Life Science Journal 2014;11(9) An Investigation of the longitudinal fluctuations of viscoelastic cores

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1 Lif Sin Journl (9) h://wwwlifiniom n Invigion of h longiuinl fluuion of violi or Kurnov Ni yg, Bjnov Vul Gmz Drmn of Gnrl Mh, Sumgi S Univriy, Sumgi, ZE 5, zrijn vul@gmilom r: I i nry o l rolm from ynmi rolm of violiiy ou fluuion of h violi ym whih iion r onoli o Volir' ingro-iffrnil quion of h II y h oluion of hi quion rquir rolm of n nlyil y of rnl, or h quion olv wih vriou numril mho In hi r h roxim oluion of hi quion for ny rnl mll vioiy i roo h iion in h form of row i riv, h originl of whih fir mmr i h oluion of hi quion riv y nown mho vrging, n h ouning of h uqun mmr of row imrov ojiv ury Influn of h uqun mmr of row on h iion i lul for zhniin' rnl n hown h i inr inr in frquny [Kurnov N, Bjnov V G n Invigion of h longiuinl fluuion of violi or Lif Si J (9):557-56] (ISSN:97-835) h://wwwlifiniom 9 Kywor: violiiy, hrogniy, uniformiy, longiuinl, niy, img, originl, inn moul of liiy, vrging mho Inrouion I i nown h h oluion of nonionry ynmi rolm for vriou ign h nlyil y of rnl of rlxion in' givn hrfor iion r unr onruion y mn of om roxim mho whih giv finl oluion of h ingro-iffrnil quion of fluuion of h violi ym, vrging rliz y mho, frzing mho, mho of oninuion n mho of ingrl rnformion of Ll, Fourir, Mllin n hir ominion [,,8,3] Howvr, mho of ingrl rnformion r inrly onn wih omlx rolm of h invr rnformion whih in of mor rl wn nion n formion invily rul in n of lrgr numr of u on rnh in h our of onour ingrion [,5] Mril n Mho In hi ril h roxim oluion of h quion of longiuinl fluuion of violi or for ny rnl mll vioiy i roo h img of h iion in h form of row i rzn, h originl of whih fir mmr i h oluion of hi quion riv y mho of vrging, n h ouning of h uqun mmr imrov h ury of h oluion of n ojiv I i now h h quion of h longiuinl fluuion of li or h h following form [,,]: x, ux,, u E () x G, E - Poion' numr whih hng in mll limi n hrfor i onir furhr onn, - mril niy, E - h innnou Young' moulu u x, - h movmn, - Lm' onn ling wih in () n oin: u x, u x, u x, x x ~ u x, x ing ino oun hi in h l quion n oin: ~ G n o um h h mril of or o mll vioiy, h ingrl mll rhr o uni, hrfor i oiiv n hrfor n oin following quion: 557

2 Lif Sin Journl (9) h://wwwlifiniom u x, ux, u x, lying Ll' ingr E () rnformion o h quion (5) r o im x x rmr n ing ino oun (3), n iniil oniion in h following oin: form: (7) u x, x u x, (3) x mll vlu of im rmr - i rhr lrg If w onir mril wih inn n ounry oniion w in h liiy, h img wih inr n o zro hrfor h inquliy i xu: u x, x u x, x l () Whr l - or lngh h ril oluion of h quion (), i inil no qul o zro w loo for in following: ux, X x ing ino oun i in h () for fining of funion n, w oin wo innn quion: X x X x Solving h fir quion unr ounry oniion (), w fin x X x o,,, l E - h of wv iriu hu, h ommon oluion of h quion of fluuion of violi or h following form: x, X x (5) u (6) X x - h oorin funion foun h oluion of h orroning li rolm lo on' n on h rmr hrrizing viou rori of mril of or, n funion i h oluion of h ingroiffrnil quion (5) hu, h rolm of rmin of i in or i ru o rmin of funion from h quion (5) hn h quion (7) n rrn in h or in in in n in n (8) o o in o o in o o If o h following ignion: in o o in, hn w r oin: in o in in o h l formul in Ll' n 558

3 Lif Sin Journl (9) h://wwwlifiniom 559 Coniring i in (8), w riv: (9) hrfor w n wri formul (9) in () From hr for h fir mmr fr h invr Ll' rnformion i i foun: () in o x h l formul i h oluion of h ojiv, riv y n vrging mho [,] For fining of h following roh w will rn i in loo: L () g f g f L - h oror of h rurn rnformion of Ll Mn, i i nry o lul h originl of funion For hi uro w will rn i in following: hn (3) in o x in x L gnrion of originl of h following roximion of row () on' rn iffiuly From () n () riv h xin of vioiy of mril in () l o nuion of ummry fluuion of or unr h xonnil lw n h hif i orv For lulion of influn of h mmr () on h iion, w will onir zhniin' rnl [,,] x Whr, - onn, - om mll rmr For hi rnl from formul () n oin: in in o x o o in o in o 6 in rg in

4 Lif Sin Journl (9) h://wwwlifiniom o rg - Eulr' Gmm funion ul For olyroyln r onru grh funion n h following vlu of rmr: 5 9 Fig Grh funion n for rmr: Fig Grh funion rmr: n for From figur i i viil h h ouning of h uqun mmr of row imrov h iion ury h gr vlu of frquny h rror i mll, n wih inr in frquny i inr mliu om vlu of im m 5% mliu Corroning uhor: Bjnov Vul Hmz - PhD in hnil in, oi rofor of "Gnrl Mh" Sumgi S Univriy, ZE5, zrijn E-mil: vul@gmilom frn Filov N vrging mho in iffrnil n ingro - iffrnil quion hn: FN, 97, 79 My VI Fluuion of ioroi violi ylinril hll, Mhni of olymr, 97,, Lrionov G S rh of fluuion rlxil ym vrging mho//mhni of olymr, 969, No 5, onov YuN Elmn of h iry Mhni of Soli Boi, M, Sin, Joh, D D Flui Dynmi of Violi Liqui / DDJoh // Sringr-Vrlg, 99 6 Muroh, I mr on h founion of linr violiiy / I Muroh//J Mh Phy Soli 99-Vol, 7-P Soo, Z Diffrnil quion n hir ingrl following from violriiy / Z Soo // hn CSV 99 - Vol 39, 6 - P Br C, Jng-Horng Yu Linr oniuiv rlion in ioroi fini violiiy // J of Eliiy Vol Chrinn M, Nghi PM Linr nonlinr violi oli // Mhni- 967 Vol P - 56

5 Lif Sin Journl (9) h://wwwlifiniom Colmn BD, Noll W Founion of linr violiiy // viw of Morn Phy- 96 Vol 33 - P 39-9 Govinj S, S rnion n omrion of wo lrg formion violiiy mol // J Engin M n hnol Vol P 5-55 Gurin Moron E, Hru Willim J On nrgi for nonlinr violi mril of ingl-ingrl y // Qur l Mh Vol P Kim В -K, Youn S -K violi oniuiv mol of rur unr mll oillory lo urimo on lrg i formion // rhiv of l Mh Vol 7- P Pr SW, Shry violi oniuiv mol for riul omoi wih growing mg // In J Soli Sruur Vol P /8/ 56

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