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IBO GIAO DUC VADAO TAO
I. .' .
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
}riaso : 1.02.21
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TOM TAT LU!N AN
Ph6TienSi KhoaHQcTDanLy - ---
Thanhph6H~ChiMinh
- 1995 -
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"..
\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;>cT6ng Hqp Thanh ph6 H6 Chi Minh
vao hie giG , ngay thang flam 1995
C6 th€ tlm hi~u lu~ an ~i cae Thu vi~n
-Tw<mg D~i Hc;>cT6ng Hqp T19.H6Chi Minh
- Khoa Hc;>cT6ng Hqp Tp.If6 ChI Minh .
- Trung Tam Khoa Hc;>cTg Nhien va C6ng Ngh~ Qu6c
Gia Vi~t Nam (Van Phong 2).
LOIN6IDAU
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
hoWlchinh, n~n chUngWi ding dii kiem nghi~m tru6c, sau d6 mm <TUI!C
Hnhloan 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 dQngva 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. .
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CHlJONGI
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 mQtthanh 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
trong t24][25][26][27][28] [29]. I'
3. Bai loan dQngl,!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 Hnhloan 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 ngubn 0 OOiembO sung hen bien, mQt sO kef qua c6 dtlgc,
chUngtoi ~ ~p Mn hong [17].
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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~ngdla 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») Iblsin0(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 &jiUeua bili 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'ngminh duqc sv ph\! lhu<>c
nftylit 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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