~1- ~ 10. (eJ/<-; 
~. 0/c-b~Jlt-,1
 
HACTABHO-HAyqHOM BEliY
 
MAlIIMHCKor <l>AKYJITETA Y HMlIIY
 
OJJ,JIyKOM HaCTaBHO-HaY4Hor Beha MaWI1HCKOr <!JaKyJITeTa YHHBep311TeTa y Hnury, 6p. 612­
465-12/2014 OJJ, 14. jyna 2014. rOJJ,I1He, I1MeHOBaHI1 CMO sa 4JIaHOBe Kovncaje sa oueay 11 0JJ,6paHy 
)].OKTopCKe zurceprauaje HBaHa I1aBJIOBl1na, )].l1nJI. Maw. I1H)I(, non Ha311BOM 
"~HHaMH1.JKa cTa6HJlHOCT BHCKOeJlaCTH1.JHHX KOHTHHyaJlHHx CHCTeMa non ,nejcTBoM 
cnysajnnx nopesrehaja" 
HaKoH npernezia JJ,OKTopcKe JJ,I1CepTaUI1je, CarJIaCHO 3aKoHy o BI1COKOM očpasoaarsy 11 
CTaTyTy MaWI1HCKOr <!JaKyJITeTa YHI1Bep311TeTa y Hnury, Kovncnja nOJJ,HOCI1 CJIeJJ,enl1: 
M3BElIITAJ 
Ilonaun o xannunary 
KaHJJ,I1JJ,aT HBaH naBJIOBl1n pohen je 02. 11. 1979. rOJJ,I1He y Hl1llJY. OCHOBHy WKOJIy 11 
rl1MHa311jy "CBeT03ap Mapxonnh" (pa-iyuapcxo-nporpaaepcxa cvep) 3aBpWI10 je y Hl1llJY. 
MaWI1HCKI1 <}laKyJITeT y Hmuy yrmcao je WKOJICKe 1998/99. rOJJ,I1He, a JJ,l1nJIOMl1paO je HOBeM6pa 
2003. rOJJ,HHe Ha cuepy Pa4yHapcKI1 nonpxcane np0I13BOJJ,He TeXHOJIOrl1je, ea npoce-raov oueaov 
9,06 11 oueaov 10 Ha )].l1nJIOMCKOM I1cnI1TY. Teva JJ,l1nJIOMCKOr pana KaHJJ,I1JJ,aTa 611JIa je 
"Ilpojesrosan,e JJ,eTepMI1HI1CTl1lJKI1X 11 CTOXaCTI14KI1X MyJITI1Bapl1ja6l1JIHI1X CI1CTeMal1 I-hI1XOBa 
rtpnaeaa Ha peurasarsy npaKTI14HI1X np06JIeMa". TOKOM crynnja OJJ, 2000 JJ,O 2003. rOJJ,I1He 
Y4eCTBOBao je Ha Maunranjanava Kao TaKMI14ap y snau.y 113 MaTeMaTI1Ke 11 I1H<popMaTI1Ke 11 y 
cnOpTCKI1M TaKMI14efhl1Ma y 0JJ,60jul1 11 CTOHOM reancy. .ll:06110 je uarpaziy BJIaJJ,e Peny6JII1Ke 
Cpčuje sa najčorse CTyJJ,eHTe y 2001. rOJJ,I1HI1. Taxohe, JJ,06110 je narpaay 2002. rOJJ,I1He aa najčorser 
cTyJJ,eHTa 4eTBpTe rOJJ,I1He MaWI1HCKOr <}laKyJITeTa y Huury. Y nepnony OJJ, 2001. )].0 2003. rO)].I1He 
6110 je npeJJ,ceJJ,HI1K cTyJJ,eHTcKe acounjauaje MaWI1HCKOr <}laKyJITeTa y Hnury. 
nOcJIeJJ,l1nJIOMCKe cryztaje ynncao je WKOJICKe 2004/05. rO)].I1He Ha MaWI1HCKOM <}laKyJITeTy 
y HHWy, estep Ayrovarcxo ynpaan.aa,e 11 P060TI1Ka. 
OJJ, neuevčpa 2003. rOJJ,I1He JJ,O Maja 2006. rOJJ,I1He 6110 je anraacosaa Kao I1CTpa)l(I1BalJ 
CTl1neHJJ,I1CTa Ha npojexry MI1HI1CTapCTBa npocsere, nayxe 11 TeXHOJIOWKOr paasoja Peny6JII1Ke 
Cp611je "CaBpeMeHO JJ,aJhI1HCKO ynpaan.atse CI1CTeMI1Ma aa BOJJ,OCHa6)].eBal-he 11 TpeTMaH OTnaJJ,HI1X 
BOJJ,a", ea. 6p. 6370, PYKoBoJJ,I1JIau npojexra JJ,P BJIaCTI1Ml1p HI1KOJIl1n, pen, nporp. OJJ, 2006. JJ,O 
2010. rOJJ,I1He 6110 je anraacosan Kao I1CTpa)l(I1Ba4 npanpasaax Ha npojexry MI1HI1CTapCTBa 
rtpocsere, nayxe 11 TeXHOJIOWKOr paseoja Peny6JII1Ke Cp611je non Ha311BOM "JJ:eTepMI1HI1CTI14Ka 11 
CTOXaCTI14Ka cTa611JIHOCT MeXaHI14KI1X CI1CTeMa" ea, 6p. 144023, pyKOBOJJ,I1JIaU npojexra JJ,p PaTKo 
naBJIOBl1h,peJJ,. npo<}l. 
OKT06pa 2009. rOJJ,I1He ynncao je JJ,OKTOpCKe cryziaje 113 06JIaCTI1 npl1Mel-heHa MeXaHI1Ka. 
Mapra 20 l O. rOJJ,I1He 113a6paH je sa aCI1CTeHTa Ha KaTeJJ,pl1 sa MexaHI1Ky. Y npOTeKJIOM nepaoziy 
6110 je aurascosan Y HaCTaBI1 Ha naaohersy Be)l(6al-ha Ha cnenelurv npeJJ,MeTI1Ma: MeXaHI1Ka 1­
2 
CTaTI1Ka, MeXaHI1Ka II-KI1HeMaTI1Ka, OTnOpHOCT MaTepl1jaJ1a, I1H)I(el-bepcKa rpadnnca, I1HTepHeT 
ynpaan.aise 11 TeXHI14Ka <p113I1Ka. 
0110 je 4J1aH OpraHI13aUl10HI1X ozičopa BI1We MeljyHapo,nHI1X HaY4HI1X «ondiepemurja. 
Y nepnony on 2009. no 2013. rozurue 6110 je anraacosaa Kao I1CTpa)l(I1Ba4 Ha 611J1aTepaJ1HI1M 
,[(AA,[( npojexruva MaWI1HCKOr cPaKyJ1TeTa y Huury 11 HHcTI1TyTa aa ayToMaTI1Ky HAT 113 Bpevena 
"Robust Vision for Rehabilitation Robotic" 11 "Novel Approach in Human Detection in Robotic". 
On 2013. rozuine anraacosaa je Ha 611J1aTepaJ1HOM ,nAA,n npojeicry MaWI1HCKOr rpaxynrera y 
Hmuy 11 I1HcTI1TyTa aa MexaHI1KY TeXHI14KOr YHI1Bep311TeTa y OepJ1I1Hy "Intelligent control of smart 
structures" . 
Tpenyruo je auraaconau Ha npojexry MI1HI1CTapCTBa npocsere, aayxe 11 TeXH0J10WKOr 
passoja Peny6J1I1Ke Cp611je nozi Ha3I1BOM ",nI1HaMI14Ka cTa611J1HOCT 11 HeCTa611J1HOCT MeXaHI14KI1X 
CI1CTeMa non nejcraoa CTOXaCTI14KI1X nopevehaja'' ea, 6poj. 1740 l 1, pyKOBO,nI1J1aU npojexra np 
PaTKo naBJ10Bl1n, pen, nporp, 
KaH,nI1,naT je ayrop 11J111 xoayrop 22 HaY4HI1X 11 CTPY4HI1X panoua 06jaBJbeHI1X y 
4aCOnl1CI1Ma 11J111 113J10)l(eHI1X Ha ,nOManI1M 11 MeljyHapo,nHI1M xoudrepeauajaaa. 
Pa,nOBI1 icaunanara 06jaBJbeHI1 y MeljyHapo,nHI1M 4aCOnl1CI1Ma ea ISI J1I1CTe KOjl1 cy 
nenocpenno nOBe3aHI1 ea TeMoM ,nOKTopCKe ,nl1cepTaUl1je cy: 
Pao06U «auouoama O6ja6.1benUy epxynctcuu MeljynapoonUM uaconucuua (M21): 
1.	 Pavlović R., Pavlović I.: Influence of rotatory inertia and transverse shear on stochastic 
instability of the cross-ply laminated beam, International Journal ofSolids and Structures, 
(2005), Vol. 42( 18-19), str. 4913-4926. 
2.	 Pavlović R., Kozić P., Rajković P., Pavlović I.: Dynamic stability of a thin-walled beam 
subjected to axial loads and end moments, Journal ofSound and Vibration, (2007), Vol. 
301(3-5), str. 690-700. 
3.	 Pavlović R., Rajković P., Pavlović I.: Dynamic stability of the viscoelastic rotating shaft 
subjectet to random excitation, International Journal ofMechanical Sciences, (2008), Vol. 
50(2), str. 359-364. 
4.	 Pavlović R., Kozić P., Pavlović I.: Dynamic stability and instability of a double-beam 
system subjected to random forces, International Journal ofMechanical Sciences, (2012), 
Vol. 62( 1), str. 111-119. 
5.	 Pavlović I., Ćirić 1., Đekić P., Nikolić V., Pavlović R., Ćojbašić Ž., Radenković G.: 
Rheological model optimization using advanced evolutionary computation for the 
analysis of the influence of recycled rubber on rubber blend dynamical behavior, 
Meccanica, (2013), Vol. 48(10), str. 2467-2477. 
Paooeu «auouoama otijae.uenu y ucmannymum uehynapoouuu uaconucuma (M22): 
1.	 Pavlović R., Rajković P., Pavlović I.: Amost sure stability of a moving elastic band, 
Trans. ASME Journal ofApplied Mechanics, (2008), Vol. 75(4), str. 041016. 
2.	 Pavlović R., Kozić P., Mitić S., Pavlović I.: Influence of rotatory inertia on dynamic 
stability of the viscoelastic symmetric cross-ply laminated plates, Mechanics Research 
Communications, (2012), Vol. 45, str. 28-33. 
Pa006U «auouoama očjae.uenu (WlU tiuhe očjaenenu) y MeljynapoonUM uaconucuma (M23): 
1.	 Pavlović R., Kozić P., Mitić S., Pavlović I.: Stochastic stability of rotating shaft, Archive 
ofApplied Mechanics, (2009), Vol. 79( 12), str. 1163-1171. 
3 
2.	 Pavlović I., Pavlović R., Kozić P., Janevski G.: Almost sure stochastic stability of a 
viscoelastic double-beam system, Archive of Applied Mechanics_(2013), Vol. 83(11), str. 
1591-1605. 
3.	 Janevski G., Kozić P., Pavlović I.: Moment Lyapunov exponents of the parametrical 
Hill's equation under the excitation of two correlated wideband noises, Structural 
Engineering and Mechanics , Pazi ne 6J1TJ1 WTaMnaH y 2014. rOj(J1HJ1. 
Pa008U O6ja 8.1b enUy «aconucuua Hau.UOHaJlH02 snauaja (M50): 
1.	 Ćirić 1., Ćojbašić Ž., Tomić M., Pavlović M., Pavlović V., Pavlović I., Nikolić V.: 
Intelligent control of DaNI robot based on robot vision and object recognition, Facta 
Universitatis, (2012), Vol. 11(2), str. 129-140. 
Caontumetea «auouoama Ha Me~YHapOOHUM CI<yno8UMa tumaunana y 36oPHuU.UMa paooea 
(M33): 
1.	 Nikolić V., Ćojbašić Ž., Ćirić I., Pavlović I.: Advanced Control Concept for the Remote 
Heating System of Niš, Proceedings ofthe IX Triennial International SAUM Conference on 
Systems, Automatic Control and Measurements,ISBN 978-86-85195-49-5, (2007), str. 45-49, 
Niš. 
2.	 Pavlović R., Kozić P., Pavlović I.: Influence of rotatory inertia on dynamic stability of 
the symmetric cross-ply laminated plates, 2nd International Congress ofSerbian Society 
of Mechanics (IConSSM 2009), Section D-04 (Interdisciplinary and Multidisciplinary 
Roblems) Palić (Subotica), Serbia. 
3.	 Pavlović I., Ćirić 1., Đekić P.: Optimal rheological model parameter setting for 
viscoelastical elements, l" International Conference (Mechanical Engineering in the 2Jst 
century), (20JO),str. 37-40. Niš, Serbia. 
4.	 G. Janevski, P. Kozić, Pavlović I.: Moment Lyapunov exponents and stochastic stability 
of a thin-walled beam driven by real noise, 3rd International Congress ofSerbian Society 
ofMechanics (IConSSM 201 J), str. 517-533 (C-21), Vlasina lake, Serbia. 
5.	 Pavlović R., Pavlović I., Stojanović V.: Influence of transverse shear and rotary inertia 
on vibration and stability of cross-ply laminated plates, 3rd International Congress of 
Serbian Society ofMechanics (IConSSM 2011), str. 975-985 (D-06), Vlasina lake, Serbia. 
6.	 Pavlović R., Rajković P., Pavlović I.: The numerical treatment of fractional differentiai 
4th equations for the lateral vibrations of an axially compressed visco-elastic rod, 
Serbian-Greek Symposium, (D-06), Vlasina lake, Serbia. 
7.	 Ciric 1., Pavlovic I., Petrovic E., Djekic P., MilisavIjevic J.: Evolutionary computation for 
viscoelastic element model parameters estimation, Proceedings ofthe 28th Danubia-Adria 
Symposium on Advances in Experimental Mechanics (2011), str. 241-243, Budapest, 
Hungary. 
8.	 Janevski G., Nešić N., Kozić P., Pavlović I.: Transverse vibration of a damped beam 
4th with one step change subjected to axial force, International Congress of Serbian 
Society ofMechanics (IConSSM 20J3), str. 541-546, (C-44), Vrnjačka Banja, Serbia. 
9.	 Pavlović I., Pavlović R., Kozić P., Janevski G., Cirić 1.: Stochastic stability of a 
viscoelastic double-beam system under wideband noises, 4th International Congress of 
Serbian Society ofMechanics (IConSSM 2013), str. 559-564. (C-47), Vrnjačka Banja, Serbia. 
10. Pavlović I., Pavlović R., Kozić P., Janevski G., Cirić I.: Stability of a Viscoelastic 
2nd Nanobeam Under Real-Noise Excitation, International Conference (Mechanical 
Engineering in the 21st century), (2013), str. 45-48, Niš, Serbia. 
4 
Caontumetsa «auouoama Ha cxynoeuua HaU.UOHaJlH02 suauaja tumamnana y 36opHUl(UMa 
paooea (M63): 
1.	 Nikolić V., Ćojbašić Ž., Ćirić L, Pavlović I.: Savremeni koncepti upravljanja 
dislociranim objektima komunalnih sistema, Vodovod i kanalizacija, 2007,Zbornik 
radova, str. 48-54, Tara, Serbia. 
2.	 Nikolić V., Ćojbašić Ž., Pavlović I., Ćirić L: Inteligentno daljinsko upravljanje sistemima 
za vodosnabdevanje i tretman otpadnih voda, 31. naučno-stručni skup sa međunarodnim 
učešćem HIPNEF 2008, Zbornik radova, str. 455-460, Vrnjačka Banja, Serbia. 
Texuuuka petuema «anouoama (M80): 
1.	 Ćojbašić Ž., Nikolić V., Ćirić L, Pavlović I.: Heypo-tpaan KJIacH<JlHKaTop 06jeKTa KO):( 
p060TcKe BH3Hje CJIO~eHOr peXa6HJIHTaUHOHor p060TcKor CHCTeMa <l>PIIEH,lJ: (20 ll). 
Yuetuhe «auouoama y nayuno uCmpaJICU6all«UM HaU.UOHaJlHUM npojesmuua: 
1.	 HaY4Ho-HCTpaJKHBa4KH npojexar KOjH <pHHaHCHpa MHHHCTapCTBO sa nayxy H 3awTHTy 
JKHBOTHe cpezunte Peny6J1HKe Cpčuje. Caapesieuo ):(aJbHHCKO ynpaan.an.e CHCTeMHMa aa 
nonocaafiaenau,e H TpeTMaH oTna):(HHX nona, EB. 6poj 6370. PYKoBonHJ1au npojexra np 
BJ1acTHMHp l-IHKoJ1Hn, pen. nporp, 
2.	 HaY4Ho-HCTpaJKHBa4KH npojexar KOjH <pHHaHCHpa MHHHCTapCTBO sa aayxy H 3awTHTy 
JKHBOTHe cpenuue Peny6J1HKe Cpčnje, ,lJ:eTepMHHHCTH1.IKa u CTOXaCTU1.IKa cTa6HJIHOCT 
MeXaHH1.IKHX CUCTeMa. EB. 6poj 144023. PYKoBo,nHJ1au npojexra np PaTKo naBJ10BHn, pen, 
npodi. 
3.	 HaY4Ho-HcTpaJKHBa4KH npojexar KOjH <pHHaHCHpa MHHHCTapCTBO aa aayxy H 3awTHTy 
JKHBOTHe cpennae Peny6J1HKe Cpčnje. ,lJ:HHaMH1.IKa cTa6HJIHOCT H HeCTa6HJlHOCT 
MeXaHH1.IKHX CHCTeMa non ):(ejcTBoM CTOXaCTH1.IKHX nopesrehaja. EB. 6poj 174011. 
Pyxoaozurnau npojexra np PaTKo naBJ10BHn, pen, nporp, 
Yuetuhe «auouoama y nayuno UCmpaJICU6all«UM Me!jyHapooHUM npojetonuua: 
1.	 EHJ1aTepaJ1HH npojexar DAD-MNTR RS, y OKBHpy nporpaua "PPP Serbien" Bremen-Niš. 
Robust Vision for Rehabilitation Robotics, 2009-2011. 
2.	 EHJ1aTepaJ1HH npojexar DAD-MNTR RS, y OKBHpy nporpasia "PPP Serbien" Bremen-Niš. A 
novel apprroach to human detection and tracing in robotics, 2012-2013. 
3.	 OHJ1aTepaJ1HH npojexar DAD-MNTR RS, Y OKBHpy nporpava "PPP Serbien" Bremen-Niš. 
Intelligent control of smart structures, 2013-2014. 
AHaJIH3a norcropcice nnceprauaje 
,nOKTopcKa ,nHcepTaUHja KaH,nH,naTa I1BaHa naBJ10BHna, zumn. Maw. HHJK, nanacaaa je Ha 
156 crpana ES diopwara. Op06J1eMaTHKa anannaupana y ,nHcepTaUHjH H3J10JKeHaje y 8 nornaarsa y 
OKBHpy KOjHX cy yao.aaa paavarparsa H 3aKJhY4aK. Canpxcaj zurcepraunje nar je Ha n04eTKY pana. 
Ha xpajy pana je cnucax rnrreparype ea 72 6H6J1HOrpaQ>cKe jezuraue. ,[(HcepTaUHja canpxca 58 
rpacPH4KHx npnnora. 
Canpxcaj TeKCTa noxropcxe ,AHCepTaUHje H3J10JKeH je Kp03 cneneha nornasrsa: 
l.	 YBO,n. 
2.	 OCHOBH BHCKOeJlaCTH4HHX MaTepHjaJla. 
3.	 HeJlOKaJlHa reopnja eJlaCTH4HOCTH. 
4.	 CJly4ajHH npouecu. 
5 
5. ,[(I1HaMI14Ka cTa611J1HOCT CI1CTeMa BI1CKOeJ1aCTI14HI1X rpena, 
6. ,[(I1HaMI14Ka cTa611J1HOCT uanocrpyxrypa. 
7. CTOXaCTI14KO ycpezuseu,e zipyror pena, 
8. 3aKJbY4aK. 
L(OKTopCKy zmceprauajy «annnnara Hsana naBJ10Bl1na, zumn, Maw. I1H:>K, 411HI1 ocav 
nenosa KOjl1 cy 3ace6HO QlopMl1paHI1 no nornaersnaa. 
Y npBOM nornaarsy nar je npernen HajHoBHjl1X I1CTpa:>KI1Bafha Kp03 ananasy panosa y 
06J1aCTI1 CTOXaCTI14Ke cTa611nHOCTI1 .nI1CKpeTHI1X 11 KOHTI1HyanHl1x MeXaHI14KI1X CI1CTeMa. Zlare cy 
.ne<l>I1HI1Ul1je CTOXaCTI14Ke cTa611J1HOCTI1 11 MeTo.ne sa onpehnaan,e CTOXaCTI14Ke cTa611J1HOCTI1 
KOHTI1HyaJ1HI1X CI1CTeMa: ,[{l1peKTHa MeTo.na Jbanynoaa, MeTo.na KOHCTpyKUl1je <PYHKUI10Hana 
Jbanynoaa 11 MeTo.na .nI1CKpeTI13aUl1je. Taxohe, npaxasaa je nocrynax onpehnearsa excnouerrra 
Jbanynosa 11 MOMeHaTa excnouenara Jbanyaosa npl1MeHOM neprypčauaoue MeTo.ne. 
Y npyro» nornaarsy npaxasaa je yrnuaj speaena 11 TeMnepaType Ha nerpopuauaje 11 
nanose y MaTepl1janl1Ma xana OHI1 ucnon.aaajy BI1CKOeJ1aCTI14He ocočune. Y tenaca-moj reopajn 
eJ1aCTI14HOCTI1 aese 113Meljy nanona 11 .ne<popMaUl1ja cy J1I1HeapHe 11 He 3aBI1Ce on spevena jep cy 
yseneae npernocrasxe o Manl1M .ne<popMaUl1jaMa y MaTepl1jany na ce MO:>Ke npl1MeHI1TI1 npaaunn 
cynepnosauaje aa orrrepehersa 11 nerpopaauaje. EKCnepl1MeHTI1 cy noxaaanu na HaKOH HarJ10r 
nejcrsa orrrepehen.a, Koje 3aTI1M ocraje KOHCTaHTHO, .ne<popMaUl1ja pacre ea BpeMeHOM. 06pHYTO, 
HaKOH HarJ10r yxnarsarsa orrrepehersa nerpopaaunja ce He ry611 TpeHyTHO. Y unrsy omrcaaarsa 
OBaKBl1X <}leHoMeHa <popMynl1caHe cy onurrnje aese 113Meljy nanoaa 11 nerpopvauaja Koje Y311Majy y 
06311P l1 apeve. npOMeHJbI1BOCT MeXaHI14KI1X ocočnua MaTepl1jaJ1a TOKOM spevena Mo.nenl1pa ce 
KOM611HOBafbeM l1.neanHO enaCTI14HOr Tena 11 BI1CK03HOr <}lnYI1.na. EnaCTI14He ocočnne MaTepl1jaJ1a 
onncyjy ce Hook-OBI1M, a BI1CK03He Newton- OBI1M 3aKOHOM. Pe0J101IIKI1 Mo.nen enaCTI14HOCTI1 je 
onpyra ea J1I1HeapHoM KapaKTepI1CTI1KOM, npu 4eMy je Koe<pI1Ul1jeHT nponOpUl10HanHOCTI1 Mo.nyn 
enaCTI14HOCTI1, a peOnOlIlKI1 Mo.nen BI1CK03HOCTI1 je nparyumaua Koja I1Ma xapaxrepncrmcy na je 
6p311Ha nponopunonanna narrony. 0pI1Ka3aHI1 cy aaj-reurhe KOpl11I1neHI1 Mo.nenl1 MaTepl1jana ea 
BI1CKOeJ1aCTI14HI1M ocočanava: Voigt-Kelvin-os Mo.nen, Maxwell-os Mo.nen, reaepanacana 
Maxwell-os Mo.nen, craunapnna BI1CKOenaCTI14HI1 Mo.nen (Zener-os) 11 TponapaMeTapCKI1 Mo.nen. 
Y rpehev nOrJ1aBJbY y KpaTKI1M uprava ormcaaa je HeJ10KanHa 'reopnja enaCTI14HOCTI1 
yBoljelheM nonyacxe Eringen-ose jenna-tane aese 113Meljy noxannor 11 HenOKaJIHOr nanona. 
TIpeTnOCTaBJbeHa je <pyHKUl1ja jesrpa Kao Green-OBa <pyHKUl1ja, a I1HTerpaJ1Ha aesa 113Meljy 
nOKaJ1Hor 11 HenOKaJ1HOr nanoua npencraan.ena je y eKBI1BaneHTHoj .n11<pepeHUl1jaJ1Hoj <l>OpMI1, rne 
je .n11<pepeHUl1janHI1 oneparop Helmholtz-osor I1nl1 bi-Helmholtz-osor runa, 0pl1Ka3aH je Mo.neJ1 
je.nHo.nI1MeH3I1oHor KOHTI1HyaJ1HOr Mo.nena HaHO .nI1MeH311ja KOjl1 ce .ne<pI1Hl1lIIe Kao HaHO rpena, 
TaKaB Mo.nen ce 1I1l1pOKO KOP"CT" Y I1H)I(elhepcKoj npaKCI1. Taxohe, npl1MeHOM HeJ10KanHe 'reopaje 
eJ1aCTI14HOCTI1 11 aa CJ1y4aj Voigt-Kelvin-osor Mo.nena MaTepYljana 113Be.neHe cy OCHOBHe .nI1HaMI14Ke 
je.nHa4HHe HaHO rpena Euler-Bemoulli-jesor, TI1MOWeHKoBor 11 Reddy-jeaor runa. 
Y 4eTBpToM nornaarsy nare cy oCHOBHe BeJII1411He cny-rajnnx npOMeHJbI1BI1X 11 cnysajnnx 
npoueca (<pyHKUl1ja pacnoziene sepoearuohe 11 <pyHKUl1ja rycrune pacnoziene aeposaruohe, 
MaTeMaTI14KO 04eKI1Balhe 11 CTaTI1CTI14KI1 MOMeHTI1, KOpeJ1aU110He <pyHKUl1je 11 <pyHKUl1je 
cnexrpamre rYCTI1He). Canpxcaj osor nornaan.a OrpaHI14eH je Ha onacaaan,e CJ1y4ajHl1x npoueca 
KOjH npencraarsajy nofiyne y .nI1HaMH4KI1M CI1CTeMHMa, pa3MaTpaHI1M y zurceprauaju. ,[{eTaJbHO cy 
npaxasaua CJ1y4ajHI1 npouecn: GaUSS-OB 11 xapMoHl1jCKI1 npouec, Wiener-os npouec, npouec 6enor 
uryaa, npouec peannor uryva (Ornstein-Uhlenbeck-os npouec), npouec OrpaHI14eHOr uryva. 
Taxohe, nare cy OCHOBe 'reopaje CTOXaCTI14KI1X )lI1QlepeHUl1jaJIHI1X jenna-urna, Itć-ose 11 
CTpaTOHOBI14eBe, Kao 11 penaunje 113Meljy CTOXaCTI14KI1X I1HTerpaJIa y Itć-osoj 11 CTpaTOHOBI14eBoj 
6 
mrrepnperaunja. Ha xpajy onor nornasrsa 113J10:>KeHa je MeTo,na CTOXaCTI14KOr ycpezueersa npsor 
pena xojy je pa3B110 CTpaTOHOBI14. Ona npeztcraan.a npuveny MeTo,ne ycpezuseisa Boron.yčon­
MI1TpOnOJbCKOr sa 06114He ,n11<pepeHUl1jaJ1He jezuta-taue ea MaJ1I1M napaverpoa Ha CTOXaCTI14Ke 
,n11<pepeHU11j aJ1He jenna411He. 
Y neTOM nornaarsy aaanaanpaa je MeXaHI14KI1 CI1CTeM KOjl1 ce cacroju on nae napanernre 
xovoreue BI1CKOenaCTI14He Euler-Bemoulli-jese rpene non nejcreov aKCl1jaJ1HI1X orrrepeheaa, Koje 
cy KOHTI1HyaJ1HO cnojeue Winkler-oaav eJ1aCTI14HI1M cnojev. AKcl1jaJ1He npl1TI1CHe CI1J1e nenyjy Ha 
xpajesnaa rpezia 11 I1Majy ,neTepMI1HI1CTI14KI1 11 ~TOXaCTI14KI1 neo. Kopauihersea ,nl1peKTHe MeTo,ne 
Jbanynosa 11 MeTo,ne excnoneirra Jbanyuosa o.apeheaa cy YCJ10BI1 CKOpO cnrypae cTa611J1HOCTI1 sa 
npouece KOjl1 He canpxce 6eJ111 cnexrap (Gauss-os 11 xapMoHl1jCKI1 npouec) 11 sa umpoxonojacne 
npouece 6enor, pearmor 11 OrpaHI14eHOr uryva, 06nacTI1 CKOpO cnrypne cTa611J1HOCTI1 ,n06l1jeHe cy 
y q>yHKUl1jl1 spevena perapnaunje, casojue KpyTOCTI1, KpyTOCTI1 Winkler-osor enaCTI14HOr cnoja, 
I1HTeH311TeTa nerepM11 HI1CTI14 KI1X KOMnOHeHTI1 axcnjarnurx orrrepehen,a 11 napaverapa 
CTOXaCTI14KI1X npoueca, 3a CTOXaCTI14Ke npouece xoja He canpxce 6enl1 cnexrap HyMepl14KI1 
pe3YJ1TaTI1 ,n0611jeHI1 cy 3aMeHOM HecBojcTBeHI1X mrrerpana CyMOM npoaasona «oediauujeuara 
GauSS-OBI1X xeanparypanx diopvyna 11 Benl1411Ha no,nI1HTerpaJ1HI1X cPyHKUl1ja cpa-ryaarux y 
HyJ1aMa opTOrOHaJ1HI1X nOJ1I1HOMa. 3a CJ1y4ajHe npouece KOjl1 I1Majy Gauss-osy pacnoneny rycruue 
eepoaaruohe npnvea.ene cy Gauss-Hermite-ose xaanparypae diopvyne, a sa npouece KOjl1 I1Majy 
xapuonnjcxy pacnoneny rycrune sepoaaraohe xopaurhene cy Gauss-lJe6111IIeBJbeBe xsanparypne 
<popMyJ1e. 
3aTI1M je aaanasnpan cnysaj xana je rop-sa rpena orrrepehena npl1TI1CHOM Cl1nOM Koja I1Ma 
,neTepMI1HI1CTI14KI1 11 CTOXaCTI14Kl1 neo, a ztoisa je l13nO:>KeHa cavo nejcray ,neTepMI1HI1CTI14Ke 
npl1TI1CHe cl1ne. 3a OBaKaB cnY4~ npl1TI1CHOr onTepenel-ba TaKolje cy o,npeljeHI1 ycnoBI1 CKOpO 
cnrypae cTa611nHOCTI1 sa npouece KOjl1 He canpzce 6eJ111 cnexrap (Gauss-os 11 xapMoHl1jCKI1 npouec) 
H npouece KOjH I1Majy 6eJ111 cnexrap, Ha OCHOBy ,n06HjeHl1x pe3YJ1TaTa 3aKJbY4eHo je na ce 
CMal-belheM casojnax KpyTOCTI1 aoca-ta cMalhyjy 06nacTI1 cTa611J1HOCTI1. AHaJ111311paH je yrnuaj 
npoveae KpyTOCTI1 Winkler-osor enaCTI14HOr eneja 11 3aKJbY4eHo je .aa ce noaeharsev KPYTOCTI1 
rtosehaaa očnacr cTa6I1nHOCTI1. OBO nosehan,e je 3Ha4ajHI1je sa Mal-be Bpe,nHoCTI1 KpyTOCTI1, ,nOK ce 
noseharsea KpyTOCTI1 cnoja renneuuaja ysehan.a 06nacTI1 cTa6I1nHOCTI1, anasajno cMafhyje. 3a 
npouece KOjl1 He canpxce 6enl1 cnexrap yrspheao je raxohe, na cy 06nacTI1 cTa611nHOCTI1 sa Gauss­
OB npouec Bene Hero sa xapMoHl1jCKI1 npn je,nHaKI1M napaverpava CI1CTeMa. Kana cy 06e rpene 
orrrepehene npl1TI1CHJIIM cnnava, Onl1CaHJIlM CTOXaCTI14KI1M npouecnua fl Ct) 11 fz Ct) KOjl1 I1Majy 
HOpMaJ1Hy pacno,neJ1y BepOBaTHone, 3aTI1M Ka,na cy 06a npoueca HeKopenHpaHI1 6eRI1, peaJ1HI1 11 
OrpaHI14eHI1 WyMOBI1 onpeheue cy 06J1aCTI1 cTa611nHocTH y <pyHKUl1jl1 nncnepaaja cnysajuux 
npoueca. Yrspheuo je na nopacr spevena perapnaunje 11 KpyTOCTI1 rpena anasajno YTH4e Ha 
noaehaa.e 06J1aCTI1 cTa611nHOCTI1 rpena, ,nOK je yruuaj nosehaa,a KpyTOCTI1 Winkler-oaor 
enaCTI14HOr eneja 3HaTHO Mal-bl1. 
Y weCTOM nornann.y y npBOM neny ananaanpaaa je ,nI1HaMI14Ka cTa611nHocT pa3nl1411TI1X 
nanocrpyxrypa. Hsaeneaa je ,nl1cPepeHUl1janHa jenaa-nnra TpaHC<pep3anHI1X ocuanauaja 
Bl1CKOenaCTl14He naaorpene Voigt-Kelvin-osor Mo,nena MaTepl1jana, Ha OCHOBy ,nI1HaMI14KI1X 
jennavuna «pera-sa eneverrrapnor nermha rpene, Hajnpe je onpeheua očnacr CKOpO curypne 
cTa6I1nHOCTI1, yHl1cPopMHe BI1CKOeJ1aCTI14He Rayleigh-jese naaorpene 113nO:>KeHe nejcrsy 
TpaHCBep3aJlHOr orrrepehen.a no je,nI1HI1UI1 ,nY:>KI1He ql 11 qz 11 axcnj aJ1 HOj CI1J111 npl1TI1CKa, 
xopmnheu.e« ,Al1peKTHe MeTo,ne Jbanynoaa 11 MeTo',nOM MOMeHaTa excnouenra Jbanyuosa. Y 
cny-iajy kana je npl1TI1CHa cnna GaUSS-OB 11 xapMoHl1jCKI1 npouec ofinacr CKOpO cnrypae 
cTa611J1HOCTI1 ozipehena je «opnurhersea ,nl1peKTHe MeTo,ne Jbanynosa, a xaaa je npl1TI1CHa cuna 
runa peannor H OrpaHI14eHOr uryva očnacr CKOpO cnrypue cTa611nHOCTI1 ,ll,06l1jeHa je 
7 
cpa-tyaasatsev MOMeHaTa excnoueirra Jbanynosa. BaJ1H.n.aUHja .n.06HjeHHx pe3YJ1TaTa H3BpweHa je 
MeTo.n.OM cHMyJ1aUHje xojy je opHrHHaJ1HO pa3BHO H npHMeHHO xaazuutar. 06J1aCTH cTa6HJ1HOCTH 
.n.06HjeHe cy y <pyHKUHjH speveaa perapnaunje, aapajanca (nacnepauje) CToxaCTH4KHX npoueca, 
reoverpajcxnx napaverapa, KOeQlHUHjeHTa HaHOCKaJ1HpaI-ba H HHTeH3HTeTa .n.eTepMHHHCTH4Ke 
KOMnOHeHTe aKcHjaJ1HOr orrrepehersa. Jenan on Ba:>KHHX 3aKJbY4aKa koja nasce sa uaaocrpyxrype, 
jecre na ce 06J1aCT cTa6HJ1HOCTH nosehaaa CMal-bHBal-beM KoecPHUHjeHTa HaHOCKaJ1HpaI-ba H 
noaehaearsev epeveaa perapnaunje. 3a Helmholtz-OB THn jesrpa 06J1aCTH cTa6HJ1HOCTH cy Bene 
Hero sa bi-Helmholtz-OB. OnWTe rosopehu, HeJ10KaJ1HH eQleKTH cvan.yjy 06J1aCT cTa6HJ1HOCTH 
Rayleigh-jese nanorpezte. 
Y npyrov neny osor nornasn,a aHaJ1H3HpaH je MexaHH4KH CHCTeM KOjH ce cacrojn on nse 
TaHKe xovorene aaaorpezie cnojene eJ1aCTH4HHM CJ10jeM Winkler-onor runa. Fpezie cy aKcHjaJ1HO 
orrrepehene npHTHCHHM CHJ1aMa Koje HMajy .n.eTepMHHHCTH4KH H CToxaCTH4KH neo, YCJ10BH CKOpO 
cnrypae CToxaCTH4Ke cTa6HJ1HOCTH onpehene cy npHMeHOM ,nHpeKTHe MeTo,ne Jbanynoaa, 3a 
CJ1y4aj xana je CToxaCTH4KH neo npHTHCHHX CHJ1a npouec KOjH He canpxor 6eJ1H cnekrap YCJ10BH 
CKOpO cnrypue CToxaCTH4Ke cTa6HJ1HOCTH ,n06HjeHH cy y QlyHKUHjH KoecPHUHjeHTa BHCK03Hor 
npuryurea,a, KpyTOCTH eJ1aCTH4Hor cnoja, KoecPHUHjeHTa HaHOCKaJ1Hpal-ba H HHTeH3HTeTa 
.lleTepMHHHCTH4KHX KOMnOHeHTH aKcHjaJ1HOr npHTHCHor orrrepehersa. Yrspheno je na ce 
CMal-bel-beM KpyTOCTH Winkler-osor eJ1aCTH4Hor cnoja cvan.yje 06J1aCT cTa6HJ1HOcTH. Kao H y 
nperxoznrov npinrepy rako H sa onaj MexaHH4KH CHCTeM yrspheno je na je 06J1aCT cTa6HJ1HOCTH aa 
Helmholtz-os THn jesrpa Bena Hero sa bi-Helmholtz-OB. Kana ce .n.eTepMHHHcTH4KH neo npHTHcHHX 
CHJ1a cMal-byje raxo na OHe nocrajy 3aTe3He Ta nojaaa H3a3HBa noaehan,e 06J1aCTH cTa6HJ1HOCTH, 
,nOK noaehan,e KoecPHUHjeHTa HaHOCKaJ1Hpal-ba cvan.yje 06J1aCT cTa6HJ1HOCTH. 
Y ce,nMoM nOrJ1aBJbY najnpe je H3J10:>KeH nocrynax CToxaCTH4Kor ycpemsersa zipyror pena, 
a 3aTHM je aHaJ1H3HpaHa cTa6HJ1HOCT xperaa,a MexaHH4Kor CHCTeMa 4Hje xperarse onucyje 
ztaonapaverapcxa Hill-ona ,nHQlepeHUHjaJ1Ha jenna-mna npn nejcrny .n.Ba KOpeJ1HpaHa 
unipoxonojacna npoueca, Ha ycpeznseae Itč-ose ,nHQlepeHUHjaJ1He jenna-nure Koje oztroaapajy p­
TOM creneny aopve npaveiseaa je MeTo,na CToxaCTH4Kor ycpezuseisa npsor Itf .n.pyror pena, 
EKcnOHeHT Jbanynosa H MOMeHTH excnoueara Jbanyaosa onpehean cy Kao penosa MaJ10r 
cPJ1yKTyaUHoHor napaMeTpa E. ~OMeHTH eKcnOHeHTa JbanyHoBa cy Ba:>KHH KapaKTepHCTH4HH 
čpojean KOjHM ce onncyje ,nHHaMH4Ka cTa6HJ1HOCT CToxaCTH4KHX CHCTeMa. Kana je p-TH MOMeHTH 
excnouerrra Jbanyuoaa HeraTHBaH peureu.e Koje onncyje «pera-se CToxaCTH4Kor CHCTeMa je 
cTa6HJ1HO. OBaKO onpehenn aHaJ1HTH4KH H3pa3H sa eKcnOHeHT Jbanynosa H MOMeHTe excnoaenra 
Jbanynosa HCKopHIIIneHH cy sa aHaJ1H3Y CKOpO cnrypne cTa6HJ1HOCTH H cTa6HJ1HOCTH MOMeHaTa 
CTaUHOHapHor peurersa Koje ornrcyje xperan-e TaHKe xouorene rpene H3J10:>KeHe aKcHjaJ1HOM 
nparucxy H npnryuren.y. OBe BeJ1H4HHe cy unrponojacna He3aBHCHH CToxaCTH4KH npouecu MaJ10r 
HHTeH3HTeTa. Fpaunue CKOpO cnrypne cTa6HJ1HOCTH H cTa6HJ1HOCTH MOMeHaTa onpehene Ha OCHOBy 
aHaJ1HTH4KHX aspaaa, a cpa-iynare cy H HyMepH4KH npHMeHOM cHMyJ1aUHOHOr aJ1rOpHTMa KOjH 
onrosapa MeTo,nH MOHTe Kapne. OBaKO ,n06HjeHH pe3YJ1TaTH noxasyjy BeJ1HKY nonynapnocr 4HMe 
ce norsphyje Ta4HOCT anpOKCI1MaTI1BHI1X aHaJ1HTI14KHX pe3YJ1TaTa. 
Y 3aKJbY4KY ayrop naje Ha CI1CTeMaTI14aH Ha411H 3aKJbY4Ha paavarpan,a csaxor cerveirra 
.n.OKTopCKe nnceprauaje H HCTI14e Haj6HTHHje pe3YJ1TaTe no KOjHX je nourao HCTpa:>KHBaJheM, a 
raxohe nasonn KOj H cy MorynH .n.aJbH npasun ncrpaaoreaisa y OBOj 06J1aCTH. 
3AKJbyqAK II TIPE,l(JIOr 
Ha OCHOBy H3J10:>KeHe aHaJ1H3e noxropcxe zinceprauaje H OCTBapeHHX pe3YJ1TaTa 4J1aHOBH 
KOMHcHje sa oueuy H ončpany saxn.yuyjy na: 
8 
.:. canpxcaj nonnere jlOKTOpCKe jlHCepTaUHje y nornyaocrn onrosapa TeMH npaxsahenoj on 
crpane HaCTaBHO-HaY4Hor Bena MaWHHCKOf QlaKYJ1TeTa YHHBep3HTeTa y HHWy, 
.:. KaHjlHjlaT je OBJ1ajlaO nOTpe6HHM 3HafbHMa H3 pa3J1H4HTHX 06J1aCTH, a Hap04HTO H3 
06J1aCTH OCUHJ1aUHja H cTa6HJ1HOCTH CToxaCTH4KHX MexaHH4KHX CHCTeMa, 
.:. xanzuinar je HCnOJhHO norpečny caMOCTaJ1HOCT H HHBeHTHBHOCT y HaY4HOHCTpa)KHBa4KOM 
pany, 
.:. KaHjlHjlaT je nourao no opHrHHaJ1HHX pe3YJ1TaTa KOjH cy ny6J1HKOBaHH y 
BHCOKopaHfHpaHHM -racorurcnua H caonurrenu Ha KOHQlepeHUHjaMa H3 yace naysue 
06J1aCTH KOjOj npnnana reva jlOKTOpCKe jlHCepTaUHje, 
.:. jl06HjeHH pe3YJ1TaTH npyxcajy MorynHocT sa narsa HyMepH4KO-TeopHjcKa HCTpa)KHBaIha y 
OBOj 06J1aCTH, 
.:. pan je onronapajyhe KOHUHnHpaH, TeXHH4KH KBaJ1HTeTHO ypahen H ouoryhana npernezuro 
npahetse H3J10)KeHor canpscaja H jl06HjeHHx pe3YJ1TaTa ncrpaxoiaan,a. 
Ha OCHOBy cnera H3J10)KeHOr, 4J1aHOBH KOMHcHje cy MHWJbefba na nozurera jlOKTOpCKa 
zurceprauaja npencrasn,a spenaa jlOnpHHOCT H3Y4aBafbY np06J1eMaTHKe jlHHaMH4Ke cTa6HJ1HOCTH 
BHCKOeJ1aCTH4HHX MexaHH4KHX CHCTeMa non nejcraov CJ1y4ajHHx nopevehaja. KOMncaja 
npennaxce HaCTaBHO-HaY4HOM sehy Maunnrcxor QlaKYJ1TeTa y Hmuy zta nonaeru pazi xanzurnara 
IIBaHa UaBJIOBHlia, zurnn. Maw. HH)K. nozt Ha3HBOM 
",l(HHaMH'lKa cTa6HJIHOCT BHCKOeJIaCTH'lHHX KOHTHHyaJIHHX CHCTeMa nOL{ nejcraosr 
cny-iajnnx nopesiehaja" 
npHXBaTH Kao jlOKTOpCKy jlHCepTaUHjy H KaHjlHjlaTa n030Be Ha ycveuy jasuy ončpany, 
Y HHWy, Beorpany 4J1AHOBI1 KOMI1CI1JE 
oxročpa 2014. ron, ~~~.npo~.
 
MaWHHCKor ~aKYJlTeTa YHHBep3HTeTa y "HWy 
Yxca nay-raa 06J1aCT: Teopnjcxa H npauea.eaa examnca, 
G(Y.-Đ~ /' 
np Fopan H CK", noueur 
MaWHHCKor «I>aKyJlTe a YHHBep3HTeTa y "HWy 
Y)I{a H~J1aCT: Teopajcxa H npnverseua MexaHHKa. 
'Jtfl~tU (jJ Jle rzlCL .~ 
r pnpe.npar PajKoiHft, pen. npodi 
MaWHHCKor ~aKYJlTeTa YHHBep3HTeTa y HHWy 
Yaca aaysna 06J1aCT: MaTeMaTHKa H HH<popMaTHKa. 
~-r- ~Y'fD2L4?s-'/
 
np Haraura TpHWOBHIi, BaH. npodi, 
MaWHHCKor «I>aKyJlTeTa YHHBep3HTeTa y Beorpany 
Y)f(a nay-ura 06.naCT: .llHHaMHKa KOHCTpyKUl1ja. 
.a /~
 
LlP 30paH Fo.nyčoa ,pe.n. npodi. ~ eH3HjH 
MaWHHCKor ~aKYJlTeTa YHHBep3HTeTa y Beorpany 
Ysca aayvaa 06J1aCT: Teopujcxa H npHMefheHa MexaHHKa