Математичне моделювання механічних коливальних процесів в силових напівпровідникових приладах на основі методу скінченних елементів: Автореф. дис… к

Aea?aeaaiee oi?aa?neoao “Euea?anueea iie?oaoi?ea”

Ia i?aaao ?oeiieno

IAEA? AIEIAeEIE? IE?INEAAIAE*

OAeE 539.3:517.959

IAOAIAOE*IA IIAeAETHAAIIss IAOAI?*IEO EIEEAAEUeIEO I?IOeAN?A A NEEIAEO
IAI?AI?IA?AeIEEIAEO I?EEAAeAO IA INIIA? IAOIAeO NE?I*AIIEO AEAIAIO?A

Niaoe?aeuei?noue 01.05.02 — Iaoaiaoe/ia iiaeaethaaiiy oa

ia/enethaaeuei? iaoiaee

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Euea?a – 1999 Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia o Euea?anueeiio aea?aeaaiiio oi?aa?neoao? ?iai? ?aaia
O?aiea I?i?noa?noaa ina?oe Oe?a?ie

Iaoeiaee ea??aiee : eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

Aeeye ?aai ?aaiiae/,

Euea?anueeee aea?aeaaiee oi?aa?neoao ?iai? ?aaia O?aiea,

aeioeaio eaoaae?e i?eeeaaeii? iaoaiaoeee.

Io?oe?ei? iiiiaioe : aeieoi? oaoi?/ieo iaoe, i?ioani?

Noao?a Iao?i A?eai?iae/,

caa?aeoaa/ eaoaae?e oai?aoe/ii? oa caaaeueii? aeaeo?ioaoi?ee
Aea?aeaaiiai oi?aa?neoaoo “Euea?anueea iie?oaoi?ea”;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

coa?oee iaoeiaee ni?a?ia?oiee,

Aa?athe A?eoi? ?aaaiiae/,

caa. a?aeae?eii neioaco oa iioei?caoe?? ea?iaaieo nenoai ?inoeoooo
i?eeeaaeieo i?iaeai iaoai?ee ? iaoaiaoeee ?i. ss.N. I?aeno?eaa/a IAI
Oe?a?ie.

I?ia?aeia onoaiiaa : Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie
“Ee?anueeee iie?oaoi?/iee ?inoeooo”, oaeoeueoao ?ioi?iaoeee oa
ia/enethaaeueii? oaoi?ee (i. Ee?a).

Caoeno a?aeaoaeaoueny 20 aeiaoiy 1999 ?ieo i 16 aiae. 00 oa. ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.052.05 o Aea?aeaaiiio
oi?aa?neoao? “Euea?anueea iie?oaoi?ea” (290646, i.Euea?a,
aoe.N.Aaiaea?e, 12, aoae.226).

C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? Aea?aeaaiiai
oi?aa?neoaoo “Euea?anueea iie?oaoi?ea” (i.Euea?a, aoe.I?ioani?nueea,1).

Aaoi?aoa?ao ?ic?neaiee “18 ” aa?aniy 1999 ?.

A/aiee nae?aoa? niaoe?ae?ciaaii? a/aii? ?aaee,

eaiaeeaeao oaoi?/ieo iaoe, aeioeaio Oea/aiei N.I .

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Oaeaeeee ?icaeoie ia?aoai?thaaeueii? oaoi?ee oa ??
canoinoaaiiy iaeaea a on?o aaeocyo ia?iaeiiai ainiiaea?noaa aenoaathoue
iia?, niaoeeo?/i? aeiiae uiaei yeino? oa ianyao ?ioi?iaoe?? noiniaii
aeaeo?e/ieo, oaieiaeo oa iaoai?/ieo ia?aiao??a neeiaeo
iai?ai?ia?aeieeiaeo i?eeaae?a (NII). Iaae?ei?noue NII oa ia?aoai?thaa/?a
ia ?o iniia? cia/iith i??ith aecia/a?oueny iaoai?/ieie iai?oaeaiiyie o
iai?ai?ia?aeieeia?e no?oeoo??, coiiaeaieie oaiia?aoo?iei iieai o
i?eeaae? oa eiai ci?iith a /an?. I?iaeaia aecia/aiiy oaiia?aoo?iiai ?
oa?iii?oaeiiai iie?a, oa ?o aieeao ia i?oei?noue NII ia nueiaiaei?oi?e
aeaiue aeinoaoiuei aea/aia oa aena?oeaia o iaoeiai-oaoi?/i?e e?oa?aoo??.
O oie aea /an, ca?aeii c aeiiaaie ae?th/eo noaiaea?o?a oa oaoi?/ieo
aeac?aie, on? NII iiaeii? iaia’yceiai i?ioiaeeoe ia?aa??eo ia i?oei?noue
oa no?ee?noue a oiiaao ae?? iaoai?/ieo iaaaioaaeaiue aeey aecia/aiiy
iiaeeeaino? aenieoaoaoe?? ?o a oiiaao a?a?aoe?e, oaea?ieo iaaaioaaeaiue,
aenieeo oene?a ? o.ae. O oeueiio aeiaaeeia? ?aeeiei aeaea?aeii
?ioi?iaoe?? noiniaii iaoai?/ieo oa?aeoa?enoee ? aenia?eiaio. Oae, iaeaea
on? i?eeaaee i?ioiaeyoue aei?iaiaoaaiiy aeey aecia/aiiy ?aciiainieo
/anoio, ia oaea?io i?oei?noue oa a?a?ino?ee?noue. Aei?iaiaoaaiiy aeey
aecia/aiiy ?aciiainieo /anoio i?iaiaeyoueny c iaoith ciaoiaeaeaiiy
aeanieo /anoio NII aai eiai ie?aieo aeaiaio?a. Aei?iaiaoaaiiy ia oaea?io
i?oei?noue i?iaiaeyoueny aeey ia?aa??ee caeaoiino? NII i?ioenoiyoe
aeano?oeoeai?e ae?? oaea?ieo iaaaioaaeaiue ? caa??aaoe nai? iniiai?
ia?aiao?e i?ney ?o i?eieiaiiy aai iiaeeeaino? iaae?eii ooieoe?iioaaoe a
oiiaao aaaaoie?aoieo oaea??a. E??i oiai, i?e ioe?ioe? i?oeiino? NII
aaaeeeaa cia/aiiy ia? aeine?aeaeaiiy aieeao iaoai?/ieo iai?oaeaiue ia
aeaeo?e/i? aeanoeaino? iai?ai?ia?aeieeiaeo no?oeoo? NII, a?aeiiiai a
e?oa?aoo?? ye aeaoi?iaoe?eiee aoaeo. Ne?ae caoaaaeeoe, ui eiino?oeoe??
NII, na?aae yeeo iae?iciianthaeaeai?oeie ? e?aii??a? ae?iaee oa
oe?enoi?e, oa?aeoa?ecothoueny aaee/aciith ??ciiiai?oi?noth. I?iaaaeaiiy
aei?iaiaoaaiue ia iaoai?/io i?oei?noue oa no?ee?noue aeey eiaeiiai
iiaiai oeio NII ? o?oaeii?noeith oa aeiaaio?eaaeith iia?aoe??th, yea aei
oiai ae cia/ii ca?eueoo? oa?i?ie i?iaeooaaiiy. Aaaeaii aoei a oaea ia
aoai? i?iaeooaaiiy i?iaiaeeoe aiae?c ia o?eueee aeaeo?e/ieo oa oaieiaeo
ia?aiao??a, a e ia?aiao??a iai?oaeaiii-aeaoi?i?aiiai noaio (IAeN) a
aeaiaioao NII, cie?aia o iai?ai?ia?aeieeiaeo no?oeoo?ao NII, ye? ?
iaea?aceea?oeie a nain? i?oeiino?. Oiio aaaeeeaith e aeooaeueiith
i?iaeaiith aeine?aeaeaiue ? iiaoaeiaa aaeaeaaoieo ?ic?aooieiaeo
iiaeaeae, ye? aeicaieythoue c aenieith oi/i?noth aecia/aoe ia?aiao?e
IAeN o iai?ai?ia?aeieeiaeo no?oeoo?ao NII, a oaeiae aoaeoeaieo iaoiae?a
aeine?aeaeaiiy oeeo iiaeaeae. Aeei?enoaiiy iaoaiaoe/iiai iiaeaethaaiiy
?c canoinoaaiiyi no/anii? ia/enethaaeueii? oaoi?ee aeicaieeoue ciaioeoe
ianya aenia?eiaioaeueieo aeine?aeaeaiue i?ae /an ?ic?iaee iiaeo
i?eeaae?a, nei?ioeoe oa?i?ie i?iaeooaaiiy oa i?aeaeueoe ye?noue NII.
Ni?iuai? iaeiiaei??i? iaoaiaoe/i? iiaeae?, ye? aeei?enoiaoaaeeny
aaaaoueia aaoi?aie aeey aeine?aeaeaiiy oaiia?aoo?ieo caaea/, ia
a?aeia?aaeathoue ?aaeueii? iiaaae?iee NII i?ae ae??th iaoai?/ieo
iaaaioaaeaiue. Iiaiioe?iio ea?oeio ianoaoe?iia?ieo i?ioean?a i?oaeiiai
aeaoi?ioaaiiy aeaiaio?a NII iiaeia io?eiaoe ca oiiae aeai?o
ni?aa?aeiioaiue e?i?eii? i?inoi?iai? oai??? i?oaeiino? ai?cio?iiiiai
o?ea ye iaoaiaoe/ii? iiaeae?. A?aooaaiiy ?aaeueii? aaiiao???
aeine?aeaeoaaieo ia’?eo?a cia/ii iaiaaeo? aeei?enoaiiy o?aaeeoe?eieo
aiae?oe/ieo iaoiae?a iaoai?ee oaa?aeiai aeaoi?i?aiiai o?ea. Iaiao?aeia
aeei?enoaiiy no/anieo /enaeueieo iaoiae?a, oaeeo ye iaoiae ne?i/aiieo
aeaiaio?a, ?ic?aoiaaieo ia iiooaeio ia/enethaaeueio oaoi?eo. O oeueiio
aeiaaeeia? ia ia?oee ieai aenooiathoue ieoaiiy aoaeoeaiino? oa
aeiiiiiino? ia/enethaaeueiiai i?ioeano, ui aeiaaa? ?ic?iaee iiaeo
/enaeueieo noai, ye? a a?aoiaoaaee niaoeeo?eo iiaoaeiaaieo iaoaiaoe/ieo
iiaeaeae, eiino?oeoeaieo iniaeeainoae oa o?ceei-iaoai?/ieo oa?aeoa?enoee
aeaiaio?a NII. Aeine?aeaeaiith oa ?ica’ycaiith oeeo caaea/ i?enay/aia
aeaia aeena?oaoe?y.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, oaiaie, ieaiaie. ?iaioa aeeiiaia
a ?aieao ieai?a iaoeiaeo aeine?aeaeaiue oa aea?aeathaeaeaoii? oaiaoeee
eaoaae?e i?eeeaaeii? iaoaiaoeee Euea?anueeiai aea?aeaaiiai oi?aa?neoaoo
?iai? ?aaia O?aiea, a naia :

Ieaio ?ia?o ii oai? II-536A “?ic?iaea noai, aeai?eoi?a ? iaeao?a i?ia?ai
aeey ?ica’ycoaaiiy ii/aoeiai-e?aeiaeo caaea/ iaoaiaoe/ii? o?ceee ia
iniia? eiia?iiaaieo iaoiae?a a?aie/ieo ? ne?i/aiieo aeaiaio?a”, ?
aea?ae?a?no?aoe?? 0193V041998.

Ieaio ?ia?o ii oai? II-114A “Iaoaiaoe/ia iiaeaethaaiiy ? /enaeueia
aeine?aeaeaiiy o?ceei-iaoai?/ieo iie?a a na?aaeiaeuao c iaeeie
iaiaeii??aeiinoyie”, ? aea?ae?a?no?aoe??.07.02-IA/**-97.

E??i oiai, i?iaaaeaiiy aeine?aeaeaiue o ?aieao aeaii? aeena?oaoe?eii?
?iaioe aoee /anoeiai i?aeo?eiai? I?aeia?iaeiith Ni?in?anueeith
i?ia?aiith i?aeo?eiee iaoee ? ina?oe a aaeoc? oi/ieo iaoe, a?aio
?PSU061060 ca 1996 ??e.

Iaoith aeaii? ?iaioe ? ?ic?iaea oa i?ia?aiia ?aae?caoe?y aeai?eoi?a
iaoaiaoe/iiai iiaeaethaaiiy aeeiai?/ieo i?ioean?a i?oaeiiai
aeaoi?ioaaiiy iayieo neeiaeo iai?ai?ia?aeieeiaeo i?eeaae?a oeio
e?aii??aeo ae?iae?a oa oe?enoi??a ia iniia? iai?aaiae?oe/iiai iaoiaeo
ne?i/aiieo aeaiaio?a. Aeinyaiaiiy iinoaaeaii? iaoe aeiaaa? ?ica’ycaiiy
ianooiieo iniiaieo caaea/ :

?ic?iaea iaoaiaoe/ieo iiaeaeae aeey iieno iaoai?/ieo eieeaaeueieo
i?ioean?a iayieo neeiaeo iai?ai?ia?aeieeiaeo i?eeaae?a.

?ic?iaea caaaeueii? iaoiaeeee /enaeueiiai aeine?aeaeaiiy iiaoaeiaaieo
iaoaiaoe/ieo iiaeaeae ia iniia? eiia?iaoe?? /enaeueieo ? aiae?oe/ieo
iaoiae?a.

-aaeaioeaii? aa?n?? iaoiaeo ne?i/aiieo aeaiaio?a.

Noai?aiiy ia iniia? ?ic?iaeaieo iaoiaeee i?ia?aiiiai caaacia/aiiy oa
i?iaaaeaiiy ia/enethaaeueieo aenia?eiaio?a c iaoith aeine?aeaeaiiy
oi/iino? oa ca?aeiino? iiaoaeiaaieo /enaeueieo noai.

Aeine?aeaeaiiy iaoai?/ieo aeeiai?/ieo oa?aeoa?enoee iayieo neeiaeo
e?aii??aeo ae?iae?a oa oe?enoi??a, ye? oe?iei canoiniaothoueny a
aeaeo?ioaoi?oe?.

Iaoiaee aeine?aeaeaiue. I?e aeeiiaii? ?iaioe aeei?enoiaoaaeenue iaoiaee
oa iaoaiaoe/iee aia?ao oai??? i?oaeiino? ai?cio?iiiiai o?ea, oai???
aa??aoe?eieo caaea/, oai??? iaoiaeo ne?i/aiieo aeaiaio?a, iaoiaee
i?ia?aioaaiiy, iaoiaee nenoaiiiai aiae?co.

Iaoeiaa iiaecia ?acoeueoao?a. O aeai?e aeena?oaoe?ei?e ?iaio? io?eiaii
ianooii? iia? ?acoeueoaoe :

Cai?iiiiiaaia iiaa iaoaiaoe/ia iiaeaeue o aeaeyae? aaaaoioa?iai?
eiino?oeoe??, yea a?aoiao? iniiai? eiino?oeoeai? aeaiaioe, aeey
aeine?aeaeaiiy iaoai?/ieo caaea/ aeeiai?ee aeey iayieo NII oeio
e?aii??aeo ae?iae?a oa oe?enoi??a.

Aeey iaoaiaoe/iiai iiaeaethaaiiy aecia/aiiy ?aciiainieo /anoio oa
oaea?ii? i?oeiino? iayieo NII ia iniia? iiaoaeiaaii? iiaeae? ?icaeiooee
i?aeo?ae, yeee iieyaa? o aeei?enoaii? ni?aa?aeiioaiue i?inoi?iai?
aeeiai?/ii? oai??? i?oaeiino? ai?cio?iiiiai o?ea, ? yeee ia a?aei?io
a?ae a?aeiieo i?aeoiae?a aeicaiey? a?aoiaoaaoe ai?cio?iii? aeanoeaino?
iai?ai?ia?aeieeiaeo no?oeoo?, a oaeiae i?iaiaeeoe aeine?aeaeaiiy
aeaoi?iaoe?eiiai aoaeoo.

Iiaoaeiaaia iiaa iaoiaeeea /enaeueiiai aeine?aeaeaiiy aeeiai?/ieo caaea/
i?inoi?iai? oai??? i?oaeiino? ai?cii?iiiiai o?ea, yea a?aoiao?
niaoeeo?eo cai?iiiiiaaii? iaoaiaoe/ii? iiaeae?, ? caaacia/o?
oe?e?ni?noue oa aeiiiii?noue ia/enethaaeueiiai i?ioeano.

-ioe?iee iiaoaeiaaia iiaa /enaeueia noaia i?aeaeuaiiy oi/iino?
?ic?aooie?a aeey aeine?aeaeaiiy noaoe/ieo caaea/ e?i?eii? oai???
i?oaeiino? ai?cio?iiiiai o?ea.

I?iaaaeaii aeaoaeueia aeine?aeaeaiiy oi/iino? oa ca?aeiino? iiaoaeiaaieo
/enaeueieo noai ia aaaaoueio oanoiaeo i?eeeaaeao oeyoii ii??aiyiiy c
a?aeiieie aiae?oe/ieie oa /enaeueieie ?ica’yceaie. Aeine?aeaeai? oaea?ia
i?oei?noue ?aaeueieo eiino?oeoe?e iayieo NII oa aieea eiino?oeoeaieo
aeaiaio?a ia ??aaiue iaoai?/ieo iai?oaeaiue o iai?ai?ia?aeieeia?e
no?oeoo??.

Aeinoia??i?noue io?eiaieo ?acoeueoao?a caaacia/o?oueny: no?iaith
iaoaiaoe/iith iinoaiiaeith oa ei?aeoi?noth noi?ioeueiaaieo caaea/;
ii??aiyiiyi io?eiaieo ?acoeueoao?a aeey oanoiaeo caaea/ c aiae?oe/ieie
?ica’yceaie aai c ?acoeueoaoaie a?aeiia?aeieo ?ic?aooie?a i?iaaaeaieo ia
iniia? aeueoa?iaoeaieo i?aeoiae?a; aiae?cii iaaeeaeaieo ?ica’yce?a,
io?eiaieo i?e ??ci?e e?eueeino? /eai?a, oo?eiaieo a ?yaeao Oo?’? ?
?iceeaaeo ca aeanieie oi?iaie eieeaaiue.

-aaeaioeaia iiaeaethaaiiy. Noai?aia i?ia?aiia caaacia/aiiy iiaea aooe
aeei?enoaia ye yae?i nenoai aaoiiaoeciaaiiai i?iaeooaaiiy. Ca
aeiiiiiaith i?ia?aiiiai eiiieaeno “OE?AI” i?iaaaeaii aeine?aeaeaiiy
iaoai?/ieo aeeiai?/ieo oa?aeoa?enoee cae/aeiiai oa “/anueeiai” aa??aio?a
iayieo neeiaeo e?aii??aeo oe?enoi??a.

Ai?iaaaeaeaiiy ?acoeueoao?a ?iaioe. ?acoeueoaoe aeena?oaoe?eii? ?iaioe
aeei?enoai? ia AI “Ia?aoai?thaa/” (i.Caii??aeaey), o O?ceei-iaoai?/iiio
?inoeooo? ?i. A.A.Ea?iaiea IAI Oe?a?ie (i.Euea?a), a oaeiae o
iaa/aeueiiio i?ioean? Euea?anueeiai aea?aeaaiiai oi?aa?neoaoo ?iai?
?aaia O?aiea i?e /eoaii? iaa/aeueiiai eo?no ”Iaoiae ne?i/aiieo
aeaiaio?a”, ui i?aeoaa?aeaeaii a?aeiia?aeieie aeoaie.

Iniaenoee aianie caeiaoaa/a. Aaoi?ii naiino?eii noi?ioeueiaai? oa
ae??oai? iniiai? iieiaeaiiy, ye? neeaaeathoue nooue aeena?oaoe?eii?
?iaioe. O ioae?eaoe?yo, ye? iaienai? o ni?aaaoi?noa?, caeiaoaa/o
iaeaaeaoue: [3,8] — ?ic?iaea aeai?eoi?a iaoaiaoe/iiai iiaeaethaaiiy
aecia/aiiy ?aciiainieo /anoio oa oaea?ii? i?oeiino? iayieo NII;
[1,4,5,7] — ?ic?iaea caaaeueii? iaoiaeeee /enaeueiiai aeine?aeaeaiiy
aeeiai?/ieo caaea/ e?i?eii? i?inoi?iai? oai??? i?oaeiino? ai?cio?iiiiai
o?ea; [2,8,9] — coai?aiiy a?aeiia?aeiiai i?ia?aiiiai caaacia/aiiy oa
i?iaaaeaiiiy aeine?aeaeaiiy oi/iino? oa ca?aeiino? iiaoaeiaaieo
/enaeueieo noai.

Ai?iaaoe?y. Iniiai? ?acoeueoaoe i?iaaaeaieo aeine?aeaeaiue
aeiiia?aeaeeny oa iaaiai?thaaeeny ia: i?aeia?iaeieo iaoeiai-oaoi?/ieo
eiioa?aioe?yo «Aeina?ae ?ic?iaee oa canoinoaaiiy i?eeaaei-oaoiieia?/ieo
NAI? i?e?iaeaeo?ii?ee» (i.Euea?a, 1995,1999 ?.); anaoe?a?inueeeo
iaoeiaeo eiioa?aioe?yo «Canoinoaaiiy ia/enethaaeueii? oaoi?ee,
iaoaiaoe/iiai iiaeaethaaiiy oa iaoaiaoe/ieo iaoiae?a o iaoeiaeo
aeine?aeaeaiiyo» (i.Euea?a, 1995, 1996, 1998 ?.); nai?ia?? «I?eeeaaei?
i?iaeaie iaoaiaoeee oa ?ioi?iaoeee» (i.??aia, 1996); anaoe?a?inuee?e
eiioa?aioe?? «Iiaeaee?iaaiea e enneaaeiaaiea onoie/eainoe nenoai»
(i.Ee?a, 1996); i?aeia?iaei?e iaoeia?e eiioa?aioe?? «Numerical Methods
in Continuum Mechanics» (Aenie? Oao?e, Neiaa//eia, 1996), a oaeiae ia
ui??/ieo iaoeiaeo nai?ia?ao eaoaae?e i?eeeaaeii? iaoaiaoeee
Euea?anueeiai aea?aeaaiiai oi?aa?neoaoo ?i. ?aaia O?aiea.

Ioae?eaoe??. Iniiaiee ci?no aeena?oaoe?eii? ?iaioe aena?oeaiee o 10
ioae?eaoe?yo, c ieo: 6 noaoae o oaoiaeo aeaeaiiyo, 4 oac aeiiia?aeae.

No?oeoo?a oa ianya ?iaioe. Aeena?oaoe?y neeaaea?oueny c? anooio, oanoe
?icae?e?a c aeniiaeaie, caaaeueieo aeniiae?a oa nieneo e?oa?aoo?e. Aiia
i?noeoue 150 noi??iie oaenoo, a oiio /ene? 44 ?enoiee oa 21 oaaeeoe?.
A?ae?ia?ao?/iee nienie neeaaea?oueny ?c 140 iaeiaioaaiue e?oa?aoo?ieo
aeaea?ae.

INIIAIEE CI?NO ?IAIOE

O anooi? ei?ioei oa?aeoa?eco?oueny no/aniee noai i?iaeai, ye?
?icaeyaeathoueny o aeena?oaoe?ei?e ?iaio?, iaa?oioiao?oueny
aeooaeuei?noue aea?aii? oaie. Noi?ioeueiaai? oe?e? aeine?aeaeaiiy,
iaoeiaa iiaecia oa i?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a.
Aeeeaaeai? iniiai? iaoeia? iieiaeaiiy, ui aeiinyoueny ia caoeno. Iiaeaia
aiioaoe?y aeena?oaoe?? ii ?icae?eao.

O ia?oiio ?icae?e? aeine?aeaeothoueny ieoaiiy iiaeaethaaiiy iayieo
neeiaeo e?aii??aeo ae?iae?a oa oe?enoi??a a eiioaeno? ?ica’ycaiiy
iaoai?/ieo caaea/ aeeiai?ee. ?icaeyaea?oueny aeaa oeie eiino?oeoe?e:
“cae/aeia” oa “/anueeiai” aa??aioa. Iiaeaeue aeacaieo i?eeaae?a
aoaeo?oueny ia iniia? aiae?co ?o oeiiai? oiiieia??, ui aeicaiey?
cai?iiiioaaoe iiaee i?aeo?ae aei iiaeaethaaiiy NII iayii? eiino?oeoe??.
Nooue oeueiai i?aeoiaeo iieyaa? a oiio, ui NII iayii? eiino?oeoe?? oeio
e?aii??aeo ae?iae?a oa oe?enoi??a ?icaeyaeathoueny ye inaneiao?e/i?
eoneiai-iaeii??aei? ia’?eoe c ?aeaaeueiith aaeaac??th i?ae aeaiaioaie. O
oeueiio aeiaaeeia? ia?eae?iiaeueiee ia?aoei eiino?oeoe?? iiaeaeth?oueny
iaai?ii o?aiaoe?e, eiaeia c yeeo iieno? aaiiao??th iaei??? c neeaaeiaeo
/anoei i?eeaaeo (iniiaa ei?iono, oa?iieiiiainaoi?, iai?ai?ia?aeieeiaa
no?oeoo?a ? o.ae.). Iiaoaeiaai? oaeei niiniaii iiaeae? aeey aeaio aeua
cacia/aieo aeae?a i?eeaae?a cia?aaeai? ia ?en.1.

-aaeaioeaieo /enaeueieo noai. Iaa?oioiaaii iaiao?aei?noue i?iaaaeaiiy
iiaeaeueoeo aeine?aeaeaiue o oeeo iai?yieao.

, caienaia iaoaiaoe/ia iinoaiiaea i?inoi?iai? caaea/? aeeiai?/ii?
oai??? i?oaeiino?, c yei?, ye /anoeia? aeiaaeee, iiaeia io?eiaoe
iinoaiiaee caaea/ i?i a?euei? eieeaaiiy ? noaoe/ii? oai??? i?oaeiino?.
*enaeueia i?ioeaaeo?a ?ica’ycaiiy aeacaieo caaea/ oai??? i?oaeiino?
ii/eia?oueny c oi?ioethaaiiy a?aeiia?aeieo aa??aoe?eieo iinoaiiaie. Oae,
o aeiaaeeo aeeiai?/ii? caaea/? oai??? i?oaeiino? ia?ii ianooiio
aa??aoe?eio caaea/o:

, (1)

— aaiaoiaee i?ino?? ooieoe?e.

Aa??aoe?eia iinoaiiaea caaea/? i?i a?euei? eieeaaiiy oi?ioeth?oueny oae:

, (2)

— e?oaiaa /anoioa a?eueieo eieeaaiue.

Aa??aoe?eia iinoaiiaea noaoe/ii? caaea/? oai??? i?oaeiino? ia? aeaeyae:

. (3)

iiaeaii o aeaeyae? ne?i/aiii? noie ?yaeo Oo?’?:

, (4)

, (5)

— a?aeii? eiao?oe??ioe ?iceeaaeo eiiiiiaio aaeoi??a iiaa?oiaaiai
iaaaioaaeaiiy oa ianiaeo nee,

, iiaeia noi?ioethaaoe aa??aoe?eio caaea/o ciaoiaeaeaiiy iaa?aeiieo
eiao?oe??io?a ?iceeaaeo a ?yae Oo?’?:

oaeo, ui

,

. (6)

-i? aa?iii?ee, io?eio?ii caaea/o Eio? aeey nenoaie cae/aeieo
aeeoa?aioe?aeueieo ??aiyiue, yea a iao?e/ieo iicia/aiiyo ia? aeaeyae :

, (7)

, (8)

— aaeoi? ooeaieo aoceiaeo cia/aiue ia?ai?uaiue, ca aeiiiiiaith yeiai
iaaeeaeaiee ?ica’ycie caaea/? (6) aecia/a?oueny ianooiiei ?iceeaaeii ca
aacenieie ooieoe?yie

. (9)

O aeai?e ?iaio?, ye aaceni? ooieoe?? aeei?enoiao?ii a?e?i?ei? oa
a?eaaae?aoe/i? o?i?oi? ooieoe?? ia ?ciia?aiao?e/ieo /ioe?eeooieo
ne?i/aiieo aeaiaioao ne?aiaeeiiaiai oeio.

o aeaeyae?

, (10)

io?eiai? c ianooiii? aeaaa?a?/ii? i?iaeaie ia aeani? cia/aiiy

. (11)

iacaeaaeieo cae/aeieo aeeoa?aioe?aeueieo ??aiyiue aeey ciaoiaeaeaiiy
ocaaaeueiaieo ia?ai?uaiue:

, (12)

c ii/aoeiaeie oiiaaie :

, (13)

— e?euee?noue ia?oeo aeanieo ia? caaea/? (11).

O caaaeueiiio aeiaaeeo ?ica’ycie eiaeiiai ??aiyiiy (12) ooea?ii o
aeaeyae? ?ioaa?aeo Aethaaiaey :

, (14)

aecia/a?ii c ii/aoeiaeo oiia (13).

-i? aa?iii?ee ciaoiaeeii noia?iiceoe??th ?aaeoe?e nenoaie ca an?ia
aeanieie oi?iaie ca?aeii oi?ioee (10). Caaaeueio ?aaeoe?th nenoaie
io?eio?ii oeyoii noioaaiiy ia?ai?uaiue ca an?ia aa?iii?eaie ca?aeii
oi?ioee (5).

. Oiae? ooeai? ia?ai?uaiiy i?aaenoaaeii o aeaeyae?

. (15)

-i? aa?iii?ee ocaaaeueiaio i?iaeaio ia aeani? cia/aiiy

, (16)

-i?oiaiiaeueiino?, ooea?ii ca aeiiiiiaith iaoiaeo ?oa?aoe?e o
i?aei?inoi??.

-aaeaioeaiee i?ioean, iaoith yeiai ? aaoiiaoecaoe?y i?ioeaaeo?e
io?eiaiiy /enaeueiiai ?ica’yceo caaeaii? oi/iino?, aeeth/a? o?e aoaie,
ye? iiaeii? aooe canoiniaai? oeeee?/ii :

io?eiaiiy ?ica’yceo ia ii/aoeia?e n?ooe? oa ioe?iea eiai oi/iino? ca
aeiiiiiaith aiinoa??i?ii? ioe?iee iioeaee;

iaea?eueo aoaeoeaia i?iaiicoaaiiy eieaeueiiai caouaiiy n?oee iio??aiiai
aeey aeinyaiaiiy caaeaii? oi/iino?;

caouaiiy n?oee, io?eiaiiy iiaiai ?ica’yceo ? ioe?iea iiai? iioeaee c
ianooiiei iiaa?iaiiyi ia ae?oaee e?ie, yeui iiaa iioeaea ia?aaeuo?
aaaeaio.

, ia eiaeiiio ne?i/aiiiio aeaiaio?, ?ioa?iieththoueny ca aeiiiiiaith
o??? ae nenoaie aacenieo ooieoe?e, ui eiiiiiaioe aaeoi?a ia?ai?uaiue,
oiaoi:

, (17)

aeei?enoiao?oueny ??aiyiiy i?iaeooaaiiy:

. (18)

Ia?aoai?eaoe (18), ia?ii:

, (19)

— iao?eoey aeeoa?aioe?aeueieo iia?aoi??a ?c aaiiao?e/ieo
ni?aa?aeiioaiue Eio?,

.

. Ca oeei e?eoa???i, oeyoii i?iaiicoaaiiy ?ici???a ne?i/aiieo
aeaiaio?a, aaciina?aaeiuei iiaeia iiaoaeoaaoe «iioeiaeueio»
ne?i/aiiiaeaiaioio n?oeo. O aeai?e ?iaio? i?ae «iioeiaeueiith» n?oeith
?icoi??oueny n?oea, ia ye?e eieaeueia iioeaea aeene?aoecaoe?? a
aia?aaoe/i?e ii?i? ??aiii??ii ?iciiae?eaia ii aeaiaioao. Iaiao?aei?noue
iiaoaeiae «iioeiaeueii?» n?oee iaa?oioiao?oueny oei, ui aeey oaei? n?oee
aneiioioe/ia oaeaee?noue ca?aeiino? ai?ieneiaoe?e INA caeaaeeoue eeoa
a?ae iie?iii?aeueiiai ii?yaeeo aacenieo ooieoe?e, ? ia caeaaeeoue a?ae
ii?yaeeo neiaoey?iino?. Oiiaa aecia/aiiy aeaiaio?a n?oee, ui
iio?aaothoue iiaeaeueoiai ?icaeooy, ia? aeaeyae:

, (20)

-/enei ne?i/aiieo aeaiaio?a ia a?aeo/?e n?ooe?.

-ioe?iee oa iaiao?aei?noue iiaoaeiae «iioeiaeueii?» n?oee o nain?
??aiii??iiai ?iciiae?eo ii aeaiaioao eieaeueii? iioeaee aeene?aoecaoe??.
C?iaeaii aeniiaee i?i aoaeoeai?noue ?icaeyiooeo aeai?eoi?a i?iaiicoaaiiy
ae?aiao?a n?oee.

I’yoee ?icae?e i?enay/aiee ?ica’ycoaaiith iaoai?/ieo caaea/ aeeiai?ee
aeey neeiaeo iai?ai?ia?aeieeiaeo i?eeaae?a iayii? eiino?oeoe?? oeio
e?aii??aeo oe?enoi??a ia iniia? cai?iiiiiaaieo iaoaiaoe/ieo iiaeaeae
(aeea.?en.1) oa aeua iienaieo iaoiaeee. I?iaaaeai? aeine?aeaeaiiy
i?oaeiiai noaio aeey aeaio oei?a i?eeaae?a: “cae/aeiiai” oa «/anueeiai»
aa??aio?a. Iniiaia a?aei?ii?noue “/anueeiai“ aa??aioo iieyaa? o
a?aenooiino? oa?iieiiiainaoi??a. “Cae/aeiee” oei oe?enoi?a
iiaeaeth?oueny eiino?oeoe??th, ui neeaaea?oueny c aeanyoe aeaiaio?a :
aeaio i?aeieo iniia, ieaeiueiai oa aa?oiueiai iie?aaeaiiaeo
oa?iieiiiainaoi??a, e?aii??ai? no?oeoo?e, aeaio aa?oi?o i?aeieo
e?eueoe?a, o?ueio oa??a i?eiith a?aeiia?aeii i?ae ieaei?i
oa?iieiiiainaoi?ii oa ieaeiueith iniiaith, i?ae e?aii??aith no?oeoo?ith
? ieaei?i oa?iieiiiainaoi?ii, ? i?ae e?aii??aith no?oeoo?ith ? aa?oi?i
oa?iieiiiainaoi?ii. Ia?oei e?ieii ?ica’ycaiiy aeeiai?/ii? caaea/? o
?ic?iaeaiiio i?aeoiae? ? ?ica’ycaiiy caaea/? i?i a?euei? eieeaaiiy.
Ia?o? /ioe?e oeeee?/ieo /anoioe inaneiao?e/ieo a?eueieo eieeaaiue
oe?enoi??a iaio aa??aio?a, io?eiai? ia ??cieo ne?i/aiiiaeaiaioieo
n?oeao, iaaaaeai? o oaaeeoe? 1.

Oaaeeoey 1. Oeeee?/i? /anoioe (Aoe) inaneiao?e/ieo a?eueieo eieeaaiue

oe?enoi? “cae/aeiiai” oeio

140 916 23.949 39.908 51.142 69.029

299 1898 22.808 38.761 50.964 68.561

356 2246 22.408 38.727 50.879 67.404

446 2800 22.066 38.666 50.709 67.273

617 3848 21.815 38.622 50.573 67.091

“/anueeee” aa??aio oe?enoi?a

202 1314 10.419 23.284 25.524 37.948

270 1728 10.328 22.182 25.339 37.558

311 1986 10.144 22.080 25.221 37.066

423 2674 9.858 21.221 24.952 36.856

529 3332 9.809 21.111 24.781 36.834

Ooo aaaaeai? ianooii? iicia/aiiy: NEL — e?euee?noue ne?i/aiieo aeaiaio?a
ia a?aeo/?e n?ooe?, KSS – caaaeueia e?euee?noue noaiai?a naiaiaee ia
n?ooe? c NEL aeaiaio?a. C oaaeeoe? 1 aeaeii, ui iaeiaioa ?aciiainia
/anoioa oe?enoi?a cae/aeiiai oeio aaea?/? a?eueoa ca iaeiaioo ?aciiainio
/anoioo oe?enoi?a «/anueeiai» aa??aioo. Oea iiynith?oueny oei, ui aei
neeaaeo oe?enoi?a cae/aeii? eiino?oeoe?? aoiaeyoue oa?iieiiiainaoi?e,
ye?, c iaoai?/ii? oi/ee ci?o, ?iaeyoue oeae i?eeaae aei?noe?oeei. Ia
?en.2 cia?aaeaii oi?ie aeanieo eieeaaiue, ye? a?aeiia?aeathoue iaeiaio?e
?aciiaini?e /anoio?, aeey iaio aeae?a i?eeaaeo (?en.2a — –
“cae/aeiee” oei, ?en. 2a – “/anueeee” aa??aio).

, i?eeeaaeaiiai aei ieaeiuei? iiaa?oi? i?aeii? iniiae. Aiae?c
ia?ao?aeieo i?ioean?a aeicaieea aecia/eoe aaee/eio oa
i?noeaciaoiaeaeaiiy iaeneiaeueieo ?icoyaoth/eo iai?oaeaiue o e?aii??a?e
no?oeoo?? oe?enoi??a iaio oei?a. O oe?enoi?ao “cae/aeii?” eiino?oeoe??
iaeneiaeuei? iaoai?/i? iai?oaeaiiy aeieeathoue ia aa?oi?e iiaa?oi?
iai?ai?ia?aeieeiai? no?oeoo?e. O «/anueeiio» aa??aio? oe?enoi?a ciia
iaeneiaeueieo ?icoyaoth/eo iai?oaeaiue ci?uaia a noi?iio oanee.

aeey oe?enoi?a “cae/aeii?” eiino?oeoe??. Aiaeia?/i? ca ci?noii a?ao?ee
o?eueee aeey “/anueeiai” aa??aioo i?eeaaeo cia?aaeai? ia ?en. 4.

Aeey oe?enoi?a “cae/aeii?” eiino?oeoe?? i?iaaaeaii aeine?aeaeaiiy aieeao
oiaueie ieaeiueiai iie?aaeaiiaiai oa?iieiiiainaoi?a ia aaee/eio
iaeneiaeueieo ?icoyaoth/eo iai?oaeaiue o e?aii??a?e no?oeoo??. Iieacaii,
ui ca?eueoaiiy oiaueie oa?iieiiiainaoi?a iiieaeo? ??aaiue
iaeneiaeueieo ?icoyaoth/eo iai?oaeaiue o e?aii??a?e no?oeoo??.

On? iaaaaeai? aeua /enaeuei? ?acoeueoaoe aoee io?eiai? ia n?ooe? c 617
a?eaaae?aoe/ieo ne?i/aiieo aeaiaio?a c caaaeueiith e?euee?noth noaiai?a
naiaiaee 3848 aeey oe?enoi?a “cae/aeiiai” oeio (?en. 5a), a aeey
“/anueeiai” aa??aioo i?eeaaeo – ia n?ooe? c 529 aeaiaio?a c caaaeueiith
e?euee?noth noaiai?a naiaiaee – 3332 (?en. 5a).

-aaeaioeaiiai iiaeaethaaiiy.

O aeiaeaoeo iaaaaeai? aeieoiaioe, ui i?aeoaa?aeothoue oaeoe aeei?enoaiiy
?acoeueoao?a aeena?oaoe?eii? ?iaioe.

INIIAI? ?ACOEUeOAOE ?IAIOE OA AENIIAEE

O aeena?oaoe?ei?e ?iaio? ia iniia? aenieioi/ieo noai iai?aaiae?oe/iiai
iaoiaeo ne?i/aiieo aeaiaio?a, o ?aieao iiaeae? e?i?eii? i?inoi?iai?
oai??? i?oaeiino? ai?cio?iiiiai o?ea, ?ic?iaeai? iia? aeai?eoie
iaoaiaoe/iiai iiaeaethaaiiy aeeiai?/ieo i?ioean?a i?oaeiiai
aeaoi?ioaaiiy iayieo neeiaeo iai?ai?ia?aeieeiaeo i?eeaae?a oeio
e?aii??aeo ae?iae?a oa oe?enoi??a, ye? ?aae?ciaai? o aeaeyae?
i?ia?aiiiai eiiieaeno aeey no/anieo IE.

Iniiai? ?acoeueoaoe aeeiiaii? ?iaioe iieyaathoue o ianooiiiio :

Cai?iiiiiaaia iiaa iaoaiaoe/ia iiaeaeue aeey aeine?aeaeaiiy iaoai?/ieo
eieeaaeueieo i?ioean?a NII oeio iayieo e?aii??aeo ae?iae?a oa oe?enoi??a
o aeaeyae? aaaaoioa?iai? no?oeoo?e neeaaeii? oi?ie. Aeaia iiaeaeue
aaco?oueny ia oiio, ui ia?eae?iiaeueiee ia?aoei eiino?oeoe??
iiaeaeth?oueny iaai?ii o?aiaoe?e, eiaeia c yeeo iieno? aaiiao??th
iaeiiai c aeaiaio?a i?eeaaeo (iniiae, oa?iieiiiainaoi?a,
iai?ai?ia?aeieeiai? no?oeoo?e ? o.ae.).

Aeey iaoaiaoe/iiai iiaeaethaaiiy aecia/aiiy ?aciiainieo /anoio oa
oaea?ii? i?oeiino? NII oeio iayieo e?aii??aeo ae?iae?a oa oe?enoi??a
cai?iiiiiaaii aeei?enoaiiy ni?aa?aeiioaiue e?i?eii? i?inoi?iai?
aeeiai?/ii? oai??? i?oaeiino? ai?cio?iiiiai o?ea. Oaeee i?aeo?ae
aeicaiey? c ?aeeieo iiceoe?e aeine?aeaeoaaoe ye caaea/? i?i a?euei?
eieeaaiiy, oae ? caaea/? aecia/aiiy ia?aiao??a i?oaeiiai noaio
iai?ai?ia?aeieeiaeo no?oeoo?, a?aoiaoth/e ai?cio?iii? aeanoeaino?
iaoa??aeo.

?ic?iaeaia iiaa iaoiaeeea ?ica’ycaiiy aeeiai?/ieo caaea/ e?i?eii?
i?inoi?iai? oai??? i?oaeiino? aeey ai?cio?iiieo inaneiao?e/ieo o?e, yea
a?aoiao? niaoeeo?eo iiaoaeiaaieo iiaeaeae ? caaacia/o? aeiiiii?noue oa
oe?e?ni?noue ia/enethaaeueiiai i?ioeano. Aeaia iaoiaeeea aaco?oueny ia
aeei?enoaii? /enaeueieo oa aiae?oe/ieo iaoiae?a (iai?aaiae?oe/iee iaoiae
ne?i/aiieo aeaiaio?a, iaoiae ?iceeaaeo ca aeanieie oi?iaie eieeaaiue,
iaoiae ?oa?aoe?e o i?aei?inoi??). Oni?oia ai?iaaoe?y oe??? iaoiaeeee
i?iaaaeaia aeey ?yaeo iiaeaeueieo caaea/, oeyoii ii??aiyiiy c
?acoeueoaoaie io?eiaieie ca aeiiiiiaith aeueoa?iaoeaieo i?aeoiae?a.

-aaeaioeaia noaia iaoiaea ne?i/aiieo aeaiaio?a. Aoaeoeai?noue
?ic?iaeaiiai i?aeoiaeo aeine?aeaeoaaeany ia oanoiaiio i?eeeaae?, aeey
yeiai a?aeiiee aiae?oe/iee ?ica’ycie. I?aeoe/ia cia/aiiy ?ic?iaeaiiai
i?aeoiaeo iieyaa? o oiio, ui a?i aeicaiey? i?iaiaeeoe aaeaioeaia
eiii’thoa?ia iiaeaethaaiiy inaneiao?e/ieo caaea/ noaoe/ii? oai???
i?oaeiino?, o?aeooth/e eiai ye ii/aoeiaee aoai aeey aaeaioeaiiai
iiaeaethaaiiy caaea/ aeeiai?ee.

Aeine?aeaeai? iaoai?/i? aeeiai?/i? oa?aeoa?enoeee neeiaeo iayieo
e?aii??aeo oe?enoi??a na?aaeiuei? iiooaeiino?, ye? oe?iei
aeei?enoiaothoueny a aeaeo?ioaoi?oe?. Ia iniia? ?ic?iaeaieo iiaeaeae oa
iaoiaeee aeey aeaio oei?a eiino?oeoe?e i?eeaae?a, a naia “cae/aeiiai“ oa
“/anueeiai” aa??aio?a, i?iaaaeaii aiae?c aieeao eiino?oeoeaieo aeaiaio?a
i?eeaae?a ia ??aaiue iaoai?/ieo aeeiai?/ieo iai?oaeaiue o e?aii??a?e
no?oeoo??. Aiae?c ia/enethaaeueieo aenia?eiaio?a aeicaiey? c?iaeoe
ianooii? aeniiaee:

a) noiniaii oaea?ieo iaoai?/ieo iaaaioaaeaiue oe?enoi? “cae/aeii?”
eiino?oeoe?? ? aei?noe?oei i?eeaaeii, i?ae “/anueeee” aa??aio;

a) aeeiai?/i? iaoai?/i? iai?oaeaiiiy o iai?ai?ia?aeieeia?e no?oeoo??
oe?enoi?a “cae/aiiai” oeio cia/ii a?eueo?, i?ae o “/anueeiio”
aa??aio?;

a) iaeneiaeuei? ?icoyaoth/? iaoai?/i? iai?oaeaiiy o e?aii??a?e
no?oeoo?? oe?enoi?a “cae/aeii?” eiino?oeoe?? aeieeathoue ia aa?oi?e
iiaa?oi? aeeae/a aei oeaio?aeueiiai aeaiaeo, a aeey “/anueeiai” aa??aioo
ciia iaeneiaeueieo iai?oaeaiue ci?uaia aei oanee;

a) ca?eueoaiiy oiaueie ieaeiueiai iie?aaeaiiaiai oa?iieiiiainaoi?a
iiieaeo? ??aaiue iaeneiaeueieo ?icoyaoth/eo iai?oaeaiue o e?aii??a?e
no?oeoo?? oe?enoi?a “cae/aeii?” eiino?oeoe??.

-aaeaioeaiee aiae?c caaea/ noaoeee. Oi?aa?naeuei?noue ?ic?iaeaieo
iaoiaeee ca oi?iaie ia?eae?iiaeueiiai ia?aoeio aeine?aeaeoaaieo
ia’?eo?a, a oaeiae ca niiniaaie ?o iaaaioaaeaiiy aeicaiey? oe?iea
canoinoaaiiy i?ia?aiiiai eiiieaeno “OE?AI”. C?o/i? caniae
i?ai?ioeani?ii? oa iinoi?ioeani?ii? ia?iaee aeaieo aeathoue iiaeeea?noue
aeei?enoiaoaaoe ?ic?iaeai? aeai?eoie oaeiae ye neeaaeia? /anoeie nenoai
aaoiiaoeciaaiiai i?iaeooaaiiy.

NIENIE IIOAE?EIAAIEO AAOI?II I?AOeUe CA OAIITH AeENA?OAOe??

1) A?eai?aiei A.ss., Aeuye E.E., Iaea? A.I. ?aoaiea i?ino?ainoaaiiie
aeeiaie/aneie caaea/e oai?ee oi?oainoe aeey aiecio?iiiuo oae // I?eee.
iaoaieea. — 1998. — O.34, ?5. — n.24-31.

2) Aeeye ?.?., Iaea? A.I., Naaoea ss.A. Aaaaoie?eoa??aeueia iioei?caoe?y
oa?iiiai?oaeaiue o iai?ai?ia?aeieeiaeo i?eeaaeao // A?ni. aea?ae. oi-oa
‘Euea?nueea iie?oaoi?ea’. Na?. Eiii’thoa?i? nenoaie i?iaeooaaiiy. Oai??y
? i?aeoeea. -1996.- ?313.–N.9-16.

3) Aeeye ?.?., Iaea? A.I. Iaoaiaoe/ia iiaeaethaaiiy caaea/ aeeiai?ee
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AIIOAOe?ss

Iaea? A.I. Iaoaiaoe/ia iiaeaethaaiiy iaoai?/ieo eieeaaeueieo i?ioean?a
a neeiaeo iai?ai?ia?aeieeiaeo i?eeaaeao ia iniia? iaoiaeo ne?i/aiieo
aeaiaio?a.- ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 01.05.02 – iaoaiaoe/ia iiaeaethaaiiy oa
ia/enethaaeuei? iaoiaee. – Aea?aeaaiee oi?aa?neoao “Euea?anueea
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Aeena?oaoe?y i?enay/aia ieoaiiyi ?ic?iaee aeai?eoi?a iaoaiaoe/iiai
iiaeaethaaiiy aecia/aiiy ?aciiainieo /anoio oa oaea?ii? i?oeiino? iayieo
neeiaeo iai?ai?ia?aeieeiaeo i?eeaae?a oeio e?aii??aeo ae?iae?a oa
oe?enoi??a. Cai?iiiiiaai? iaoaiaoe/i? iiaeae? aeey iieno iaoai?/ieo
eieeaaiue, ?ic?iaeai? iaoiaeeee ?o /enaeueiiai aeine?aeaeaiiy, ye?
caaacia/othoue oe?e?ni?noue oa aeiiiii?noue ia/enethaaeueiiai i?ioeano.
Iiaoaeiaai? /enaeuei? noaie ?aae?ciaai? o aeaeyae? a?aeiia?aeiiai
i?ia?aiiiai caaacia/aiiy, i?aoeacaeaoi?noue yeiai aeine?aeaeoaaeanue
oeyoii ?ica’ycaiiy oanoiaeo caaea/ ? i?aeoe/ii aaaeeeaeo caaea/
?iaeaia?ii? i?aeoeee.

-aaeaioeai?noue.

AIIIOAOeEss

Iaea? A.I. Iaoaiaoe/aneia iiaeaee?iaaiea iaoaie/aneeo eieaaaoaeueiuo
i?ioeannia a neeiauo iieoi?iaiaeieeiauo i?eai?ao ia iniiaa iaoiaea
eiia/iuo yeaiaioia.- ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 01.05.02 — iaoaiaoe/aneia iiaeaee?iaaiea e
au/eneeoaeueiua iaoiaeu.- Ainoaea?noaaiiue oieaa?neoao «Eueaianeay
iieeoaoieea» . — Eueaia, 1999.

Aeenna?oaoeey iinayuaia aii?inai ?ac?aaioee aeai?eoiia iaoaiaoe/aneiai
iiaeaee?iaaiey ii?aaeaeaiey ?aciiainiuo /anoio e oaea?iie i?i/iinoe
iayiuo neeiauo iieoi?iaiaeieeiauo i?eai?ia oeia e?aiieaauo aeeiaeia e
oe?enoi?ia. I?aaeeiaeaiu iaoaiaoe/aneea iiaeaee aeey iienaiey
iaoaie/aneeo eieaaaiee, ?ac?aaioaiu iaoiaeeee eo /eneaiiiai
enneaaeiaaiey, eioi?ua iaania/eaatho oeaeiniinoue e yeiiiiiinoue
au/eneeoaeueiiai i?ioeanna. ?ac?aaioaiua /eneaiiua noaiu ?aaeeciaaiu a
aeaea niioaaonaothuaai i?ia?aiiiai iaania/aiey, ?aaioiniiniaiinoue
eioi?iai enneaaeiaaia iooai ?aoaiey oanoiauo caaea/ e i?aeoe/anee
aaaeiuo caaea/ eiaeaia?iie i?aeoeee.

-aaeaioeaiinoue.

ABSTRACT

Makar V.M. The mathematical modelling of mechanical vibration of power
semiconductor devices based on finite element method .- Manuscript.

An application thesis for obtain the candidate of engineering sciences
fellowship in speciality 01.05.02- mathematical modelling and
computational methods.- State University «Politechics of Lviv».- Lviv,
1999.

The dissertation is devoted to the investigation of vital problems of
construction of new mathematical modelling algorithms for determination
of resonance frequency and impact strength of power semiconductor
devices (PSD) such as soldered silicon thyristors and diodes. The
efficient decision of these problems will allow to simulate operation of
PSD at presence of exterior mechanical effects with the purpose of
determination of a possibility of operation them in conditions of
vibration, impact loads, high pressure etc.

The analysis of typical topology of PSD has shown that for
investigation of mechanical vibration it is needed to develop new
mathematical models which take into account such parts of devices as
package basement and so on. Besides, it is known that semiconductor
structures of PSD have anisotropic properties which presence in
mathematical model is desirable due to dynamic mechanics problems. In
this work, a new mathematical models are proposed which satisfy above
mentioned conditions. Due to these models PSD are considered as
multilayer axisymmetric construction of complex geometry. Each layer
describes the one of PSD’s parts like copper package basement, solder,
molybdenum thermoequalizers, semiconductor structure. In this case, the
investigation of mechanical vibration processes on the base of proposed
models should be carried out using equations of theory of elasticity.
Thus, from the mathematical point of view, the problem of the
mathematical modelling for determination of resonance frequency and
strength of power semiconductor devices is reduced to the solution of
dynamic problem of elasticity theory for anisotropic axisymmetric
multilayer bodies. Moreover, as the applied loading can be nonsymmetric
we need to use 3D equations.

To solve the 3D dynamic elasticity problems a new methodology is
proposed in this work. This methodology is based on the combination of
numerical and analytic methods. The discretization of corresponding
varionational problems by spatial coordinates is carried out by
semianalytical finite element method (SFEM). The main idea of SFEM is,
that on one of coordinates the basis functions are analytical functions,
definite on all gap of their determination. In the given dissertation,
components of a unknown vector of displacements, and also known vectors
of surface gains and mass forces is decomposed in a trigonometrical
series on angular coordinate. The discretization in the cross section is
realized on isoparametric finite elements of a serendipity type with
bilinear and biquadric approximation of displacements. As a result of
it, a Cauchy problem for a system of ordinary second-order differential
equations is obtained for each harmonics. To solve this Cauchy problem a
method of mode superposition is used. Use of this method ensures
integrity and economity of computational process for investigation of
mechanical vibrations. The sense of mode superposition method is, that
the solution of a Cauchy problem for the large coupled system of the
differential equations is reduced to the solution of several Cauchy
problems for separate ordinary differential equation. This is achieved
by means of expansion of general solution of initial Cauchy problem into
linear superpositon of eigenvectors, each multiplied by a general
time-varying amplitude, finding of which is carried out by Duhamel
integral formula. Eigenvectors and appropriate eigenvalues are obtained
from corresponding generalized algebraic eigenproblem using subspace
iteration method.

error estimator lays. The given accuracy is reached by construction of
an optimal finite element mesh in sense of a unique distribution on
finite elements of a local error measured in energy norm. A new
methodology for generation of finite element mesh is proposed.

The developed numerical schemes have been implemented into Fortran code
for IBM-compatible PC. The efficiency and reliability of these codes
have been tested by solving some model problems and obtained numerical
results have been compared with known exact solution or analogical
results obtained by means of alternative approaches. Tested program
codes have been inserted into sortware package “TYRAN” specialized for
numerical solving of wide range problems for PSD: from heat transfer
problems to mechanics dynamic problems. Using this software package,
resonance frequencies and corresponding modes for two kind of PSD such
as so called “usual” construction and “czech” construction have been
obtained. Zones of maximum stretching stresses in silicon structure have
been determinated for both above mentioned kind of devices. It has been
showed that, from mechanics point of view, devices of “usual”
construction are more “stiffen” than devices of “czech” construction.
The influence of constructive parameters of devices on level of dynamic
mechanics stresses in silicon structure has been investigated.

-adaptivity.

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