DIEN DAN KHOA HOC CONG NGHE
l/NG XI/ CUA KHOI Ll/dNG CHUYEN DONG TREN MO HINH NEN BA LdP
• •
suf DUNG PHl/ONG PHAP PHAN TUf DAM NHIEU LdP CHUYEN fiONG
• •
DYNAMIC RESPONSE OF A HIGH-SPEED MASS ON A THREE-LAYER FOUNDATION USING MOVING FRAME METHOD LLTdNG V A N HAI, N G U Y I N D U Y P H U , C A O T A N N G O C T H A N ,
D A N G N G U Y I N T H I E N T H U , T R A N V A N M l i N
TOM TAT
Trong bai b^o n^y cac nghien cijfU dufdc trien khai d l phan tfch ufng xuf dong cua mo hinh vat the chuyin dSng vdi too do cao trfn mdt he ket ciu n^n phufc tap. Trong d6, he kit clu nen difdc m6 hinfi h6a nhif mdt he ba Idp dim. Phifdng phap phSn tijf nhilu Idp dim chuyin dong MFM 6\lQc suf dung d l phan tfch cac bai toan. Trong do, ma tran kit cau cua he nIn ba Idp dim dif(3c thilt lap trong h6 toa dd tifdng dli gin lien vdi vat the chuyin dong. Cac phan tich s6 dufdc triln khai nhlm xac dinh nhdng Snh hifdng cua cac ylu to quan trong din ufng xi? ddng ciJa he vat thi - nIn, nhif: van toe va khdi lifdng cua vat ttil, sif khong ho^n hJo cfla mat difdng va do cijfng cua nen ba Idp... Oing thdi hien tifdng cdng hifdng cung difdc xem x6t va giSi quylt.
TiJf khoa: V|t thi chuyin dong, Phifdng ph^p phin tuf nhilu Idp chuyin dong, Nin ba Idp.
ABSTRACT
In this paper, a computational study is carried out to investigate the dynamic response of a high speed moving mass on a complicated foundation. The foundation is considered as a three-layer beam model. The moving frame method IVIFM is employed to model the foundation, where structural element matrices are formulated based on a convected coordinate sys- tem attached to the moving mass. A parametric sftidy is carried out to understand the effects of various significant factors on the dynamic response of the mass-foundation such as the speed and weight of moving mass, the severity of railhead rough- ness (track iregularity) and the foundation stiffness. The resonant phenomenon is also considered and investigated.
Keywords: High-speed mass, Moving Frame IVIethod, Three-layer beam model.
I.GIOflTHIEU
Trong xu t h i phat trien va hdi nhap or nudrc ta vao thdi diem hien tai, eae tuyln dudmg d td cao t i e duoc dua vao sCf dung khai thac hoac trong qua trinh xay dung dang d i n trd thanh nhufng hlnh anh quen thudc.
Ddng thdi, viec xem xet xue t i l n d i u tu xay dung tCmg budc ddi vdi mot sd tuyln dudng s i t cao t i e ndi eae thanh p h i kinh t l trong (Jiem, hudng tdi viec xay dung tuyln dudng s i t cao t i e Ble-Nam trong tuong lai khdng xa cung da duoc cac phuong tien truyin thdng nhilu i l n d l cap. Tuong ttr, eae dudng bang san bay - mdt loai k i t c l u n I n thudng xuyen chju sirtuwig tac vdi khii luwig di chuyen d t i e dp cao cua may bay trong qua trinh chuan bj elt canh va sau khi khi ha canh - cung duoc xem nhu mdt trong eae loai nIn dudng cao tdc ma bai bao nay mudn d l cap.
Vl vay, ling x(t ddng eua he gdm eae phuong tipn cao t i e di chuyen tren cac loai nIn dudng dupe c l u tao phu hpp vdi loai phuong tien dd ludn mang tfnh phite tap rIt cao. Dae biet, ^ l u nay se ed nhOng anh hudng vd cung nguy hiem cho phuong tien khi di chuyen vdi t i e dp cao n l u nhu sir hoan hao eua mat dudng (hoac mat ray) va c l u tao nIn dudng khdng dat dupe sir phij hpp eIn thilt theo yeu c l u ky thuat. Do dd, viec nghien cufU eae ufng xtir ddng nay la rIt quan trpng va e l p thilt. Theo nhOng phuong phap khao sat truyin thing, dudng cao tdc (hoac mdt he ray-nin cao tic) dupc khao sat nhu he nIn dan-nhdt mdt hoac
nhilu Idp chju eae tai trpng di ddng thay doi theo ea thdi gian va khdng gian. Vf du nhu, vao d i u nam 1974, Timoshenko et al. [1] da d l xult Idi giai de phan tfch ddng d i m don gian tua tren nIn Winkler chju cac tai di ddng bang phuong phap chdng chit eae dang dao ddng. Mathews [2] da nghien eufu v i n d l tren blng each suf dung phuong phap biln doi Fourier (Fourier Transform Method - FTM). Phuong phap FTM ed the cho Idi giai ehfnh xac nhung trd nen b l t i c khi he khao sat gdm eae vat chuyen ddng va nIn dudng ghep ehung lai phijfc tap. Chang han nhi/ eae loai phuong tien dupe md hlnh hda thanh he nhilu bac tir do vdi nhilu diem tutmg tac giufa banh xe va mat nIn dudng, hoac eae tai trpng di ddng ed lien quan d i n viec tang t i c va giam tie. Phuong phap phin tCr huru han truyin thing (Finite Element Method - FEM) cung dupc thilt lap de giai quylt nhilu v i n d l phufC tap. Filho [3] da trinh bay mdt danh gia v l viec sO dung FEM de giai eae bai toan d i m tilt dien khdng doi chju tai trpng di ddng. Andersen et al. [4] da dua ra dupc each thanh lap edng thiic FEM cho bai toan d i m tren nIn Kelvin chju tai dilu hda ehuyeri ddng.
Trong viec giai quylt v i n d l tai trpng di ddng, phuong phap FEM truyin thing gap khd khan khi tai di ddng tiln d i n g i n bien eua miln hijfu han phin tCr va di chuyen vupt ra ngoai bien. Nhufng khd khan nay ed the khIc phue blng each sd dung mdt miln kfch thudc du Idn nhung thdi gian tfnh toan lai tang len
NGUdl XAY DUNG SO THANG 7 & 8 - 2014
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dang ke. Trong mdt nd luc de vupt qua nhufng khd khan gap phai bdi phuong phap FEM, Krenk et al. [5]
da d l xult viec s(t dung phuong phap FEM trong he tpa dp chuyen ddng de tlm ung xd cCia mdt nCra khdng gian dan hdi chju mdt tai trpng di chuyen. Lpi feh quan trpn^ ed dupe bdi phuong phap nay la kha nang giai quyet tdt vin d l edn tdn tai da neu do tai trpng di chuyen tren mdt miln hOru han. Koh et al. [6] da lay y tudng v l he tpa dp chuyen ddng de giai quylt bai toan tau-ray-nin va dat ten la phuong phap phin tO chuyen ddng (Moving Element Method - MEM). Phuong phap MEM da cho thIy tfnh i/u viet vupt bac so vdi phuong phap FEM truyin thing trong cac phan tfch ung xCi dpng cua he gdm tai trpng di chuyen tren mdt kit clu nIn va da dupe cac nha nghien euru sur dung de trien khai sau dd [7, 8]. Trdn eo sd eua phuong phap MEM, mOt phuong phap mdi da dupe trinh bay bdi Thi et al.
[9] vdi ten gpi la phuong phap phin tCf nhilu Idp chuyen ddng (Moving Frame Method - MFM) de giai quylt bai toan nIn ba Idp dim. Trong phuong phap MFM, mdt doan huu han (truncation) dupe xem nhu di chuyen cung van tie vdi mdt he true tpa dp chuyen ddng (convected coordinate) dupre gin chat vdi tai trpng di ddng. Bang viec rdi rac hda doan hi]fu han, c^c phin tir nIn nhilu Idp dupe hlnh thanh va dupe gpi la "phin tCr chuyen ddng MFM" (Hlnh 1). Qua dd, tai trpng di ddng cd the dupe xem nhu la "dung yen"
tai nut eua cac phin tCf thudc doan huru han dang xet.
Dilu nay nham tr^nh dupe viec cap nhat eae veeto tai trpng hoac chuyen vj do sir thay doi vj trf eiJa diem tuong tac giufa tai trpng di ddng va nIn.
Muc dfch eua bai bao nay nhlm phan tfch eae ung xijf ddng eua mdt he khao sat gdm md hlnh vat the mdt bac tu do chuyen ddng tren nIn ba Idp sCr dung phuong phdp MFM. Vat the va nIn ba Idp d day lin lupt 6iiac xem la dai dien cho mdt loai phuong tien cao tie va mdt nIn dudng cao tdc. Cac kit qua nghidn cufu se gdp phin cai thien mdt sd vin d l ky thuat chuyen ng^nh lidn quan din edng tac thilt k l va bko tri eae loai kit clu dudng chuyen dung cho eae phuong tien cao tie.
II.COSdLYTHUYET
Cac true tpa dp trong phuong phap MFM the hidn d Hlnh 1 bao gdm true x ed djnh la hudng di chuyin eua tai F^va true chuyen ddng r la true dUPe gin vao tai di chuyen F, vdi van tie V khdng doi.
Di^mdlu
itm hOtt hftn MFM F.
M til fit f t t fit If
Phjn t\i MFM Di8m cu6i I I do?n hOu h ^ MFM NiSti j
Hinh 1: H$ toa dd MFM vi md hinh nhn ba Idp dUdc rdi rac hda
He true tpa dp chuyen ddng r dupe xac djnh nhu sau:
r = x-Vt (1)
Trong dd t la thdi gian di chuyen eua tai F,.
Md hlnh dupe chpn cho phan tfch ung xOddng cua he khao sdt gdm v§t the chuyen ddng tren nIn ba Idp
6^c the hien d Hlnh 2, bao gdm: (1) Vat the mot b$ctu do ed cdc thdng sd dae trung la m (khdi lupng), k (dp cung Id xo), c (dp giam xlc) vk u (chuyin vj dung), di chuyen vdi van tie V theo phuong x duong; (2) N§n ba Idp dupc nrid hlnh hda nhu ba Idp dim Euler- Bernoulli tren nIn dan-nhdt vdi eae thdng sd dac trung nhu sau: khdi lupng {m,., m, , m^ ya dp cung chdng udn {E, I, ,EJ,, El, If,) cua ba Idp dim; he sd dp cufng tuong duong {k,, k,, kj,) va he sd edn tuong duong (a,
,a,, (Th) eiJa ba Idp nIn. Trong dd, cac ehi sd r,svab
lin lupt la dai dien eua cac Idp nIn 1, 2 va 3. Cac thdng sd y^, y^ va y,, iln lupt la chuyen vj dung cua cdc Idp dim 1, 2 va 3.
vat thi
cl
"1,
?•
Hi
m„ E,I,
M=i
ty
OJ s yj ' >4i
li > ty > li
k,,a, m.,E,I,
"lb. Eili,
Hlnh 2: Md hinh vat th4 chuyin ddng trdn nhn ba idp
Phuong trinh chu dao eiJa md hlnh nIn ba Idp nhir sau:
' dx" ^' ' ' dx*dt ' di" \dt dt,
tx" dx^dl dt^ \dt dt )
(2)
(3)
E,h
5V*
dx T + %E,I,
dx*dt + m.
-K{ys-yi,)+a,^+Ky,. Qy,
8t' 0
-a. {dt dt j
(4)
Trong do 5 la ham Dirac-delta; 0„ ^, va ^^ iln loot la cdc hd sd can trong cua eae Idp dim 1, 2 va 3; F, la luc tuong tac tai diem tilp xue giufa vat thi vk mat nIn.
Cac chuyen vj y^, y^ va y,, iln lupt la cac ham phy thudc tpa dp x va^ thdi gian di chuyen t ciia vat thi.
Bang phep biln doi toan hpe dua vao quan he ti^cdng thufC (1) de chuyen^>',, y^ va y,, thdnh cdc ham phu thudc tpa dp chuyen ddng r va thdi gian t va blng each ap dung phuong phap Galerkin, phuong trinh tdng quat cho phin tCr chuyen ddng MFM ba I6p (Hlnh1) dupe xac djnh nhir sau:
^ e r y r + C ^ y r + ^ . r y r = - f c ^ ( r )
'^Js+C„y,+K„y,=0
(5) (6)
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^e,ys+c^h+^e,yB=o (7)
Trong dd M^„ C„ va AT,, i l n lupt la ma tran khdi li^o^ng, ma tran can va ma tran dd cung eCia eae Idp 1 (/• = I), Idp 2 (/ = s) vk Idp 3 (/ = i)) eija phin tCf MFM.
Ti^ do xac djnh dupe ma tran k i t c l u ciia phin td chuyen ddngMFM:
M^=M„+M.,+M,
c^=c„+c.
' e *(8) (9)
K ^ = K + K , + K '•ef-"-^^"^e,'^"^el, ( 1 0 ) Dao ddng eiJa he gdm vat the va n I n xay ra ehij
y l u do sir khdng hoan hao eua mat n I n , ben canh nguyen nhan do anh hudng eua tai trpng luc di chuyen. De thuan tien cho cac phan tfch t i l p theo, dp khdng hoan hao eua mat n I n dupe gia t h i l t tuan theo quy luat hlnh sin va dupe gpi la dp n h i p nhd. Gia trj nay difpc the hien d cdng thdc sau:
yt = a, sin(2nx /X^ (11) vdi a, va A, i l n lupt la bien dp vk budc sdng eua dp
n h I p nhd mat n I n . Theo dd, luc tuong tac F^ dupe xac djnh nhu sau:
K = ciyr+y,-u)+k{y^-y^-u) (12) Phuong trinh chuyen ddng tong quat ciJa md hlnh
vat the:
mu = F^-mg (13) vdi g la gia t i e trpng trudng.
TCr cdng thiic (13) ed t h i t h I y luc tuong tac F^ ed gia trj b l n g tong lue tmh va luc ddng. De xem xet mOc dp anh hudng eiJa luc ddng, he sd k h u l e h dai ddng D/AF (Dynamic Amplification Factor) - la ti sd giOa giOa tdng luc tuong tac ddng F^ Idn n h l t va luc tmh - dupc xac djnh theo edng thunc:
DAF = \ + g
(14)
N I U DAF< 2 thi anh hudng eiJa luc ddng la khdng ddng ke va n l u DAF> 2 thi anh hudng cua luc ddng Id ddng ke vd luc nay ed the xem b i t d i u x u l t hien hidn tupng "ndy bdnh xe".
Thuc hidn viec ghep n l i cdc ma tran eon eua md hlnh vat the - n I n MFM ba Idp, he phuong trinh vi phan chuyen ddng t d n ^ the cho md hlnh gdm vat the vd n I n ba Idp dupe thiet lap ed dang n h u sau:
Mz+Cz+Kz=P (15)
vdi z = Oy Ol y2 02 yN^N u / l a vee to chuyen vj nut tdng the cua md hlnh vat the-nin; P la vee to tai tdng the; M, C va K Id cdc ma tran k i t c l u tdng the.
Phuong trinh (15) dupe giai blng phuong phdp tfch phan Newmark.
III.VfDUSO
Cdc bai todn dupe thyc hien de khdo sat hien tupng edng hudng cua he gdm vat the chuyen ddng va n I n ba Idp (he vat the - ndn) vd dng xd ddng eua he vat the - n I n khi tang khdi lupng vat the vd khi thay ddi
dp cung eua nIn ba Idp. De gidi cdc bdi todn phan tfch, mdt chuong trinh MFM dupc vilt blng ngdn ngur lap trinh Matlab vd cdc kit qud se dupe kiem ehung so sanh vdi idi giai gidi tfch.
Bang 1, Bang 2 vd Bang 3 ben dudi the hien cdc thdng sd ehung dupc sd dung trong eae bai toan phan tfch.
Bang 1: Thdng sd v l vat the chuyen ddng m
4100 kg
k 8,0x10^ N/m
c 6,7x10'Ns/m
g 9.81 m/s^
Bang 2: Thdng sd v l n I n ba Idp Thdng s6
m.
E,
h
k,
C,-
Ldp nIn 1 60,0 kg/m 2.1x10" Pa 3.217x10-5 m<
6,0x10^N/m2 47,7x10'
2 V'"r *r
Ldp nln 2 1275 kg/m 3.9x10'" Pa 8.5x1 a*m^
9,0x10" N/m^
83,0x10'
U^sK
Ldp nIn 3 2340 kg/m 3.0x10" Pa 3.3x10-3 m<
6.0x1 O^N/m^
90,0x10' 2ylm^k^
{Ghi chu: i = r, s, b tuong ung lin luat vdi I6p nin 1,2, 3) Bang 3: Thdng sd quy djnh v l dp n h I p nhd mat n I n
Misc66 Bign dd nh^p nho a, (mm) Glin nhl/trdn (nearly smooth)
NhIp nhfi \iiii ph§i (moderate) Rat nhap nhd (severe)
0,05 1 4
Ngoai trd cdc gid trj khdc dupe chpn cu the trong tCmg bdi todn, gid trj cdc thdng sd trong Bang 1, Bang 2 vd Bang 3 d tren se 6\jrac sd dung cho t i t ed cdc bdi todn phan tfch dupe khdo sdt.
1. Bai toan 1 : Kiem chiPng chi/tfng trinh l\/latlab Viec kiem chdng dupc thuc hien blng each so sdnh k i t qua dat dtrpe td chuong trinh Matlab eua bdi todn sd dung MFM vdi k i t qua tuong dng td ldi gidi gidi tfch. Bai toan ndy dupe thuc hien theo cdch so sdnh chuyen vj mat nIn theo chilu ddi doan hdu han vdi gid thilt mat nIn hodn todn tron. Cdc s i lieu d i u vdo ciJa bdi todn dupe tdm tdt theo Bang 4.
Bang 4: Tdm tat cdc thdng sd ehfnh vantflcvatthi
i/=180krTVh (50m/s)
DO itfilp vt\6 mat n^n a, = 2.0mm; A,, = 1m
eija Bai todn 1 Thdng s6 kfiac Bang 1 & Bang 2
Bieu dd d Hlnh 3 the hien k i t qua so sdnh chuyen vj mat nIn gida phuong phap gidi tfch vd phuong phdp phin td chuyen ddng MFM. Bleu dd cho thIy k i t qua dat dupc td chuong trinh Matlab va k i t qua dat dupc td ldi gidi gidi tfch khd trung khdp vdi nhau. D i l u nay da chdng td dd tin cay eua chuong trinh Matlab trong eae bai todn phan tfch MFM.
NGUdl XAY DUNG SO THANG 7 & 8 - 2 0 1 4
oa
-0.1
"§•-0.3
E -0.5
-0.7
-1.1
I h e o M F M theo P P G i i tfch
UfNG xuf CUA K H 6 | laONG CHUYEN OONG TREN MO HINH...
Bang 5: Tdm t i t cdc thdng sd chfnh eiJa Bdi todn 2
-40 -30 -20 -10 0 10 20 30 40 TpadO r(m>
Hinh 3: Chuyin vj mat nhn theo chihu dai doan hufu ban 2. Bai toan 2: Khao sat hien tuomg cong hu'orng cua he gdm vat the chuyen dong va n l n ba Idp
Bai todn nay chu y l u xem xet mdt sd v i n d l co ban v l hidn tupng cdng hudng lien quan d i n he khdo sdt gdm vat the vd n l n ba Idp. T i n s i rieng/„ eiJa md hlnh vat the - n l n dUPc xdc dinh nhu sau:
vdi CO dupe xac djnh theo bai todn trj rieng:
det(K - ffl^M) = 0 , 0 7 ) Trong dd M vd K i l n lupt la cdc ma tran khdi lupng
vd dp cung tdng the eua he vdt the - n l n .
T i n s i kfch thfch ddng/^, dupe sinh ra do sir khdng hoan hao eua mat n l n phu thudc vao van t i e v eua vat the vd budc sdng v, eua dp nhIp nhd mat n l n , dupe xdc djnh theo edng thdc:
'•-i
(18)Hidn tupng edng hudng xdy ra khi gid trj t i n s i kfch thfch ddng/e xIp xi vdi t i n s i rieng/„ vd dilu nay xay ra khi vdt t h i chuyen ddng vdi van t i e dat van t i e gay ra edng hudng v^:
v. = A/„ (19) Nhu vay, hidn tupng edng hudng xult hidn bao
gdm nhilu nguyen nhan dupe dilu khien bdi cdc thdng s i : van tdc v^t the, budc sdng nhIp nhd mat n l n vd cdc thdng sd dae trung eua he vat the - n l n . De khdo sat su phu thupc ciJa t i n s i kfch thfch ddng /^ vao cdc thdng sd van t i e \/eiJa vat the vd budc sdng nhIp nhd l^ eiJa mat n l n , bdi todn nay khdo sdt cdc gid trj van tdc i^td72 km/h d i n 324 km/h (20 m/s d i n 90 m/s) va budc sdng I, td 0,5 m d i n 4 m. Ddng thdi, de khdo sdt dnh hudng eua dp edng n l n ba Idp d i n t i n sd rieng / „ ciJa he vat the - n l n , mdt trudng hpp anh hudng dien hlnh dupc xem xet vdi viec cho tdng ddng thdi cdc dp edng k, va ki, eua Idp n l n 2 va 3 vdi k, = nx (9x10«) N/m^ykk^^nx(6x10^ Wm\ trong dd
« = 1H- 5. Cdc thdng s i ehfnh cua bdi todn dupe tdm t i t trong Bdng 5. Cdc thdng sd lien quan khdc dupc l l y theo Bang 1 vd Bdng 2.
vantdci' Bi/dc sdng X, DO cOng k, va k^
Tif 72km/h d6n 324kiTi/h Tif 0.5m (20m/s dSn 90m/s) 6hn 4.0m
yt, = /Jx(9x10'^N/m2 it, = nx(6x10')N/m«
trong dd n = 1 + 5 Hlnh 4 bieu diln su thay ddi ciJa t i n s i kfch thfch ddng /^ theo budc sdng nhIp nhd A, cua mat nln va theo van t i e v eua vdt the chuyen ddng. Ddng thdi bieu dd dupe the hien d Hlnh 5 bieu diln sir thay ddi eua t i n sd rieng /„ eua he vdt the - n l n theo dp eiing cdc Idp n l n 2 vd 3.
-«-V4nt6c72laiVh Hi-V4ntfol26kni(h -*-V4ntfcl80kmAi -H-V4nt4o2S2ianA<
-*-V«ntic324kfiVh
O.S 1.5 2 ^5 3
Bi/iicsAng ntijp nhO;!, (m)
Hinh 4: T^n s6 /^ thay dd'i theo bifdc sdng A, va van t6c v
1.5 zs 3 as
k. (x9x10» N/rrt»); 1^ (xOxlO'N/m")
4.5
Hinh 5: T4n s6/„ thay ddi theo k, va k,, tang d6ng thdi Cdc bieu dd dupfc the hien d Hlnh 4 cho thIy mile dp tang eua t i n s i kfch thfch ddng /^ ty le thuan vdfi mdc dd tang van t i c v eua vat the, ddng thdi, ty l§
nghjeh vdi mdc dp tang eua bi/de sdng A, eua dd nhIp nhd mat n l n . Nhuvay, v^n t i e vwk budc sdng A, Id hai thdng sd quan trpng nhlt ed anh hudng d i n suthay ddi eua t i n s d / ^ : khi vdn t i e vedng tang thi t i n sd/«
edng tdng vd mdc dp tang ndy eua t i n s i /^ cdng manh khi A^ edng nhd, cung nhu sir tang cdng y l u v&
t i l n d i n ddn mdc dp khdng ddng ke khi A, edng Idn (mat n l n edng hodn hdo).
Bieu dd dupe the hien d Hlnh 5 cho thIy gid trj ciia t i n s i rieng/„ tang khi tang dd edng ciJa cdc Idp nln cung nhu dp edng tdng thd eua n l n ba Idp. Hidn tupng edng hudng xdy ra khi t i n s l / ^ dat x I p xi vdi t i n s6 ridng / „ vd luc nay van t i e edng hudng ed thd dupc
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xdc djnh theo edng thdc (19). Mdt vdi vf du dupc liet ke d Bang 6.
Bang 6: Van t i e edng hudng phu thudc dp edng eua n§n ba Idp vd budc sdng eua dp n h I p nhd mat n l n
DO cufng Idp ngn thi}2va3
* , = 5x9x10«N/m2 k, = 5x6x10'N/m2 k, = 1x9x10«N/nf
*4 = 1x6x10'N/m^
it, = 5x9x10*N/m2 ifcj = 5x6x1 O^N/m^
T ^ s 6 rieng f„
22.56 Hz (Hinh 5) 16.59 Hz
22.56 Hz
Bt/dc sdng
1.0 m
1.0 m
2.25 m
van tdc cOng hodngv, =\/„
22,56 m/s (81,22 km/h)
16,59 m/s (59.72 km/h)
50.76 m/s (182,74 km/h) Theo d d , de ed the tang van t i e vat the d i n mdc dp mong m u l n m d khdng Idm hien tupng cdng hudng x u l t hien thi viec tlm bien phdp Idm gidm hpp ly t i n sd kfch thfch d d n g ^ cung nhi/ Idm tang hpp ly t i n sd r i e n g / , ciia he vat the - n l n Id vide vd cung c i n t h i l t trong thuc t l t h i l t k l n l n dudng cao t i e . Qua dd, ed the ddnh gid dupc viec tang phij hpp budc sdng A, cOa dp n h I p nhd mat n l n (chang han nhi/ trong qua trinh duy tu bao dudng mat dudng, ray cao t i e , . . . ) k i t hpp vdi vide tang phu hpp dp edng eua n l n ba Idp ed dnh hudng r I t quan trpng trong viec loai t r d hien tuprig edng hudng lien quan d i n vdt the chuyen ddng vdi t i e dp cao tren mat n l n ba Idp.
3. Bai t o a n 3 : Phan t i c h i^ng xH d o n g c u a he v a t the - n l n l(hi t a n g Ichoi iirorng v a t t h e
Bdi toan ndy khdo sdt anh hudng eua viec tang khdi lupng vdt the vdi TM = n x (4,1x10^) kg, trong dd n = 1 ^ 5, d i n dng x d ddng eua he vat t h i - n l n . Cdc bieu dd trong Hlnh 6 d i n Hlnh 8 the hien s i / t h a y ddi khdi lupng vat thd tai true hodnh vd cdc thdng sd chfnh eua bdi todn dupc tdm t i t trong Bdng 7. Cdc thdng sd lien quan khdc dupe l l y theo Bang 1 vd Bang 2.
Bang 7: Tdm t i t cdc thdng sd ehfnh eua Bdi todn 3 Khdi lUdng/nvav^ tdc Dd nhap nhd cua DO cAig Idp nen
k'ciia vat thi matn^n thijf2va3 m = nx (4,1x10^) kg
trong dd /7 = 1 -^ 5 i^= 180 km/h (SOnr^s)
a, = 0,05 + 4 mm it, = 4,5x10' N/m^
k,=^m itj = 3.0x10«N/m2
Hlnh 6 d i n Hlnh 8 trinh bay cdc bieu dd the hien i l n lupt sir thay ddi gid tri Idn n h l t ciJa chuyen vj y^
ciJa diem tuong tdc vd eiJa chuyen vj vat the u cung nhl/ sir thay ddi gid trj Idn n h l t cua he sd k h u l e h dai ddng DAF theo khdi lupng m ciia vdt t h i vd bien dp n h I p nhd a, eua mat n l n . Cdc bieu dd dupc ve dua tren cdc gid tri am Idn n h l t (hudng xudng) ddi vdi y ^ ^ vd M; vd dua tren cdc gid trj duong Idn n h l t d l i vdi hd
S6DAF ^ , .
Cdc b i l u dd chuyen vj Idn nhdtjVmw ta' diem tuong tdc vd chuyen vj Idn nhlt u ciJa vdt thd dng vdi cdc gid tri khdi lupng m thay ddi cua vat the vd dnp vdi tdng gid tri khao sat eua bien dd nhIp nhd mat nen a, dupc
the hien tren Hlnh 6 va Hlnh 7 cho thIy: khi khdi lupng m tang thi cdc chuyen vj Idn nhlt cua y„ij vd u nhln ehung cung tang tuong dng; tuy nhidn, do anh hudng ddng nen quy luat ndy khdng dupc hodn toan tudn thu, dae biet Id khi khIi luting m chua diJ Idn vd khi bien dp a, edng tang. Trong cdc khodng tang khdi lupng vat the td m = lx(4,lxl00kg d i n m = 3x(4,lxlO') kg ddi vdi bieu dd chuyen vj Idn nhlt j „ y vd td w = lx(4,lxl0')kg d i n m = 2,5x(4,lxl00kg d l i vdi bieu dd chuyen vj Idn nhlt u, cdc chuyen vj nay vilra ed khodng tang vda ed khoang gidm vd cdc khoang tang/gidm ndy dupc the hidn edng rd ret khi bien dp a, tang d i n . Tuy nhien, trong cdc khodng tang b i t d i u td m = 3x(4,lxl0')kg ddi vdi bieu dd chuyen vj Idn vhiXy^i^ vd b i t d i u td m = 2,5x(4,lxl0')kg d l i vdi bieu dd chuydn
-»-BKn d9 n h ^ nhA m$t nin O.OSmn -•-Biin d( nhip nhO mQl nin 1 mm -*-Biin (V nhip nM ti4t nin 2nni -4«-Biin d9ntiip nhO in$tnin3iT -w-Bien d i nhip nhO m$t nin 4mm
25 3 35 Khii luang m (x4,1x1(F kg)
Hlnh 6: Chuyin vj Idn nh^tj^^^^thay dd'i theo kh6i lUdng m
-•-Bifln <K nhip nhO m$t nin O.OSmm -•-Bien 09 nhip nhO mdt nin Imm
1.5 i 5 3 3.5 4
Khii Uivng m (x4,1x10> kg)
Hinh 7: Chuyin vj Idn nhSt u thay dd'i theo kh6i li/dng m
10.0
14.0 12.0 10.0
^ 80 6.0 4.0 ' 2^0
-«-Bi«n en nhip nhO mat nin 0,05mm -•-Bidn an nhip nhO mSt nin 1mm ik-Bifin et> nhip nhfi mW nin 2mm
•4<-Bi4n(II> nhip ntifim^t nin 3mm -«-Bian dO nhip nhfi mjt nin 4mm
— "•* • • .^—.
" - • - • • — — m
1.5 2 2.5 3 3.5 4 4.5
Khii lupng m (x4,1x103 kg)
Hinh 8: He s6 DAF Idn nhSt thay dd'i theo khoi lUdng m
NGUOil XAY DONG SO THANG 7 & 8 - 2 0 1 4
UfNG xuf CUA KHOI L U O N G CHUYEN nONR TREN MO HINH...
vj Idn nhlt u, todn bd cdc chuyen vj ndy d i u ed su tang tuong dng theo quy luat g i n nhu tuyln tfnh vd khi bien dp a, edng nhd hoac khi khdi lupng m edng tdng thi su tang eua cdc chuyen vj nay edng theo quy luat tuyln tfnh rd ret hon. Ddc biet khi a, = 0,05 mm (mat n l n g i n nhu tron) thi cdc chuyen vj Idn nhlt ciJa y„,ia va u d i u tang theo quy luat tuyln tfnh khdng phu thudc khdi lupng m cua vat the.
Vdi cdc bieu dd the hien su thay ddi cija he so khuleh dai ddng DAF\dn nhlt dng vdi cdc gid trj khdi lupng m thay ddi cQa vat the va dng vdi tdng gid trj khao sdt eiJa bien dp nhip nhd mat n l n a, dupe the hien tren Hlnh 8 cho thIy: Quy luat thay ddi eua DAF Id rd rdt, the hien qua vide khdi lupng m cdng tang thi DAF edng giam vd mufC dp gidm ndy edng nhanh khi a, edng Idn (mat n l n edng khdng hoan hdo) cung nhu mdc dp gidm edng cham khi a, edng nhd (mat nen cang hodn hdo). Khi a, = 0,05mm (mat n l n g i n nhu tron) thi D>4F h l u nhu khdng thay ddi dng vdi eae gid trj eiJa khdi lupng m cCia vat the.
Vide thay ddi tang khdi lupng m eiJa vat the, ngodi dnh hudng bit Ipi Idm cho chuyen vj mat n l n tai diem tilp xue vdi vat thd cung nhu chuydn vj ciJa ban than vat the cang tang len, se lam giam rIt ddng ke ddi vdi hd sd khuleh dai ddng DAF vdi mdc dp gidm cdng nhanh khi dp khdng hodn hdo mat n l n edng tang.
Dilu nay cho thIy khi vat the chuyen dpng vdi t i e dp cao trong dilu kien mat n l n ed dp nhip nhd Idn thi vide tang khdi lupng vat the Id mdt gidi phdp phu hpp trong vide Idm giam dnh hudng eua cdc dng xd ddng bit Ipi trong dilu kien mat n l n x l u . Tuy nhien, khi dp hodn hao eiJa mat n l n cdng cao thi vide tang khdi lupng vdt the lai khdng edn thuc su c i n thilt nda vl lue nay he sd DAF khong bj dnh hudng eua vide tang nay.
4. Bai toan 4: Phan tfch iPng xil' dong cua he vat the - nln khi thay ddi do ciing cua nln ba Idp
Vide thay ddi dp edng eua n l n ba Idp dupe thuc hien blng cdch thay ddi dp cdng tdng Idp hoac thay ddi ddng thdi nhilu Idp trong sd ba Idp n l n . Bai toan nay khao sat mdt sd trudng hpp dien hlnh eua thay ddi dp edng ddi vdi Idp n l n thd 2 vd 3 (dng vdi cdc dp cdng k, vd ki,) vdi viec cdc dp edng k, vd k^ dupe thay ddi iln lupt theo quy luat k, = nx (4,5x10') N/m^ va ki, = n X (3,0xlb«) N/mS trong do n = 1 ^ 5. Theo dd, dng xd ddng ciJa hd vdt the - n l n do dnh hudng ciJa vide thay ddi cdc dp edng k, vd k^ cung se dupc khao sdt. Viec thay ddi cdc gid trj k, vd k^ cung 6[Mc thue hien theo 3 cdch thdc: (1) Chl tang gid trj k;, (2) Chl tang gid trj k^, (3) Ca hai gid trj k, vd k^ ddu eijng tang. Cdc bleu dd dudi day td Hlnh 9 d i n Hlnh 11 se the hien suthay ddi cua k, vd k^ tai triic hodnh. Cdc thdng sd chfnh eua bdi toan dupe tdm t i t trong Bang 8 vd cdc thdng sd lien
Bdng 8: Tdm t i t cdc thdng sd ehfnh eua Bdi todn 4 van t6c vat thi a, Mk X, mat n^n Dd cilng Idp n^n 2 va 3
^ = 72knv^
(20 m/s)
a, = 2,0 mm X, = 1,0 m
it, = /Jx (4,5x10«)N/m2 it, =/Jx(3,0x10'')N/m2 trong dd/j = 1 -i-5
quan khdc dupe l l y theo Bdng 1 vd Bang 2.
Su thay ddi eua chuyin vj Idn nhlt y^^ tai diem tuong tdc vd eua chuyen vj Idn nhlt u ciia vat the, vd su thay ddi ciJa hd sd khuleh dai ddng D>4F dng cdc gid trj thay ddi cung nhir cdc cdch thdc thay ddi cCia do cdng k^ eua Idp n l n 2 vd eiJa dd edng kf, eua Idp nln 3 dupe the hien tren cdc bieu d l td Hlnh 9 d i n Hlnh
11 cfio thIy: cdc bieu dd the hien sir thay ddi eiJa cdc chuyen vj va he sd DAF dupe khao sdt ed su tuong ddng v l dac diem vd hlnh dang vdi viec khi dp cung cua cdc Idp n l n 2 vd Idp n l n 3 thay ddi theo chilu hudng giam thi cdc chuyen vj vd he sd DAF ndy ddu thay ddi theo chilu hudng giam vd ngupc lai. Theo do, mdc dd thay ddi eua cdc chuyen vj vd he sd DAFnky Id khdng dang ke khi ehi thuc hien vide thay ddi dd edng k, eua Idp n l n 2 vd Id rIt ddng ke khi thuc hien viec thay ddi ddng thdi gid trj cdc dd edng k^ eua Idp
1 1.2 1.4 1.6 1.8 2 22 2.4 2.6 28 3 3.2 3.4 3.6 3.8 4 42 4.4 4.6 4.6 5
*,(x4.5x10' Wm2); ATD (X3,QX10» Wm*)
Hinh 9: Chuyin vj Idn n\\ky„ij thay dd'i theo do cufng k, va k,,
-8.5
-*-Ctil thay dii dO cOng Mrp nin 2 -a-Chl thay dii d( ciimg Mp nin 3 -*-E)0 cOng Wp n ^ 2 & 3 cikig they dil
-11.5
1 1.2 14 1 6 1 8 2 22 2.4 2.6 2.8 3 32 34 3.6 38 4 *2 4.4 46 48 5 k, (x4,Sk109 NIaf); kt (x3,Qx10' NInf)
Hinh 10: Chuyen vj Idn nhit u thay dd'i theo do cijfng k, va k,,
-*-Chl thay dii dO cOng Idp nin 2 -•-Chl thay dii d» ci>ng Mp nin 3 -«-€>0 ci>ng Mrp nin 2 & 3 cOig thay dii
1 ^2 1.4 1.6 18 2 22 2* 2.6 28 3 3.2 3.4 36 38 4 *2 44 46 4 i 5
*, (X4.5K10» l*m»); *» (x3,Qx10> N/m»)
Hinh 11: Hg s6 DAF Idn nhat thay dd'i theo do ciifng k, va k^
NGUdl XAY DI/NG SO THANG 7 & 8 • 2014
IJfNG xuf CUA KHOI
L U O N GCHUYEN flONG TREN MO HINH...
ndn 2 vd k,, ciJa Idp n l n 3 cung nhu khi chi thuc hien vide thay ddi dp cung it^, eiJa Idp n l n 3. Ddng thdi, dnh hi/dng eua viec cung thay ddi ed k, vd k^ , Mk dnh hudng eua vide chi thay ddi k,, Id chenh lech rIt ft trong trudng hpp ndy. D i l u ndy cho thIy gid trj dp edng k, eua Idp n l n 2 nay da du cdng (so vdi dp edng it^ eua Idp ndn 3) ndn vide cho k, tang them Id khdng mang lai hidu qua ddng ke. Ngodi ra, nhu dupc the hien d cdc bieu dd dang khao sdt, vide tang gid trj dd cdng it^
ciJa Idp n l n 3 cung chl ed anh hudng rIt dang ke trong mdt khodng tang dp cdng nhlt djnh. Va trong cdc khodng tang dp cdng t i l p theo sau dd thi anh hudng ndy edng gidm di vd ed chilu hudng gidm v l mdt gid trj dn dinh.
IV.KETLUAN
Td cdc k i t qud nghien cdu, mdt s i k i t luan ed the dupc rut ra nhtr sau:
• Hien tupng edng hudng Id mdt hidn tupng vd Cling nguy hiem khi lam cho cdc dng xdddng, dae biet Id he sd khuleh dai ddng DAF, eua he dat cue dai d mdc dp rdt cao. Hien tupng edng hudng xult hidn bao gdm nhilu nguyen nhan dupe d i l u khien bdi cdc thdng sd: van t i e vat the, budc sdng nhip nhd mat n l n vd cdc thdng sd dae trung lien quan eiJa n l n . Vide tang phij hpp budc sdng A, eCia dp nhip nhd mat n l n (phu thudc edng tdc duy tu bao dudng mat dudng, ray, ...) k i t hpp vdi vide tang phu hpp dp edng cua cdc Idp n l n Id mdt trong nhdng bien phdp hdu hieu de loai trd hien tupng cdng hudng lien quan d i n vat thd chuyen ddng cao t i e tren n l n ba Idp. Khi tang A, cung phdi dam bdo trdnh cdc gid trj A, gdy ra cdng hudng.
• Mdt trong cdc bien phdp chu y l u dd Idm giam anh hudng eua hd sd DAF\k tang khdi lupng vat the.
Vide tang khdi lupng ndy ed mdt sd dnh hudng b i t lpi, dae biet Id khi mat n l n edng hodn hao, nhu lam tang chuyen vj cua vdt the vd ciJa mat n l n tai diem tuong tdc. Tuy nhien, mdc dp tang eiJa cdc chuyen vj nay nhln ehung nho hon so vdi mdc dp gidm cua he sd DAF, ddc biet Id khi dp khdng iiodn hdo mat n l n edng tang. Ddng thdi, vide tdng khdi lupng v | t the de Idm giam dnh hudng cua he sd DAF cung eIn phdi ed sir kiem sodt phu hpp, cu the Id viec tdng khdi lupng chi nen dupc tang d i n mdt gidi han nhlt djnh (tuy theo tdng trudng hpp cu thd) thi mdi dat hieu qud cao nhlt.
VI n l u tdng tfiem nGfa ed thd mdc dp gidm cua he sd DAFse rIt cham theo chilu hudng gidm v l mdt gid trj DAF on djnh. Ngoai ra, khi mat n l n edng hodn hdo thi viec tdng khdi lupng edng khdng edn c i n thilt vl mdc dp gidm eiJa hd sd DAF se cham d i n khi mat n l n cdng hodn hdo. Trong trudng hpp ly tudng khi mat n l n hodn todn tron thi he sd DAF ludn khdng ddi vdi mpi miic dd thay ddi eua khdi lupng vat the.
• D p edng eua cdc Idp n l n trong n l n ba Idp ed dnh hudng r I t quan trpng d i n cdc dng x d d d n g eua he vat the - n l n . Vide tang dp edng cdc Idp n l n , nhln eliung, se lam gidm dng x d ddng (chuyen vj, he s i DAF) ciJa hd khdo sdt. Ddng thdi, de dat hieu qua cao, viec tang dd cdng cdc Idp n l n e I n cd s u kiem sodt phu hpp, cu the Id dp edng tdng Idp n l n chl nen dupe
tang d i n mdt gidi han n h l t djnh (tuy theo tdng trudng hpp cu thd) thi mdi dat hieu qud cao n h l t , vl n l u tang them nda thi mdc dp giam cua cdc dng x d ddng lien quan se r I t cham theo c h i l u hudng gidm d i n v l mdt gid trj dn djnh.Q
TS. Lifting Vdn Hal, TS. Tran Vin Mi6n
Khoa Ky Thuat Xay Difng, Tn/dng Oai Hoc Bach Khoa - Oai Hoc Quoc Gia TRHCM
Email: [email protected] Bi6n thoai: 0944282090 KS. Nguyin Duy Phu
Hoc vien cao hoc, Khoa Ky Thuat Xay Di/ng, Tn/dng Oai Hoc Bach Khoa - fiai Hoc Qu6c Gia TRHCM
ThS. Cao Tan Ngoc Thin
Bo mdn Ky Thuat XSy Diflig, Khoa Cdng Nghg, Tn/dng flai Hoc Can Thd
KS. Bang Nguyin Thien Thu
Hoc vien cao hoc, Khoa Xay Diing, Tn/dng Oai Hoc Md TRHCM
TAI LIEU THAM KHAO
1. S. Timoshenko, D. H. Young, W. Jr. Weaver, Vibration Problems in Engineering, 4^*^ Edition, John Wiley, New York, 1974.
2. R M. Mathews, Vibrations of a beam on elastic foundation.
Journal of Applied Mathematics and Mechanics, 38, pp. 105-115, 1958.
3. Venancio Filho F, Finite element analysis of stmctures under moving loads. Shock and Vibration Digest, 1978; 10:27-35.
4. L. Andersen, S. R. K. Nielsen and R H. Kirkegaard, Finite ele-
ment modeling of infinite Euier beams on Kelvin foundations exposed to moving loads in convected co-ordinates, Journal of Sound and Vibration, 241 (4) (2001) 587-604.
5. S. Krenk, L. Kellezi, S. R. K. Nielsen and R H. Kirkegaard, Finite elements and transmitting boundary conditions for moving loads, Proceedings of the 4th European Conference on Structural Dynamics, Eurodyn, Praha, June 7-1, Vol. 1, pp. 447-452,1999.
6. C.G. Koh, J.S.Y Ong, D.K.H. Chua, J. Feng, Moving Element Method for Train-Track Dynamics, International Journal for
Numerical Methods In Engineering, 56, pp. 1549-1567, 2003.
7. K.K. Ang, Jian Dai, Tran Minh Thi, Luong Van Hai, Analysis of high-speed rail accounting for jumping wheel phenomenon.
International Journal of Computational Methods, Vol. 11, No. 3 (2014) 1343007 (12pages).
8. K.K. Ang, Tran Minh Thi, Luong Van Hai, Track vibrations dur- ing accelerating and decelerating phases of high-speed rails, The Thirteenth East Asia-Pacific Conference on Structural Engineering
and Construction EASEC-13, Sapporo, Japan, 11-13/09,2013.
9. Tran Minh Thi, K.K. Ang, Jian Dai, Luong Van Hai (2013).
Moving Frame Method for Dynamic Anaiysis of High-Speed Train Slab Track-Viscoeiastic Foundation System. Hoi nghj Khoa hoc toan qu6c Cd hoc Vat ran biln dang iln thuf XI, Tp.HCM, 7-9/11/2013.
'-Mt-^' Ldl CAM ON
Nghien cdu nay dupc tdi trp bdi Dai hpe Qudc gia Thanh phd Hd Chf l^inh (VNU-HCIVI) trong khudn khd d l tdi ma sd B2013-20-07.
NGUdl XAY DONG SO THANG 7 & 8 - 2 0 1 4
