adQ, bhng each klu10 sat !.fuh
nita xac d!nh duang va hennit. cia tOaD tit vi phnn. ChUng tOi Om nghi~m
thco tang IlltOOg,GOngthC1ichUng minh dltgC nghi~m elm biii lotio tl1cOqufi
trlnh pMn ra ehfnh Iii nghi~m eua phuang trinh xu at pMt (D!nh Iy 1,MI!G II,
Chuang 3 cia Lu~n an).
Buoc tiep thoo, b~ng each sai phan theo thOng gian, chUng toi nh~n
dllgc cae xlfp xi h~e n cua phuong trinh sai pMn so voi phuang triah x\l1ft
phill ban dhu..
III. Mo hinh d9ng h9C tt.ra ph.tong tring Saint- Venant. 1 chn~QI.
'I110ng thuong, dtl.Hnh dong eh?y khOng 6n dinh tren h~ thong sOng ktnh
ciia vung anh hui':1ngthl1y trieu, ngtf()i ta su dl!ng phuong trlnh Saint- Venwl(
I-chiCu, trong lntemg hqp 1111y
?lnh 11ltal1gcua ma sat nh6l b! (Iii bo qua 'lit
xcm SI.tma sat clJa eMt long vii th1'mhr:\n 11'1
nan!,- kf (j (T1\y,do mu()n ~d
hi~lI (cng nh6l LacdQng I~n dong eMy, u\jng t1J~jjmuOn xua1 pIlat lir phlJ'OTlg
trinh dQng h!e l19c Navier-Stokes, phuong trlnh baa to1\n kh6i lugng, chung
16i dua fa dUllCmOt mO hinh ty:a pllltO'11gtrinh Saint- Vcnant l-chi~u, trang,
<16 e6 s~r tham gia elm thal1h ph110nhc)t trong pluto'ng trInh, ket qlla cluing wi
cIatrlnh bay trong [16].
V6i cae gia thiet san day:
- Chlft lr'mg dOng ehftt, k hOng nen lhlc;1e,dAng hu6ng,
- Ap suit li\ tll"y Hnh.
Khi eto fir h~ phuong trlnh chuyCn etQng t6ng quat baa g'orn die
tensor (tng suft't nhot 't~ cluing ta e6:
(3.1)
(3.2)
Olt
au
au
au
1 op
at + u ax + v oy + W a; = 011 -I It 01' + v
Of
ox
~ -j IV ~~oy
m
:00
] m~
m~
pax + p( ox + ay +
--}- 017+!
(10'
-9-
m~ .
-Oz--
) + Lv,
~t + m; +-~~- -Iu ,
r ( ax
0'
oz )
(3.3)
op
- =-pg
Oz
va phttC1.tlgtrlnh bao toan kh6i Itt<1ng
(3.4)
ou ov Ow
-+-+-=
O.
Ox Oy Oz
Di~uki~n tren m~t HlOangva dtt6i day dtt<1ccho nhtt san:
"
(3.5) .
wi
11
(3.6)
W
I
= m, + ul m, +vl
at
11
ah
= U -+v
-h
I
-h ax
ax
m"
11
Oy
ah
l-h -.Oy
ChUng ta gh\ thWl them rhng dQ sftu 1/
= 11+ h
cua m,!c ntt6c
khOng dang ke so v6i m~t phang nhm ngang, khi d6 chUng ta c6 th~ (ltta V8.0
cac df;liItt<1l1gd~c trung cho sv phftn bO v~n tOe trung blnh theo chi~u thang
dUng:
11
(3.7)
V(x,y,t)
= -hJ u(x,y,z,t)dz,
11
(3.8)
V(x,y,t) = J v(x,y,z,t)dz.
: -h
va cae gia thief atia M~nh d~ 1 (Mvc III, Chttcmg 3 eua Lu~n an) va C1'13
M~nh ~ san, chUngWi nh~ dttqe h~ phttC1.tlg
trlnh lien h~cchuycindQngde
xac dinh ehi~u cao Ii cling nhtt phftn b6 Wong v~ Wc V, V trong m~\t
phang Oxy. H~ cac phttong trlnh n'a.ykhac h~ phttong trlnl1Saint-Venant hai
ehi~u (j eM, c6 tbam gia eae tbanh ph~ d~o ham b~e hai cua v~ t6c.
M~nh ~ 2: Gia sit
I
(i) Moi Wemg 1ftdang htt6ng 't~ = 't;,
- 10-
"
(ii) H~ s6 nh6\: eua eMt long thee cae hl1(mg 11\ nhl1 nhau
v.=v.xy=v,
(Hi) Tensor N} duClcxap xi dltai dl;Ulg:
(3.9)
OU OF
2
8V.
N2=2vp-,
N2=vp -+,
ox
ay
ax )
( By
(iv) lrng sual teen be m~t Unhthee I1'ngsuat gi6, ,
.
N.=2vp-,
oU
2
(3.10)
1". .1/
I
= 1 9 f\W g
2
L
cos(1 g ,
21/
I
=,,2
W;'sinH
Ig p a g
l:
(v) (Jng sual ma sa(l,~i day (!nh Ihea ma sat eua dong 611djnh,
(3.11)
Lll h
= C~ P 0l!?
~ \/2)}S
1f2 --
L2Lh
= cg2P V{U2 III
:': \t ')Y
--
Khi do, h~ phur111gtrluh chuy611dl)ng mrac n()ng hai chieu cung v6i plllrur'g
trlnh Jit:n t\lc c6 dC;lng:
au
(3.12)
a u2 a UV
ot -+-fy-;/i-+- By II
8rl
= --gH ax -+-lV-l- v~U
cg ~(~:_:~_V~1~+1g2P~~2.coseg,
-- -1
I tp
av
(3.13)
&-+-
a au
-+-v a; ( ax
()V'
) --I--[~1;,I
.
iJ UV iJ \/2
8rl
iJ iJU <11/
ij-; H -+- By H :co -gl! B.y-LU - v~V -+-v By ( Ox -I-~?};) V
(
1/
)
u7 I v2 /7
g ---+"(1'.
-- (/
[(J.
-
2 Fa
- II -
p
W2sin8g
8
all aU oV
--+
+--=0
at ox 8y
(3.14)
San d6, gi<\thiel d6y cua long dan c6 d~g ntta hloh tang tl1;l,SI! thay
d6i b'e mM va day
..
theo true Oy khOng dang ke. Gii\ sa V
II
cla x va t, h,reCorilolis [= 0, h,rcgi6
= 0, -~ 11\ham
II
~ = O. Chung Wi nh~n (htqc he
phuong trlnh mOhi chuyen dQngdong cMy mQtchien:
(3.15) B Or}+--0
tJQ
ot ax(3.16)
~
8Q
gA at
+~~
QIQI = 2v o2q
ox c2A2R gA OX2
Q2 + Or}+
gAox A
.
trong d6 ,
-A
R
A
1
'
H\ di?n Hehm~tej\teua
long dan, B 111ehi(;lJ rQng m~t thoang,
-'r.' 1
"A-
= B li'tban kfnhthuy h,recua long dull,
De giro h~ (3.14),(3.15) chUng tOi sa dl;lngphuong
pMp khai trien
I
tj~m ct,\ntheo tham s6 be, bhng each d~t g = 2fi
duqc khai trieD theo lUy thira ctla 8 runt san:
m
(3.17)
Q(x,t,g) = LQ",(x,t)!>"',
",=0
m
(3.18)
l1(X,t,&) = L l1";(X,t)!>'"
",=0
- 12-
,gh\ siltdie hamQ va '1
v6i E all nho lit! c6 thl! cui Sign(Q) nhula Sign(Q)J. Trong .:16die h~ 86
Qo' 110thou h~ phuong trlnh:
(3.19) B ~llo+ ~
at
ox
=0
a ,~:! + Urlo+ QoIQ,1=,0
1 0{1 + 1
'
gA at
gA ox.l1
at
c2A2R
con cae h~ 86 Q"" 11"" f11= 1, 2, ... thoa h~ ph\1t:mgtrlnh
(3.20) B ?J", + ~g", - 0
at
ox -. ,
~~_.?f2'!!+
.3_!.
gA at
~q",.,: <7r.b.+~~q~::
gAox A
ax
l~'I(Q(I,QI,...,Q",I)
cAR
IV. Hai foan Ian fruY4!:nva khulch
tan cua l.gu;~11ga)/ ~i}II1Ihij~l1l.
Chllng fa ghi sl'r (p(x,y,z,t)
bi6u dj~n luqng nhi~m ban du<;rcIan truy:~n vit
!JlU~ch t{m c!(?ctheo quy d~o cua de h<;1tm{)i tntang chuy(!n d<>ngv6'i v~n
t6c V(x,y,z,t).
Baj loan m() l<\51!Ian truy'en va khut!ch t{in (lJa ngul'in gay
(\ nhiCm c6 o,.\ngsan:
(4.1)
--+
o<5
tuyen Hnh, d~ gic\ih~ n'!\ycMng wi con khan sat tht'h1 !fnh 6n dinh clla lai
gic\i voi die raub bu(!c v~ v~n tOe d()ng thatn cling n]n( cua bl1~5C
hr6i,
- 15 -
CHtJONGIV
M<'t s6 klt qua Hnhto{m
Trang chuang n1\ychUngwi neu ml>ts6 ket qua Hnh s6 du6i d~g
dOthi cua cac mOhlnh bai Loan,rung nhu phuong pMp tfnh Loan,da d~t ra
!rang Chttdngl va Chlfdllg/ll. Cac ket qua n1\ydt!aLIenmQts6 s6 li~u OWe
te ding nhu ghi dinh, de qua d6 danh gia ve m~t dinh tfnh cua mO hlnh va
phttong pharo
I. Tlnh toan dao d(mg va biln d~.mget'm f.hanl. d~lI1hoi. CluIng
Wi11\nluc;tf.
Hnh loan cae bai loan gall:
1. Bd; loan
u6fJ lhafJh dafJ /Wi phi
luyefJ,
Cqung wi tinb loan cho ml;)ts6
truem.ghgp neu trong Chttdng/l, M~4CI nhtt du6i dlly, cae ket qua (15du<;lC
trlnh bay !rang [2][22].Gia su cae ham g, M dtt<;lc
ch911t11baeae yell Cftll
cUa nhih1g dinh ly ve st! ton ~i, duy nhal eua.lai giai, rung nhu S\f d{mh girt
sai 86 tren 1Mgiro. Khi d6 bai loan xffp xi tuang duong v<'1ih~ phuang trlnh
phi tuyln. Trong d6 ma tr~ li~ s6 c6 d1;U1g
3 duang chen. Tit dlly, chung la
c6 the su dl!ng phuong phap truy (lu6i de Hm nghi~m.
2. Bd; loan bUamayd61lgcqc.ChungWida Hnhloan dva trenmOh}nhva
phuong phap rua bai loan d~t ra trong Chudng/l, M,!c fl, v6i cae diI li~u
thoa cae dieu ki~n da khao sat nhu sau:
- Kh6iIttongbua tir40 Mn 1O0kg,
,
- Kh6i lu<;lI1g
C9CdIng de (bQga Hip)nh~ gia Ifj lir 30 dCn90kg,
- Loxo c6 gia
- Khoang caeh
I.ti trong khoang 50000N/m,
ban dl\ll giUa bua va de c6 gfa 1rj Ui"1 Mn 9mm,
- Thn s6 quay eua dQngeCitit 110 uCn190rad/s
va mQt s6 86 li~u ve dAtdung trang quy ph~m v~ d6ng C9Cgia c6 n~n
mongo
Cac torang hgp chUng wi da khao sat baa gOm: sl! phI! thuQc giITa
dQ sAu d~t duge v6i c<;>c
va de, s\! ph,! thul;)c giUa dQ sau d~t du<;Icv6i bun,
st! ph,! thuQc giO'adQ sftu dl;\tdll<;1C,
v6i khoang cach ban dftu eiia bua va dc,
S\!ph,! thuQc giO'adQ sau dl;\tdu<;1cv6i t1\ns6 quay rua m;iy bUa,
- 16-
Tren
(;(j
so cae k~t qua s6 (Hi nhl~l1
dtt<;1e,
cluing wi nit ra l}}i?1Stj'kE~t
lu~n (cae kef qua Hnh loan chung Wi da trlnh bay trong [24]1[2,!j][2:6][2'71
[28]129]):
MO hl11hHnh loan, cung nhtt phttC1l'\gphap giiu cho kef qiia phil
hqp ve m~t d~nh Hnh so vOi bUa may Uwe 16da (11«;1(:
tlwc nghi~m.
- Hi~u qua cua va d~p Ii\ r11't16'n.Trang nhi'eu tnt.lavi dQ trong vung vjnh n~e bQ tit 1i) d~n 220,
- Gia tOe trc,mgtxuang
,< 10..1
S 1
I
.
g = 9,81m/s7,
- TTItang gi6 ill gem hai thanh phlln (1:x,1:)1)du'leI tfnh thoo GOng
thueil/ =
(31"~I~,trong d6 ~ Ia vectorv~ tOegi6, c6 g6e h'lP v6i t~c
Ox 11\81/' Thy thoo v~n tOe gi6 m1,lnhhay y~lI, gh! trj f3 dU<.1e
111yntH! san:
p=
O,98448 x 10-2 ne'u IWgl< 6,6m/s2
~
f 3,10956
X
10-2
ne'u IWgl;:::
6,6m/s2
- Ap su11'tkhf quyen 11lygia trj h~ng sO 11\97820 Mb
Tuy thco dja hmh, cl1ling tOi d5 tfnh Loan eho hai Lruang h~}p sall [8][9][10J:
3. Eai toan tan truyelz W1khuech tan cua ngu1Jngtiy 6 nhi/;n. Chung (hi cia
tfnh Loan eho hai tTItang hqp ri~ng Ie [18][19Jr20J:
- Truang hqp nguOn () nhiCm t~p trung Lr~nbi~n
- 18 -
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