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I ," , I BO GIAO DUC VADAO TAO I '''' I TRUONG D~ HCT6NG HQP THANH PHO HO CHi MINH I TRAN VAN LANG sir DI)NG PHUONGPHA? 56 VAo M9T 56 BAI rOAN CO HQC Chuyen nganh Cd''''HQCV~TRAN81(H D~G }riaso 1 02 21 r[.]

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I TRUONG D~ H<;>CT6NG HQP THANH PHO HO CHi MINH

I

TRAN VAN LANG

sir DI)NG PHUONG PHA? 56 VAo M9T 56 BAI rOAN CO HQC

Chuyen nganh : Cd'HQCV~TRAN81(H D~G

r

I

I

J

TOM TAT LU!N AN

Ph6TienSi KhoaHQcTDanLy -

-Thanhph6 H~ChiMinh

1995

"

\ LuAnan nay duoc ho3n thanh tai Khoa Toan-Tin hoc

Twang D~i Hc;>cT6ng Hqp Thanh ph6 H6 Chi Minh

Ngum hu(mg dAn

- Ph6 Giao su Ph6 Ti€n 81Ng6 Thanh Phong

- Ph6 Ti€n 81Tran Thanh Trai

Ngum nh~n-K-et-l

Ngum nh*n xct 2

Ca quaD nh~n ~ct

Lu~n an se duqc bite v~ ~i H(>idbng cham lu~ an Nha nu6'e

hc;>p ~i: Tw<mgD~i Hc;>c T6ng Hqp Thanh ph6 H6 Chi Minh

C6 th€ tlm hi~u lu~ an ~i cae Thu vi~n

- Tw<mg D~i Hc;>cT6ng Hqp T19.H6Chi Minh

- Khoa Hc;>c T6ng Hqp Tp.If6 ChI Minh

- Trung Tam Khoa Hc;>c Tg Nhien va C6ng Ngh~ Qu6c Gia Vi~t Nam (Van Phong 2).

Ngay nay, vm nhUng phuong pMp loan hQc UnIt tmin hi~n d~i, s1,f pIlat trien ciia may Hnh ngay cang nhanh, fir d6 giup nhung ngHai lam (XJ

hQc c6 the giro quyel mQt htgng 1611cac biii loan cURminh Bhng Sl! k(}thgp

ba lInh vl!c Toan hQc-Tin HQc-Co hQc, mQt hu6ng mm duqc roo ra cho

nganh Co hQc trong thai dl;\ingay nay - nganh Co Tin hQc

KhOngngoai ml!c dicIt d6, trong lu~ an n'!\ychUng Wi muOn k~l hqp hM hoa ca ba Jinh V1!C,de giai quy<!tmQt sO bM toan Co hQc~ Ihe Chung wi sit dl;1OgmQt sO phuong phap sO nhu phuong phap sai pllan,

phuong pMp pllan ra luan hu6ng Ian ~ mQt chieu, phuong pM.p phan 1"a

thco qua trlnh v~lly, phuong pMp Ga1crkin,phuong pMp phau ttr hitu h~n, phuong phap khai trien ti~m ~ theo tham sO be, de khc\o sat 1D<?ls6

phuong trinh trong co hQc.DOngthai, bling ngOnngft tl1U~ltolin, chun!~loj

da ma boa thanh chuong trlnh boi cae ngOn ngu FORTRAN 4 (chl;\YIr~n may ffiM 360/501), FORTRAN 77, C, PASCAL (chl;\ytr~n cac may vi Unh) Qua vi~ tfnh loan tr~n may tfnh, chung Wi dii Idem nghi~m v/1.m.~t dinh tfnh cua roOhinb, cling nhu m~t dinh hrqng cua phuong phap Ngoili

ra, c6 mQt sOvan <Th,do duge mO hi dum d~ng mQt phuc1i1gtrlllh loan hl?G

hoWl chinh, n~n chUngWi ding dii kiem nghi~m tru6c, sau d6 mm <TUI!C Hnh loan Il;\ibbtlgmay tfnh de baa dam bai toan d~t ra, ding nhu 1mgiiUli\ chap nh~ duq~

Lu~ an gOm4 chuong,

Chlldng 1: T6ng qUaDve mOhlnh va phuong phap giro mQt s(f hi\i

tmlh co hQc

Chlldng 2: MQt sO bili loan dao dQng va bi<!ndl,ll1gcUa thanh dan

hOi

Chl(dng 3: MQt sO bai toan dl)ng Il!c hQc mO ta bCliphlfO'ng tdnh

parabolic phi tuy<!n

Chuang 4: Ml)t sO kel qua Hnh tOtin.

Cuoi C\)ng la phau tai li~u tham khao cUa lu~ ~n..

'/, I i-"

";' , '

iHLf\:.i[;,~:'-

T6ng quaDv~m()blnb va pbll<mgpbap giai m()lso bai

toaD cO' bQc

Trong chuang n~y chUngWi triOObay mQt s6 kl!t qua nghien CUll hen Tht gi6i va hong nuercv~ cac bAiloan d~t fa hong lu~n an Cling nlll! mQt s6 ktt qua ciia chung wi dii d~t dugc so veriOOUngkef qua cii~ 1.1cgh\ hong va ngoai mt6c Nhihlg bAitmin chUngtOi kMo sat trong lu~ an nay bao gbm:

1 Bai loan bien d~g eua mQt thanh dan hbi phi luytn dugc nhung trong moi fIuemgcha:tlong Cae kef qua n~y, cluing Wida'dl1og!rong [l]l2] [21][22][23][30]

2 Bai loan thief kt bua may d6ng C9c.Cae kef qua dii dugc dl1ng

3 Bai loan dQng l,!c hQcbien t,!a I-chien .Cac kef qua etadugc d~

~p dtn trong [3][4]

4 Bat loan etQngl"c hQcbien va d~i duang Car kef qua cua mO h1OObai loan n~y da dugc dilng trong [5][6][7][8][9][10]fll][12]ft3]f14] [15]

5 Mo h1nh dQng l"c hQc t"a phtlang triOOSaint-Venant l-chi~u ktt qua ciia bai loan n~y chUngtoi c6ng b6 trong [16] I

6.Bi'ti loan Ian tnly~n va khu~h tan ciia ngubn gay ~ nhiem MOl

86 ktt qua Hnh loan chUngWietatriOObay trong [18][19](20]

7 Bai fOliov~ 51!Ian truy~n ngubn eMt ban trong mr6e dtl6i dat ChUngwi da tfob loan cho mQt 86 fIuemghgp tuy theo Ilugng nhiCm ban ban ~u va ngubn0 OOiembO sung hen bien, mQt sO kef qua c6 dtlgc, chUngtoi ~ ~p Mn hong [17]

-2-CHUONG II

M~t s6 bai toan dao d~ng va bie'n d~ng cua thanh d~mht}i

I DiU toan u6n thanh dan hoi phi tuyd!'nnhung trong JI1tli trtrang long Trong ph1lnn~y chung Wi xet sv bien d~ng dla m~\tthanh dun hbi phi tuyCn c6 kh6i luqng rieng r 0 dlt<;1Cnhunl~ hoan toan trong moi truaog chat long c6 kh6i luqng rieng r I Xuat pMt h'i ly lhuy!t c6 (lien cua

Bemoulli va Euler v~ cac xtfp xi dflDhbi mQt chil!u, lIen CCIsa gia !J,i,!t

Kirchhoff va di~u ki~n lien ket figaro cua thanh, sao chI) ducrng dan hl}j ntun trong cung mOtm~t phflng, cluIng ta rut fa dltqc phuong trlnh (1anhl)i Euler cua Ihanh d~c trong mOi truang chao khOng

(l.1) - !_-M(x,8'(x») + ,r:(x.0(x»)sin9(x) -=lex),

dx

dieu ki~n bien

\:.Ixc:(O,L)

0(0) = 0, M(L,0'(L») I blsin0(L) =b:~

Bili toan nhy (lttqc giai bimg each dua v~ d<;mgbien ph:ln V(~imilt

so ghi thi!t 1Ien cae ham M, g, f va tren cae h~ s6, bang xap xi Gale-rIcin,

chUng wi da ch(tng minh (htqc mOt 86 tinh ch11'tlien quan Mn sl! tOn t~i va duy nMt lai &jiUeuabili loan (1.1), (1.2) San <16b1mg each rai r~c: hOi1 bi'ti

toan theo plHI("Jngphlip phhn tit him ht.'o, chUng toi da chUng minh dtl,~c I;'!

hQi t\! cua lai giai xap xi v~ nghi~m ctla phuClng trinh xuat phat C:~c kef

qua da dttqc dAng trong [21][22][30]

(1.2)

San d6 chUngwi da xet sl! ph\! thuQcclla lo-igiai vao cac dit kien

cho ban dhu bJ,b2,/,g cila bai toan va da.chti'ng minh duqc sv ph\! lhu<>c

nfty lit lien tl!c va dClndi~u, van loi giMduy nh11'1cua bi'tiloan (1.2), (1.3)

II Bi\i toan boa may dong c<;'c.Co h~ ky thu~t cua bUa may d5ng c9c c6 t116xcI mQt each t6ng quat nlnt san: M<,\tbUa c6 kh6i htqng ,17/(,

dltqc n6i liCn v6i C9c va de c6 kh6i 1ttqng n72' bhng Ie)xo v6i h~ 86 oan h()j

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3-[11]T.V.LANG, D.M.NGQC, LV.THIEM,Xfiy dV11gmO hlnh toan hqG giiu s6 (rang khOng gim1 3-chi~u cho vi?c mO ta, dt! bao hii' hlqng va ch~fLIlft;1ng mcoc cua hb chUa 11111Ydi~n 'If! An 1 tllU<)Cnh6m d~ tili "OJ.!baa ch~lthlt;mg

nuoc cua hb ch(ta Thi'IYdi~n 1'rj An va roO h1nh toan", De tai Nh/l 11l(('h:

"Nghien cuu m6i truiJng sinh tluli h6 clll(a nU'<}'c TMty dien Trt An", Tp

HCM,1985

[12] T.V.LANG,D.M.NGQC,LV.TtIlEM,Xay d1.!DgmO hlnh toan hqc ghH 86

trong khOng gian 3-chi~u cho vi~c mO ta, dt! baa 11ii'hlqng va chill htr;mg

nuoc cua hb chUa Thuy di~n Tri An, liqi nght TOlIn hqc Vift Nam Lan thti Ill, Ha n<>i,07/1985.

[13]T.V.LANG,D.M.NGQC,LV.THIEM,X:\y dt!ng mO hlnh toan hqc gi:'li :~:(\ Lrong khOng gian 3-chi~u eho vi9c mO ta, dt! baa 11ii'luqng va GMt ltcr;mg

mroe cua hb chtia 'Thuy di9n Trj An, llqi thdo Cd hqc chat lOng, Nha trang, 07/1985.

[14]T.V.LANG,D.M.NGQC,LV.HIIEM,XAy d~r11gmO hl11htoan h9c giiU r,:6 lrong khOng gi:U13-ehiCu cho vi9c mO ta, dt! baa trii luqng va eh11LIHong

mro,c cua hb chua ThUy di~n Trj An, l-lqi ngh( Khoa l' oan Dqi hqc Tdng lz(jp TpHCM, 06/1985.

[15]T.V.LANG va;c~cI~cgia.Nghien c{cu dong cMy ngoai bi~n, IMi light TOIIIIhqc Vi~t Na17lLan tluHll, Ha n<)i, 07/1985 1'6m t~Ltr 133.

[16]T.V.LANGva c~clac gia, Xc! anhlnrbngnhol tTen bili toan dc)ng c:h:\y

khOngon djnh m<)tchi~u, Hqi nght Khoa hqc Lanthu V, TruiJngDIIBK II} HCM, 06/1990,cr 42-43.

[17] T.V.LANG, B.M.NGQC,CAn bhng va GMt hcq'J1gmtoc dum o1'\tlrong

mila khO, Bao do klwa hqc stf 83.203, Trung Tam l' oan Hqc (}"/1gDlfl18 WI

Tin Hqc, Vi~n KHVN, TpHCM, 1983,21 cr.

[10] T.V.LANG, N.T.PHONG,51! Ian truyCn va khu~ch h111Gila nguhn (~

nhiCm trong khOng khf, T-I~)iI1ghi Khoa hqc va C6ng I1gh(' l/il1 tilT! VI,

[19] T.V.LANG,N.T.PHONG,ve bai toan Ian truy"~n va khut!"chtan dla

ngubn 0 nhiem, Proceedings of the 5th Workshop on Appli(~d Mechanics,

4/1995, HCMC, 1995,p 13.1- 13.7:

21

-[20]T.V.LANG, N.T.PHONG, ~ bai toaD Ian tmyen va khuech tan cua

ngubn 0 nhiem, Tqp cM Khoa hqc & Gong nghf, BK & SPKT, S6 9,

(1995), Ha nQi.(Bai nh~n dang)

[21]T.Y.LANG,Blii toan u6n thanh dan hOi phi tuy6n dl1(;1cnhung trang 111\)(

cha:'t long, H{3i nghj Co' hqc V«tran hien d{Plg toan qudc Ion thl~'lV, Hi\ n<;\i,

10/1994, T6m t~t, 1r 44-45

[22] T.V.LANG,N.T.LONG,Phl1cmg pIlar phhn tic hull ban ap d~ng VaGhlii

to<1nu6n mQ1thanb dan hbi phi 1uyCn, Proceedings of the 4th Workshop on Applied Mechanics, 4/1994, Tp HCM, 1994, tr XIIII1-S.

[23]T.V.LANG, T.LCU'i1NG, H.B.lAN,Gi,\i ;86 mQ1 phl1(1J1g 11'111h phi tu)'61

lien kef v6i loan tit Bessel, Tqp eM Khoa hqe & C611gI1gh~,ilK & SPKT,

S67, (1994), HanQi, tr.13-16 "

[24] T.V LANG, at at, Mathematical Modelling of the Hammer Machine,

The 4th Congress of Vietnamese Mathematicians, Hanoi, Scpo 4-7,1990, Abst p.137;

[25] T.V LANG, at at, Mathematical Modelling of the 'Hammer Machine,

Proceedings of the HCMC Mathematics Consortium ist CO1~ferel/ce,

VaLl, 1993, p 180-186

[26] T.V.LANGvi) cae tac gia, MO hlnh to{m h9c bua t11ay,Tgp eM Khoa

Hqc va Gong N ghf, Vi~n KHVN, S6 6,(1992), tr 19-26.

[27] T.V.LANGva cae tac gia, Me hinh loan 119cbua 1118Ydong c9c, lh')i

[28] T.V.LANG,H.C.HOhl,LT.THANH.Mo hlnh loan h9~: cth btia may, Jlqi nghj Co' hqc Vqt ran bitn d{Plg toan quo(; tan tlut lV, H8 nl!i, 10/1994, Tom

[29] T.V.lANG va cae tac gia, Mo hlnh taan h9c bUa may dong C<;1C,De Idi ctfp B{3(I'ruiJng DHilK Tp HCM qudn If), Nghi~m tilt! ngay OCi/O1/l992.

[30] N.T.lONG,T.V.LANG,Th{~Problem of buckling of;t nonlinearly clafiLic

bar immersed in a fluid, De tai 2.2.10, (CII1I011gtrinh Nghien deu C(y ban,

1993) Jour Mathematics (gi3'ynh~l dang s6 15-94,ngay 22110/94, T~p

chi Tmln H9c Vi~t Nam)

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