Phan tfch dap ipng dong ILFC cua be tru tron khong neo CO ke den tu'O'ng tac chat long - thanh be va tu'O'ng tac dat nen - be chipa chju tac dong dong dat
The dynamic response analysis of the unanchored circular cylindrical tank considering of the fluid - structure interaction and the soil - structure interaction under the seismic excitation
Ngay nhan bai: 15/12/2015 Ngay sira bai: 20/02/2016 Ngay chap nhan dang: 21/03/2016
TOMTAT
Muc dich cua bai bdo la t'lm dap dng d^ng Idc cua be tru tron khong neo co ki d^n tdong tac chat long - thanh be va tiidng tac dat nen - be chila. De ti^p c i n giai quyet bai toan nay phai xdc dinh duoc ap Ii^c thiiy dong trong b^ chila v6i gia thiet thanh be roem, day be co dich chuyen va p h i i thiet lap dtfOc phifdng trinh chuydn d6ng vcti gia thiet be khong neo, dat tr£n nen dat tddng doi cilng, co the tniot va xoay khi chiu tac dpng dpng dat.
Tii kh6a: ap life thuy dpng, phUdng trinh chuyen dong, tuong tac chat long - thanh b^, tiidng tdc ddt n l n - b l chila.
ABSTRACT
The purpose of this paper is to investigate the dynamic response of unanchored circular cylindrical tank considering of the fluid -• structure interaction and the soil - structure interaction. To approach this problem solved, it's necessary to determine the hydrodynamic pressure in the tank assummg the flexible tank v/all, the tank bottom having moved and to establish the governing equation of unanchored tank, which rests on the relatively hard background, can slide and rotate under the seismic excitation.
Keywords: hydrodynamic pressure, governing equation, fluid - structure interaction, soil - structure interaction.
Nguyen Hoang Tiing
TrUcfng Cao ding Xay dUng so 1 - Bo Xay dUng [email protected]
Nguyen Hoang Tung
1 . Giori t h i f u
Ap lire thuy dong trong trucJng hdp ehung v^ cac trudng hop rieng da dUdc Natsiavas [1], [2] thiet lap. Phu'dng trinh chuyen dpng xay dUng theo nguyen ly Hamilton vdi g\h thiet be khong neo dat tren n4n tUong doi Cling, bo qua chuyen dong trUOt, c6 ke den chuyen dong xoay chiu ki'ch dong dieu hoa da ddOc Natsiavas [1], [2] cong b d . Phddng trinh chuyen dong la he phUOng trinh vi phan chila nhieu an so, trong nghien cilu cua minh, Natsiavas [1], [2] chUa gidi he phuong trinh vi phan chuyen dgng lap duac, mdi giai cho trUdng hop he eo m o t phuong trinh m o t an so va ehiu kich dong dieu hoa.
So vdi Natsiavas [1], {2] nhiing diem mdi dUOc the hien trong bai bao nay la: Phuong trinh chuyen dgng xay ddng theo nguyen 1^
Hamilton co ke den chuyen dgng t r u g i va xoay d mat tiep xuc giOa d^t nen va be chila; Phuong trinh chuyen flong dugc g\h\ la he phuong trinh vi phan bdn an sd vdi ldc kich dgng la t l i trong dgng dat Uy theo gian do gia toe phu thuge thdi gian, Oap ilng dpng luc thu dupc co tinh ehat rat phong phu, cd the riit ra nhu'ng nhSn xet co y nghia thde tien.
2. Ong xufdong ldc cua chat ldng trong be chila tru tron Anh hudng cua thanh be mem trong dng x i l d6ng lUc cua be chila dupc ke tdi. Dieu kien bien tai be mat tiep xuc vdi thanh be, day be va tai be mat thoang dugc thiet lap trong mien chat ldng.
Hinh 1. He toa do trong be dida Iru Iron p lUc chat ldng P trong be chila;
P(r,9,x,t) = P , - ^ P , = - p ^ - ^ p g [ H - trong do;
o4.2oi60nn[E[ia]i|83
1=1,2,... (2) p la khoi idpng n&ng eCia chat ldng,
P, = p g ( H - x ) IS SplUcthiiytTnheOa chat Idng, P ^ = - p 9 ^ / a t la aplUcthiHy dgng eua chat long, 4> (r. 3> X, t) la ham the nang van toe trong he tga do tru.
2.1. Be chda co kiden do mem thdnh bi
w^(x) la do vong thanh be { t h ^ hi&n bien dang hay d p mem thanh be khi ^ t&i) theo hddng kinh ddpc g\k thiet bang mgt ham dang cho tnidc, 6 day ehgn:
w^(x) = sin ( 2 m - l ) —
^ ^ ( t ) la bi^n dd 3 6 vdng eua thanh b l theo hudng kinh.
A p luc thOy ddng trong trddng hdp nay ddpc xac djnh n h u sau:
P„{r.9,x,t) = - p R c o s e { f „ ( r , x ) i | / , „ ( t ) + J [ f „ ( r , x ) A „ ( t ) ) ) (3) vdi: f„{r,x), A ^ ( t ) xac dinh theo t l ] , [2].
2.2, Bichdra dich chuyen nhdvdtthidgc theo trucz Dieh chuyen, van toe vh gia toe cua dat nen lan lUpt la Zg(t), Vg{t} va ag(t) dpc theo true z.lilcn&y w ^ ( x ) = l va \];„(t)=Z9(t).
A p ldc thiiy dong trong trddng hpp nay dupe xac djnh nhU sau:
P.(r.6,x,t) = -pReoseEf.(r,x)a^(t)+5^[f„(r,x)A„(t)]l (4) vdi: f,(r,x), f„{r,x), A „ ( t ) xae dinh theo [IJ, [2],
2.3. Be chOa xoay xung quanh true y
Van toe tai day be: f(r,0,t) = -cr(Mt)cos6 (5)
•¥ Khi c = l toan bp be cdng xoay mot gde ij)(t) xung quanh true y.
-f- Khi c=0 chl theinh b l bi xoay trong khi day be g i d nguydn theo phuong ngang.
Van toe tai thanh b l theo hudng kinh-
h[e,x,t) = x4i(t)eose (6) trong do:
if{t] la gde xoay cila be chda quanh true y;
* ( t ) - * , ( t ) - i - 4 i „ ( t ) (7) vdi: ili,{t) la gde xoay cua mdng b l quanh true y;
iti„(t) la gde xoay cila day be quanh true y khi 6hy b l bi nang len.
Ap lUe thiiy dong trong trudng hpp nay ddoe xac dinh nhdsau:
P*{r,e.x,t) = -p,Rcos6{f,{r,x)R$(t)-f£[f^,(r,x)RA^(t)]} (8) vdi:f^{r,x), f^,(r,x), A^(t) x S c d i n h t h e o [ l ] , [ 2 ] .
3. Qng x i l d o n g ldc cAa cdc bo phan t r o n g b e chila 3.1. Dgng dich chuyen cda thdnh be
Thanh be ddPc eoi n h d la vo thanh mong ma dich chuyen mat trung binh eua n d c d dang nhdsau:
u,{e,x,t)=[zg{t)+h,<ti,{t)-i-xwt)+u;(x,t)]cose O)
U9(0,x,t) = - [ z g ( I ) + h g * f ( t ) - i - x 4 i ( t ) - i - u ^ ( x , t ) ] s i n e (10) u^{e,x,t)-Rijiy(t)-hr-R(t)(t)-(-u^(x,t)]cos0 (11) trong d d :
u r { « . t ) = £ [ w „ ( x ) M < „ ( t ) ] (12)
":(x,t) = E[v™{x)4.(t)]
(13)":(''.t)=i:K(x)^^(t)] (14)
a e hhm sd dang w „ { x ) , v „ ( x ) , u „ ( x ) dddc Ida chon dda tren thue nghiem va ly t h u y l t cua cac nghien cdu di trddc, 6 day da chon:
w „ ( x ) = v „ { x ) = u „ { x ) = s i n [ ( 2 m - l ) ^ j (IS) Cac ham so theo t h d i gian ^^{t), %^{t), ; „ ( t ) la cac an so can
xae dinh cung vdi in sfi la ham ij)(t) d d d i day.
3.2. Dgng dich chuyin eda ddy be
u^(r,e,t) = [z^(t)-i-h,i|),(t)]eos9-i-u^(r,e,t) (16) uS(r,0,t) = -[z,(t)-Hh,»l.,(t)]5ine-ma,(r,e,t) (17) u;(r,e,t) = -r4.,(t)cose-HU^(r,9,t) (IB) trong d d :
u,„(i'.e.t) = -cr<ti„(t)eose 09) 3.3. M6 tiinh tifcmg tdc bichda • ddt nin
Tuong tSe b l chda - dat n l n dupc md hinh hda bdi sd thay t h i bSng hai Id xo tai trong tSm ciia m d n g b l , d day khdng ke tdi trddng hdp day be bi nang l^n. MSt Id xo ed do cdng hdu han vk han ehe sd trUdt eua mdng theo dich c h u y i n cHa dat n l n dpe true x. Ld xo cdn lai 1^ Id xo xoay, cho ph4p mdng va toan bd b l chda xoay bdi gde i/^[t) xung quanh true y
D o Cling tuong dUPng cua cac 16 xo ddpc md hinh hda nhdsau:
k ^ = F , / ( 7 i R ) , F , = k , x , + m n g , k . - w f m , (20) k ^ = M , / ( 7 i R ) , Mf = k,iti,, k, = o);i, (21) trong do:
k, vk k j 13n lupt la dp cdng eua eae Id xo chfing lai sd tm'ot va xoay cCia mong be, F, Ide ma sat ngan eSn su IrUpt cOa d^y mdng theo phUOng djch chuyin cCia dUt n l n , M, mdmen lam mdng bi xoay xung quay tmc y, k, va k| lan lupt IS dp cdng eila mdng bengan cSnsdtrUdtvaxoay, Q), tan so dao dong cCia mdng be, m, khoi Idpng cOa mfing b l , m tfing khdi lupng cCia mdng be va be chda, I, momen quan tinh cda mong b l , ^ he so Coulomb tai be mat tiepxilcgiO^ mong b l vdi dat n l n .
4. Phddng trinh d i u y l n d d n g CO k^ tf£n t i r o n g tdc be chlJa - dat n l n 4.1. Ap life thdy ddng
Ap ldc th Ciy ddng Pd dupc xac djnh n h u sau:
Pd=P,+P(+P. + Pm (32) trong dd;
P^ la ap lUe thCiy dpng phu thudc dp m i m cOa thanh be, xac djnh theo (3).
P, la ap ldc thuy dong phy thuoc vao djch ehuyen cCia be chila theo phddng z, xae dinh theo (4).
P, la ap luc do mdng xoay m d t goe i|>,{t) xung quanh true y, xac dinh theo (8).
P„ la ap lUc do c h u y i n dgng bj nang len cCia be chila, trong bai bao nay bd qua.
4.2. Thiet ldp phuang trinh chuyen ddng
Tren co sd nguy&n ly Hamilton, phUOng trinh chuyen ddng eho ilng x d cCia toan bd h& b l chda chat Idng, bfi qua hidn t u p n g day b l bi nSng ISn, duoc thiet l|p n h u sau:
M x ( t ) - H K x ( t ) - H k ( x ) - ! - P ^ ( t ) - - a , ( t ) F (23) trong dd:
84i
: i | S l 04.2016a, ( t ) gia toe nen theo phuong ngang z lay theo gian do gia toe nen thde te cOa mfit tran ddng dat b^t kJ*,
M \h ma tran khfii lddng.
eae h f so eua ma tran M ddpc Xcic ^ n h theo [1], [2], K \k ma trkn do cilng.
c 5 c h e s d c u a m a t r a n K x S c d j n h t h e o [ l l , [2].
Vec t o k p h u thudc hai 16 xo thay the ed dang,
vdi k,,, k,^xaedinhtheo[20),(21).
V6c t o P,| ( t ) ehda cae gia tri sloshing tuong ilng-
p,i(')=[(p,), (p„\ (p.,), (p,,),,]'
c^c thanh phSn cOa vec t d P,, ( t ) xae dinh theo [1], [2].
Vec t o F chda che thanh phSn ldc tUong ilng:
f " [ f . f, f, f.,]'
che thanh phan luc xac djnh theo [1], [2].
An so gfim cac thanh phan sau:
x(t) = [^|/, ^, q, ^,f T [h ky hieu eila ma tran ehuyen vi.
4.3. PhUOng trinh chuyen dpng co kidin cdn theo Rayleigh Phuong trinh (23) khi co ke den can se ed dang nhu sau;
IVlx(t) + D f X ( t ) - ^ K x ( t ) - ^ k ( x ) + P,l(t) = - a g { t ) F Ma tran can Df dUde xae dinh t d ma tran khfii lUpng M vk cdng K theo eong thde:
D, =aM-i-pK trong d d :
a, p IS cac he so e^n Rayleigh ddpc xSc dinh n h u sau.
2C
(30) tran dfi
(32)
(33)
x ' ( t ) = [m, (0, (0, ( o J (35) (Oi(i = 1,4) la tan sfi dao dfing rieng eua bdn dang dao dfing dau
tien cilia he.
Lap trinh giai phUong trinh (36) bang phan m i m Mathematlca 7.0 ta t i m ddpc bon an cCia he phdeffig trtnh, t r o n g d d hai gia trj tan sfi dau tien t i m dupc;
(0, = 2 , 7 9 ; Q ) , ^ 17,98
PhUdng trinh chuyen ddng cd ckn (30) cung ddOc g i i i bSng c^ch sil dung phan m i m Mathematlca 7.0 tren ed sd \kp trinh thuat toan Runge - Kutta de giai so.
S. GiSi so
Phan tich dao dfing cila be tru trdn thang d i l n g chda nddc, ehiu the ddng ddng dat theo phdong nSm ngang t i n h theo gia tfie n l n , vfi be dupe lam bang thep, dky tda vko mong, che tham sfi t i n h tohn cu the nhu sau: Khoi Idong rieng cua nUdc; p=1000kg/m', Chieu cao mUc nUde:
H=9m; Chieu dh\ vfi: L=10m; Ban kinh v6: R=10m; C h i l u day v d : h=1.5em; Trpng lupng rieng cila thep v d : pi=7850kg/m^ M d d u n dan hfli c u a t h e p v d : E = 2 , 1 . 1 0 ° K N / m ^ ; G i a t o c n l n ag(t) ed the lay theo gian dfi gia tfie cfia tran dgng d i t bat k^, trong hk\ tohn nay lay theo gian do gia toe nen tran dfing dat El Centro (1940); Gia tfie trpng trddng:
g=9,81 m/s'; eo ke den can.
Dieu kien dau:
M/{O) = ^ ( 0 ) = <;(O) = ,j),(0) = v ( O ) = 4 ( 0 ) - ^ ( O ) = ii),(O) = O i
MM 'f lil' m
ifinh 2 Gi^ndogia toe nln theo phuong ngar^g trong t(0.2l3)
Hinh3.Giitridiclidiuyen <y trongt(0 21s)
C, tly-sfi c3n xdc dinh theo kinh nghiem, ^ e [ 0 , 0 2 ^ 0 , 0 6 ] . D f i i vdi k i t cau dang tru ddng thddng chpn ^ = 0 , 0 5 .
m „ Wj hai tan sfi dao dpng dau tien eua k i t eau, bSng each giSi phuong trinh:
Mx"{t)-)-Kx"{t) = 0 (34) trong dd-
M, K lan Idpt \k ma tran khoi Idpng, ma tr^n do cdng nhd trong phdong trinh (23) hay (30),
An sfi eCia phddng trinh (34) bao gfim:
Hinli 4 Mat phang plia vjj-lOy; trongt(0,21s)
Hlnh 5. Gia tri did) chuyen 4trDiigt(0,21s}
mnh6.MatphJngplia 4 - 1 0 ^ trongt(0,21s)
6. Ket luan
Da lap ddde p h d d n g trinh chuyen d p n g cd ke den c h u y i n dong trdcrt, chuyen dong xoay d mat tiep xuc giila be chila va nen, co k l deti tell trpng dgng dat theo phuong ngang tfnh theo giSn dfi gia tdc phu thufic thdi gian.
Da t i m ddpc dap dng ddng ldc cua be t r u trfin khfing neo bSng each ap dung chUdng trinh Mathematlca 7.0 de giai he phddng trinh viphSri ehuyen dpng cd bon an sfi vdi tac dong dfing dat tfnh theo g i i n do gia toe phu thufic thcri gian.
Qua ket qua khao sat da lam sang t f i c i c hi§u ling dang quan tam v l Idu y khi day b l bi trdcrt vk xoay trong dng x i l eua h^ be chila ch^t Ifing.
Oap ling ddng Ide cua be t r u t r d n khfing neo cfi ke den tdcfng tac chat Idng - thanh be va tuong tac dat n l n - b l chila phan ldn l i chuyin dfing hon dfin (chaotic), vi ddfing cong pha trong mat p h i n g pha eSt nhau rat phdc tap, xem cac hinh ve mat p h i n g pha hlnh 4 , 6 , 8 .
Khi ke den can, djch chuyen theo t h d i gian cd xu hudng hinh thanh cac nhom vdi bien dp tang, giam ed quy l u i t nhU hlnh 3,5,7.
TAlueUTHAMKHAO
1 NfltsiflvasS: An analytical model forunanchoredliuid filled tanks underbaseexcitation. Journal of Applied Mechanics, Vol 55,1988.
2.Nat5iavasS.:Respoii5eandfailureoffluid-fill«itanks under base excitation. Caltfomia Institute of Tedinology, Pasadena, California, 1938.
3.Velet5D5 Ai., Tang V.: Dynamic response of flexibly supported liquid-storage tanks. Journal of Structural Engineering, 1992.
4. WiinderiichW.,SeilerC, Schwarz J., Habenberger J.: Seismic responseandfeilure mechanism of flexibly supported liquid storage tanks 12" World Conference on Earthquake Engineering, New Zealand, 2000.
Hinh7.Glatridichdiuyen q trongt(0,21s)
Hinh S. Mat phing pha q - l O q trong t(0,21s)
Hlnh 9. Gia trj g6cxo3y ^, trong t(0,21s)
Hinh 10. Mat phang pha 2<|i, -1|>, trong t(0,21s)
S g l E V S n E n ^ 04.2016