee?iae?a, aeeaaeaiiai a aei?noeo iaieio
i?e o?eeoe?eiiio iaa??aaii?.-Euea?a, 1997.-33 n. (I?ai?./ Euea?a.
aea?ae. oi-o ?i. ?. O?aiea).

Eaaeoeueeee A.I., TH?eiaoeue ?.A. Oa?iiiai?oaeaiee noai aeaioa?iaeo
oeee?iae??a o aeiaaeeo o?eeoe?eiiai oaieiooai?aiiy ia iaae? ?icae?eo//
Aeiiia?ae? IAI Oe?a?ie. -1997. -? 4. -N. 54-60.

Eaaeoeueeee A.I., TH?eiaoeue ?.A. Oieonoaaiiy a ocaaaeueiai?e ? ?ooii?e
oa?iii?oaeiino?// A?niee Euea?anueeiai oi?aa?neoaoo, na?.
iao.-iao.-1994. — aei. 40. — N. 67-72.

Eaaeoeueeee A.I., TH?eiaoeue ?.A. O?eeoe?eia aca?iiae?y inaneiao?e/ii?
ia?e aeeaaeaieo o?oa c oaieiooai?aiiyi// Iaoa??aee ?? i?aeia?iaeii?
neii. c iaoai?ee ? o?ceee ?oeioaaiiy aoae?aaeueieo iaoa??ae?a oa
eiino?oeoe?e. Euea?a-Aeoaeyie. — 1996. — N. 331-334.

Eaaeoeueeee A.I., TH?eiaoeue ?.A. Iaoaiaoe/ia iiaeaethaaiiy ?ooiieo
oeee?iae??a c oaieiooai?aiiyi// Oace 1-i? i?aeia?iaeii? iaoeiai-oaoi?/ia
eiio. c iaoaiao. iiaeae. a aeaeo?ioaoi?oe? e aeaeo?iaia?aaoeoe?. Euea?a.
-1995. — N. 84-85.

Eaaeoeueeee A.I., Iiainaae A.I., TH?eiaoeue ?.A. Aeaye? inaneiao?e/i?
caaea/? c o?aooaaiiyi oaieiooai?aiiy a?ae oa?oy// Anaoe?a?inueea iaoeiaa
eiio. c ?ic?iaee oa canoinoaaiiy iaoaiao. iaoiae?a a iaoeiai-oaoi?/ieo
aeine?aeaeaiiyo. Euea?a. — 1995. — N. 48-49.

Eaaeoeueeee A.I., Iiainaae A.I., Iieoeaae/ A.I., TH?eiaoeue ?.A.
Eiioaeoi? caaea/? c o?aooaaiiyi o?eeoe?eiiai ?ic?a??ao// Iaoa??aee
aeiiia?aeae ??? i?aeia?iaeiiai neiiic?oio c iaeeane/ieo i?iaeai oai???
oiieino?iieo aeaiaio?a eiino?oeoe?e oa o?ceei-o?i?/ii? iaoai?ee
eiiiiceoe?eieo iaoa??ae?a. ?aaii-O?aie?anuee. — 1995. — N. 111-114.

Eaaeoeueeee A.I., TH?eiaoeue ?.A. Iai?oaeaii-aeaoi?iiaaiee noai
oeee?iae?e/ieo aeaiaio?a i?e o?eeoe?eiiio ?ic?a??a?// Oace aeiiia?aeae
3-ai i?aeia?iaeiiai neiiic?oio oe?a?inueeeo ?iaeaia??a-iaoai?e?a o
Eueaia?. Euea?a. — 1997. — N. 222-223.

TH?eiaoeue ?.A. Ia?a o?oa i?e iinooiaeueiiio ?on? c oaieiooai?aiiyi
a?ae oa?oy// Oace aeiiia?aeae ?V i?aeia?iaeii? eiio. c iaoai?ee
iaiaeii??aeieo no?oeoo?. Oa?iii?eue. — 1995. — N. 71.

TH?eiaoe ?.A. ?an/ao oaeiauo e iaoaie/aneeo iieae eioaa?aeueiuo noai//
IOO «Ee?a. iie?oaoi. ?ino-oo», iao/i.-oaoi. na. «Yeaeo?. e naycue».
Ee?a. — 1998. — aei. 4, /. 2. — N. 399-404.

TH?eiaoeue ?.A. Aieea o?ainaa?naeueii? ?cio?ii?? ia
iai?oaeaii-aeaoi?i?aiee noai oeee?iae?a// A?niee Euea?a. oi-oo, na?.
o?ce/ia. — 1998.- aei. 31. N. 87-88.

TH?eiaoeue ?.A. Eiioaeoia aca?iiae?y ieineiai iaoeeaiiai oa?o ?
i?aieiueie c oa?oueiaei ?ic?a??aaiiyi// Oaoi?/i? a?no?. Euea?a —
1998/1(6), 2(7). N. 70-71.

TH?eiaoeue ?.A. Eiioaeoia aca?iiae?y i?oaeieo o?e c oaieiooai?aiiyi
a?ae oa?oy.- ?oeiien.

Aeena?oaoe?y ia caeiaoooy a/aiiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.02.04 — iaoai?ea
aeaoi?i?aiiai oaa?aeiai o?ea.- ?inoeooo i?eeeaaeieo i?iaeai iaoai?ee ?
iaoaiaoeee ?i. ss.N. I?aeno?eaa/a IAI Oe?a?ie, Euea?a, 1998.

Aeena?oaoe?th i?enay/aii aeine?aeaeaiith eiioaeoii? aca?iiae?? i?oaeieo
o?e c a?aooaaiiyi oaieiooai?aiiy a?ae oa?oy aeey aeeaaeaieo oeee?iae??a,
ooaiia oa i?ai?inoi?o. ?ic?iaeaii iaoaiaoe/iee i?aeo?ae aei
?ica’ycoaaiiy inaneiao?e/ieo e?aeiaeo caaea/ oa?iii?oaeiino? aeey
o?ainaa?naeueii-?cio?iiieo o?e. Aeine?aeaeo?oueny aieea oaieiooai?aiiy
ia neeia? oa oaiia?aoo?i? iiey ? yaeua a?aenoaaaiiy eiioaeooth/eo o?e.

Eeth/ia? neiaa: oa?iii?oaei?noue, oaieiooai?aiiy, eiioaeoia aca?iiae?y,
o?ainaa?naeueii-?cio?iiiee oeee?iae?, inaneiao?e/ia aeaoi?iaoe?y.

TH?eiaoe ?.A. Eiioaeoiia acaeiiaeaenoaea oi?oaeo oae n
oaieiia?aciaaieai io o?aiey.- ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.02.04 — iaoaieea
aeaoi?ie?oaiiai oaa?aeiai oaea.- Einoeooo i?eeeaaeiuo i?iaeai iaoaieee e
iaoaiaoeee ei. ss.N. Iiaeno?eaa/a IAI Oe?aeiu, Eueaia, 1998.

Aeenna?oaoeey iinayuaia enneaaeiaaieth eiioaeoiiai acaeiiaeaenoaey
oi?oaeo oae n o/aoii oaieia?aciaaiey io o?aiey aeey aeiaeaiuo
oeeeeiae?ia, ooaiia e iieoi?ino?ainoaa. ?ac?aaioai iaoaiaoe/aneee
iiaeoiae e ?aoaieth inaneiiao?e/aneeo e?aaauo caaea/ oa?iioi?oainoe aeey
o?ainaa?naeueii-ecio?iiiuo oae. Enneaaeoaony aeeyiea oaieiia?aciaaiey ia
neeiaua e oaiia?aoo?iua iiey e yaeaiea ionoaaaiey eiioaeoe?othueo oae.

Eeth/aaua neiaa: oa?iioi?oainoue, oaieiia?aciaaiea, eiioaeoiia
acaeiiaeaenoaea, o?ainaa?naeueii-ecio?iiiue oeeeeiae?, inaneiiao?e/iay
aeaoi?iaoeey.

Yurynets R.V. Contact interaction of stressed bodies with a heat
generation on account of friction.- Manuscript.

Thesis on competition of a scientific degree of the candidate of
physico-mathematical sciences on a speciality 01.02.04 — mechanics of
deformable solid body.- Institute of Applied Problems of a Mechanics and
Mathematics by Y.S. Pidstryhach of National Academy of Science of
Ukraine, Lviv, 1998.

The thesis is devoted to an investigation of contact interaction of
stressed bodies, taking into consideration influence of heat, which is
organized owing to friction of contacting bodies, that is embedded
cylinders, punch and half-space. The mathematical approach for a
solution of the axisymmetrical problems of a thermoelasticity for
transversely isotropic bodies. The influence of a heat generation to
force and temperature fields and appearance of lag of contacting have
been investigated.

Key word: thermoelasticity, heat generation, contact interaction,
transversely isotropic cylinder, axisymmetrical strain.

I?aeienaii aei ae?oeo 11.11.1998?.

. Iai?? io. ? 1. Aa?i. e?o. io. ae?oe.

Oiia. ae?oe. e.-1. Oe?aae 100. Cai. 1011.

Aaceiooiaii.

Aeaeaaieoeoai EION 290058, Euea?a, aoe. ?00-??//y Eueaiaa, 4

Eaaeoeueeei A.I.;

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