KHOA HOC - C 6 N G N G H E -So 10/2015
Phan tich dong lflc hoc he lien hdp
tam - day - cdt chiu tac dung cua lflc khi dong
Tdm tdt: Bdi bdo trinh bdy thudt todn phin tdhtfu hgn (PTHH) vd mit si kit qui phdn tich ding Itfc hgc cOa hi ildn hgp tim - day - cit chju tdc dgng cua itfc khi ding. Stf dgng mi hinh Itfc khi dgng Scanian, cdc tdc gii thiit i$p hg phaong trinh vi phdn md ti dao ding cua hi vd dp dgng phUdng phdp tich phdn trtfc tiip Newmark, lip trinh trong mil trudng Ansys digial. Tinh todn trdn vi dg si cho thiy khi ndng cOa thugt todn, chuong trinh da lip vd khio sdt si trdn nhiiu idp bdi todn khdc nhau, Idm cd sd itfa chgn cdc thing si hgp 1^ cho hi ilin hgp tim - ddy - dt chiu tdc dgng cOa Itfc khi ding, idm cd sd khoa hgc phgc vg Unh todn, thiit ki cdc cing trinh GTVT nhu du ddy vdng.
Tflkhda: Hi lidn hgp tim-ddy-dt, Igc khi ding.
Abstract: This paper presents a finite element algorithm (FEM ) and some analysis of the system dynamics conjugate plate - Wire - column under the effect of aerodynamic forces.
Use Scanian aerodynamic model, the authors set up differential equations describing the system oscillator and apply direct integration method Newmark, environmental programming In ANSYS to solve. Calculated on the example shows the ability of the algorithm, the program was established and examined the problem on many different layers, as a basis for selecting the appropriate parameters for conjugate system plate - Wire - columns bear the effect of aerodynamic forces, as a basis for calculating serving science, design of transportation projects, such as a cable-stayed bridge.
Keywords: Complex Systems plate - Wire - columns, aerodynamic forces.
1. Mdddu
Do Sfl phflc tgp trong tfnh todn nen din nay, khi nghidn eflu cdc kit edu cdu ddy vdng thfldng dflpc dflpe md hinh hda nhfl Id h$ Ildn hpp ddm - ddy - cOt [2],[51,[8]. Ddy Id md hlnh khd ddn gidn, khbng xem xdt den tfnh chdt xodn cua cdu khi chju tac dyng cija tdi trpng Ideh tdm vd trong chflng mflc ndo dd chfla
• PGS. TS. NGUYEN THAI CHUNG
• ThS. N G U Y I N C H I E N THANG Hgc viin Ky thuit Quin stf
• ThS. VU ANH TUAN
Trtfdng Dgi hgc Cdng nghi GTVT thl hidn sat thflc sfl lam vide cilia h$. Trong xu the phdt triln c£ia phfldng phdp vd phfldng tien tinh nhfl hi^n nay, md hinh khdng gian eho kit cdu dgng nay da bdt ddu xuat hign va dan dflpc flng dyng rdng rai, dde bidt trong phdn tieh trgng thdi chiu Iflc cua he ciiju Ifle khf dbng. Theo db, kit cdu mdt cdu dflpc md hinh hda Id dgng tam chju uln thay t h i cho dam ehju uln phdng nhfl trong md hinh vdn sfl dyng. Trong bai bao, eae tde gid xdy dflng thu^t todn, chfldng trinh phan tich ddng iflc hpe hd lidn hpp tdm - ddy - ebt (mb phdng kit cau edu ddy vdng theo mb hinh khdng gian) chju tac dyng cua Iflc khf d0ng do dbng khf ehuyin ddng vdi van tie U gay ndn. Trong db, xay dflng phfldng trinh vi phan dao dbng eCia hd trdn cd sd xdy dflng cac flng xfl ciia phdn tfl tdm chju lflc khf dOng, xdy dflng ma trdn cdc phdn tfl ddy cable, ebt.
2. Md hlnh bai todn vd cdc gid thiet Xet hd lien hdp tdm - ddy - eOt chju tdc dyng ciia Ifle khf dbng do dbng khi cd vdn tic U chuyen d|ng theo phflpng ngang gdy ndn. Md hinh bai toannhflH/n/7 2.r.
a) - luld hinh thi/c b) - Md hinh PTHH Hinh 2.1: Md hinh bdi todn Bai toan dflpc gidi quylt trdn cP sd cdc gid thilt: Vdt lieu cua kit elu ddn hii tuyln tfnh, cpt lien kit cflng vdi nin, tdm dflpc xem Id tdm mdng, tudn thD djnh ludt Kirchhoff - Love. Xem rdng Ifle khi ddng chf tdc dyng Idn tSm, edn dnh hfldng eiJa nd din cac phdn tCf day, edt xem nhfl be, dflpe bo qua.
3. Thiet lgp thiidt todn PTHH phdn tich bai todn 3.1. Phan ttf day cable [5],[8]
Phdn tfl ddy cable ddn hii bj kdo trong mat phdng thdng dflng dflpc bilu thj nhfl tren Hlnh 3.'l, vdi ehilu ddi trflde khi bj kdo L , md-dun ddn hdi v$t li^u E. didn tich thilt di§n A", trpng Iflpng tren mbt ddn vj chieu ddi trfldc khi bj kdo Id w.
55
KHOA HOC - CONG NGHE
Hlnh 3.1: Phan tO day cable D6i vdi day d i n h6i, quan hS gIDa cac hinh chigu v i cdc thinh phin lac tgi cac ddu mLJt phdn
L, =-P, —=- + ~In -
\ E A W T,-PJJ 1 • { ^ / - ^ l
Trong dd: T,, T - Cdc Ifle keo tgi 2 nut phdn tfl P, =wL„-P,;P, =-P,;T, = Jp,^ + P^
Ma trdn db cflng, ma tr^n khli Iflpng phdn tfl cdt cap (12x12) dflpe xdc djnh theo [4],[9].
3.3. Life khf ding tdc dgng ldn phin ttf tam Khi chju tdc dyng ctia luOng gid, trong mb hlnh PTHH cOa k i t cdu, mil phdn tfl tdm phSng chiu tdc dyng eua Ifle ndng phdn bd L vd md- men udn phdn bd M^, gpi chung Id lflc Khf dbng tdc dyng Idn phdn tCr tdm phdng, chiing dflpc xac dinh [1], [9]:
L, = ^-QP^B\KH;i.K)^^KH\{K)~*K'H\(Kya[ (7)
Trong dd: p - Mdt dp khdng khi; U - Vgn tdc ddng khf; B - B l rdng phdn tfl theo phfldng gid tdc dyng; K - Tdn s l thu gon va
' (K) vdi i = 1 + 3, duoc xac T.-T
(1) (2)
K = -
Tac6[11: rsL, 3P, fir
L^.
3L,1 5P, m a>,J
U[F]. 'dp. (3) Trong dd: [F] - Ma tran dd mem.
Ma tr$n db eflng tilp tuyln [KJ vd vde-tfl ndi Iflc tfldng flng ciia phdn tfl 4 bgc tfl do tgi mit eb dang:
(4) [K,]^
1 ^1 2 k.
k, -kj -K
. ( i P ) = AP,1
4P, AP, Ma tr^n [KJ l i h$ thilrc lien h& giuTa v6c-td s6 gla luc nut cua (AP. ^i ^, ^.V va vec-td s6 gla chuydn vj nut cua phSn ti/|a», ^, ^, ^.f. Ma tr^n [K,] va cic lite nut P,, Pj cin dUdc tfnh diu tISn. Cac Wc nay xem nhu da bigt tuy theo vj tri ban diu ciia cac niit phin ti!f cable, duoc sil dyng cho qui trlnh lap do cUng. Qui trlnh niy doi h6i phii bigt cic gia trj ban diu cCia cic luc P^.P^. Viic xic dinh ma trin do ci^rng cilia diy cable dUdc thuc hiOn theo phudng phip lip.
3.2.Phint£lc^tl9]
Phin til oOt a diy dUflc hilu nhu l i trudng hdp phin t\i dim khdng gian 2 digm nijt, mdl nUt c6 6 bic tu do. MO hlnh v i cic bic tU do cua phan tiif t h l hiOn nhu trSn Hlnh 3.2.
Hinh 3.2: PhSn lir c^t Vic-td chuyin vj nut cua phin tD:
K l - I " ! V, w, 6., e„ 9„ n. V, w, 6„ B.. 9,,)' (5) Nhu \iiy, trong trUOng hop niy, mOi phin til cOt cO 12 bic tu do. Quan hO nOi IUc v i bign dang
cOacOl: W=[D1W (6) C iohimA *( K),H « djnh bdi:
ir,iK) = ~Fi.). n;(K)-~U*Fik).^^ . j;(i:).^F{ki.^m.--^
.F[i:).~^\.H;m=- ,.»H1 H-Sffll
J- (9)
F ( k ) . G(k).
vdi k = K/2, cic him F(k), G(k) duoc xic dinh bfli:
500502k* + 0,512607k- + 0,2I04k + 0,021573 k* + l,035378k'+0.251293k + 0,02l508 ' 0,000146k'+0.122397k^ + 0.327214k +0,001995
k* + 2,481481k*+0,93453k + 0,089318 (10)
3.4. PhUdng trlnh dao d^ngphgn tit tgm chiu ll/c khi dfng
Dudi t i c dgng cija luc khf dgng v i t i i trong khic, i p dgng nguyin ly Hamilton cho phin t^
[2],141,[91: ,,
6H. = s[(T^-U. + WJdl = 0, (11) Trong dd: H.-T,-U,»W..H,((,'].|C].I)- Him tic dgng Hamilton: T^ - DOng nang cOa phin ti!f: U^ - Thg ning toin phin cCia phin tu: W,, - COng giy ra bdl ngoai luc tic dOng lOn phan til: {•*']•{<] - TUdng Ung l i vec-td chuyin vj, van toe nijt cDa phin til.
Ta cO phuong trlnh vi phin mO t i dao dpng cua phin td tgm nhu sau:
[.^]|,-).[c-]|,-).[K-](..).|,.|-[Ki](,-)-[c:](,-). (12) Trong dd: [^.] W- Tuong Ung l i ma trin cin khi dOng, ma trin dO cUng khf dOng cila phin til, dUdc xac dinh nhu trong [11,[9]: {F') - T i i trong trong nilt cCia phin til khOng lien quan dgn luc khf dOng.
Vigt l^i (12) dudi dang sau:
[M-](..).([c-].[c..]j|.-|.([l.->[k-.])|.-].|,-) (13) Trudng hop tam chi chiu tic dgng cOa Igc khf dOng, phUdng trlnh (13) trfl thinh:
[„-](i-).([c-].[<i])|,-|.([K-].[.ci])l,.) = M (1*) 3.5. Thu$t toin PTHH giii bii toin ViOc ghip nil cic phin til tim, phin til cOt v i phin tH diy (cable) tao thinh mO hlnh PTHH tdng 56
KHOA H p c - C O N G N G H I
thg cOa he duoc thuc hiOn bSng phuong phip dO oung true tiep va so d6 Skyline theo thuat toan Chung cCia phuong phip PTHH [3],[4],[7]. Sau khi ghep noi xiy dung cic ma trin, vec-td ting t h l v i khu biSn, ta cO phuong trinti vl phin mO t i dao dOng cua h# liOn hop t i m - diy - cOt chiu t i c dgng cua IUc khi dong xult phat tU phuong trlnh (13) nhusau:
[Ml{4)*([Cl + [C.l){i).([K] + [K.])(,}.(Fj(15)
"3y- [M|{q).[C]{4},[K]{,).(Fi (16) Trong dd: M-Bx] w-Hil-IWi'i i-i"i->i.ii-&. ix^-;"
[«]•[_«]- TUdng Ung i i ' c i c ' m a trjn khgi luong phin tu, ma trin dO cUng phan til cua kit cau (khOng llSn quan dgn luc khf dong). Cio hing sO c i n Rayleigha,, |3, duoc xic dinh thOng qua ty so c i n 5 v i hai t i n s6 dao dong rieng diu tiin cua kgt cau [9].
Cac t i c g i i sCr dgng phuong phip tfch phin true tigp Nev»mark dg giii phuong trlnh (16) v i cg thg hOa thuit toin bing viic lip trlnh tfnh toin trong mOi trUOng Ansys, chuong trlnh cO t i n Cable_Bridge_Aerodynamlc. Chuong trlnh tfnh da duoc kilm ChUng v i dim bio dp tin ciy.
4. vfdusei
Thdng sS kgl du: He liSn hop tSm - diy - cOt, trong do tam bing v i t li#u be tOng, chilu d i i Lp = 150m, chilu rgng Wp = 12m, chilu day h = 0,10m, mO-dun d i n hOi E = 3,4.10'°N/m', h i sg Poisson V = 0,3, khgi luong riing p = 2500kg/m'.
H i ggm 3 nhip, cd 4 cOt bing be tOng, mit cat ngang chO nhit b^ x b„ = 0,3m x 0,4m, chilu dai ting cOng H = 35m, phin tU mat tam din mit nin cd chigu d i i H, = 20m, bO trf doi xUng. Hai day day c i p bing thep bO trf 2 ben, vdi 20 diy mli nhjp.
Thdng so tii trgng: T i i trpng khf dOng tie dgng do dong khf chuyin dOng vOi vin toe U = 30m/s, tic dgng theo phuong ngang.
Sil dgng chUdng trinh da l i p , tign hinh tfnh t o i n dao dong riing v i phin tfch dgng IUc hoe b i l toan vdl bude tich phin 4t = 0,06s, thdi gian tfnh la t^, = 15s.
Digm xuit k i t q u i l i nut 286 (dilm chfnh giOatSm). Bieu klOn d i u : fq.!-o; {q,) = ».
Kgt qui tlnh: Hlnh 4.1, 4.2 tUdng Ung l i dip Ung ehuyen vj dUng w, gia toe chuygn vj dUng w theo thdl gian tai dilm mip ngoii v i dilm glQa t i m . Hlnh 4.3, 4.4 tuong Ung l i dip Ung mO-men ugn M^ tai chin egt v i Igc dpc N trong d i y c i p ChO theo thdi gian.
-So 10/2015
Hlnh 4.2: Bip Ong gla tSc Mng w - thdi gian
Hinh 4.3: Dip Ong md-men udn Mx - thdt gian
Hlnh 4.4: Bip ling li/c dgc N - thdl gian Bing 4.1. Tdm tit gii tri Idn nhat vi chuySn vl, gla toe, ndi ti^c t?l cic diim tlnh w
Dfllu^g GUtillftn
«™.[m]
M^ngodi 0.0054
CiOa 0,0024
* « - [ » ' ' ' ) Mip ngodi
0,0519 Gnla 0,0145
Ne'p*"!
17767 N„fN)
34630
Hinh 4.5, 4.6 tfldng flng ia dap flng v l flng sudt a,, (T^ va dap flng iflc dpc N^ trong c|t theo thdi gian.
Hinh 4.1: Ddp tfng di vdng w - thdi gian Hinh 4.5: Ddp tfng tfng suit - thdi gian
57
KHOA H O C - C O N G NGHE
Hlnh 4.6: Bip Itng ti/c dgc N , - thdi gian Bang 4.2. Tdm tat gii trj Idn nhit v$ Ong suit trong tim vi If/c dgc trong cgt
Dflluvng Cii tri U^ °bsl
d^\tilnf\
334502
aj"p*ta^]
67379 NJN]
I9173B
Nhgn xet: Ddp flng d | n g eua ha tam - day - c | t chju Iflc khi d d n g Id phflc t g p , vdl trfldng h p p cg the e u a bdi t o a n cho t h d y d a p flng c h u y e n vj, gia t i c dflng tai d i l m tinh thubc t a m v d Ifle dpc trong c | t Id I n dinh, c b n Iflc dpe trong c a p ehii va flng sudt a^ tgi d i l m tfnh t h u d e t d m ed xu hfldng t a n g theo t h d l gian. D i l u ndy cho t h d y khd nang o n djnh c u a hb la d d m b d o , song cd t h l ddn d e n t i m va cap chu bi phd h i i y vl khdng d d m b d o d i l u kign b i n .
5. K^t ludn
x a y dflng cde quan hb flng xfl va thuat toan, chfldng trlnh tfnh phan tfch ddng Iflc hpc h$ li&n hpp tdm - ddy - c$t chju tdi trpng khi dbng, trong do sfl dgng mb hinh Iflc khf ddng Scanian.
- Khdo sdt s l xac dinh ddp flng ddng dbng Iflc hpc (chuyen vj, gia t i c , ndi Ifle) ciia hd dfldi tdc dung ciia Iflc khf dbng do dbng khi c h u y i n ddng vdi van tde khdng doi gay ra, k i t qud cho phep xem xet, phan doan khd nang iam viec cua h d .
K i t qud nghi&n eflu cua bdl bao la ed sd cho v l | e khdo sat Ifla chpn eac thbng s d hpp ly eho mOt sd dgng edu day vang chju tac dgng ciia Ifle khf ddng, gdp phdn phdt trien nganh GTVT •
hi lien hdp tam - ddy - cgt chju til trgng di ding bing thiit bj Tuned Mass Damper (TMD), T u y l n tdp Cbng trinh Hdi nghj C p hpc ky thugt todn qude, Ha Ndi.
[3], N g u y i n Thdi Chung, Bui v a n T h d m , Dfldng Thj Ngpc Thu, Vu Anh T u d n (2012), Dao ding cua hi lidn hdp tam - cgt chju tdc dgng cOa tii trqng di dong, s d 147, T g p ehi Khoa hpc vd Ky thu^t, Hpe vi$n Ky thuat Quan sfl, tr.14 - 23.
[4]. Chu Qudc Thdng (1997), PhUdng f^dp (Mn ttfhOu hgn, NXB. Khoa hpc vd Ky thuat.
[5], Phan Thanh Tuan (2012), Phan tth ding ldc hi dim lien hgp chiu tdc dgng ding thdl cOa tii trgng di ding vd li/c khf ding, LuSn an T i l n sT ky thuat, Hpc vien Ky thuat Quan s f l , Hd Ndi.
[6]. Trdn T h l V a n (2012), Nghidn cCfu in djnh cua tim composite Idp chju tii trgng khf ding, Luan dn T i l n sT ky thuat, Hpc vien Ky thuat Quan sfl.
Ha Ndi.
[7]. Bathe K. J . and Wilson E. L. (1978), Numerical Method In Finite Method Analyis Prentice, Hall of India Private Limited, New Delhi.
[8]. M.F. Liu a. T.-P. Chang b, D.-Y. Zeng (2011), The interactive vibration behavior in a suspension bridge system under moving vehicle loads and virtical seismic excitations. Applied Mathematical Modelling 35(2011), pp.398-411.
[9]. >4nsys IncTheory reference, Southpointe 275 Technology Drive Canonsburg, 2010.
N g d y n h g n b a i : 29/8/2015 N g d y c h a p n h | n d a n g : 15/9/2015 Ngfldi phdn bi$n: GS. TSKH. Nguyen T i l n Khidm
GS. T S . Hodng Xudn Lflpng
T d i l i g u t h a m k h d o
[1]. Trdn Ngpc An (2014). Tinh todn in djnh khi ding flutter cua dim chu trong kit du ciu hd ddy bing phddng phdp budc ldp, Luan an T i l n sT ky thuat, Trfldng Dgi hpc Bach khoa Hd Ndi.
[2]. N g u y i n Thdi Chung, V u Anh Tudn, D d Ngpc T i l n (2014), Nghidn ctfu giim dao ding cho
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