Phân tích ổn định khí động lực và hướng kiểm soát FLUTTER cho cầu dây văng

Bai loan on dinh khf done nav van tiep tuc duac nehien cuu va phai trie'n, gan day nhd vice ap dung ky thuat 16 hgp cac dang dao dgng va bai loan tri rieng trong vice giai phuang trinh k

DAI H O C Q U O C CIA HA NOI TRUNG T A M KHOA H O C Tl' NHIEN

T R U N G TA.M HOP TAC DAO TAO VA CO.NG N G H E Q L O C GIA

MO DAU

1 Giai thieu chung 1

2 Bai hoc tu sir c6 pha buy cau Tacoma Narrow 2

3 Mien tugng mat on dinh khi dong lire Flutter 3

4 Tinh hinh nehien cuu bai toan 6n dinh khf done luc aniroc nsoai 7

5 Tmh hinh nghien cuu bai loan on dinh khf dgng luc a trong nuac 10

CHl/ON(; 1 TAC DUNG CUA GIO LEN CONG TRINH CAU

1.1 Giai thieu chung 1 1

1.2 Xae dinh van toe gio tu nhien 12

1.3 Cac thanh phan luc khf dgng 14

1.4 Cac dae irimg xac dinh phan limg cua dong khf khi qua eong trinh 15

1.4.1 So Reynold va sir hinh thanh xoay khf, vising trong 15

1.4.2 So Struohal va tan so xuat hien cac xoay khf sau eong trinh 16

1.5 Dao done tu kfeh thfeh iheo huane vuone eoc efo loi do

hien tugng Flutter 17 1.6 Cac hien tuans done luc khac ciia eio len cone trinh cau 18

1.6.1 Dao dgng cuang bue iheo hueVng vuong goc gio tai do

hien lUcTne Vortex-sheddine 18

1.6.2 Dao dgng tu kfeh thfeh iheo huang \ uong goc gio tai do

hien tugng Galloping 19

1.6.3 Dao dgng ngi\u nhien iheo hue^ng gio tai do

hien tuone Buffetine -0

1.7 Vai tro eiia cac hicMi tuone khf dowz lire trone ihiei ke eau dav vang 21

1 S Kel luan euoi ehiro'ne

-CHUONG 2 MO HINH HOA VA PHAN TICH DAO DONG CAU

DAY VANG T H E O PHUONG PH.AP PHAN TL HLX HAN 2.1 Gidi thieu chung 23 2.2 Cau tao so bg cac bg phan cau day vang 24

2.3 Mo hinh kel cau ciu day vang iheo phuang phap PTHH 24

2.3.1 Mo hinh dam cung 24

2.3.2 Mo hinh cot thap 27 2.3.3 Mo hinh day vang 28

2.3.4 Mo hinh dieu kien bien 28

2.4 Phan bo khoi luane tren kel cau '^9

o *— -^

2.5 Phan ifeh dao dgng cau day vang iheo phucmg phap PTHH 30

2.5.1 Phuang trinh vi phan ehuyen dgng cua he nhieu bae tudo 30

2.5.2 Dao dong rieng va cac dang dao dgng rieng 30

2.5.3 Giai bai loan dgng lire iheo phan tieli dao dgng 31

2.5.4 Chuan hoa ma Iran dane riene ^^

2.6 Vf du linh loan 33 2.6.1 TTiong so cau tao cau da\' vang

2.6.2 Phan tieh dao dgng rieng ciia eau 34

2.7 Kel Iuan euoi ehuitng 39

CHUONC; 3 CAC PHUONG TRINH CO BAN CLA HIEN TLONG FLLTTER

3.1 Giai thieu chung 40

}.2 Phuone irinh \i i^han ehuNcn done eua phan to dam trone done khf 41

3.3 (Vie thanh phan luc khf dong lir kfeh 4

-3.3.1 Mo hinh lire khf dgng theo thue nghiem eua Scanlan 44

3.3.2 Mo hinh luc khf done iheo eiai tieh eiia Tlieodorsen 46

3.4 Plurang irinh vi phan ehuyen dong lluiter eho he nhieu bae tudo 4"^

?*.5 Kel luan euoi elurone 49

4.2 Tfnh loan van toe gio tai han theo cone ihiJc thue nehiem Selbere 51

4.3 Lai giai bai loan 6n dinh khf dgng luc Flutter vai he hai bae tudo 52

4.4 Phuang trinh vi phan ehuyen dgng Flutter cua he nhieu bae tudo 55

4.4.1 Phuang trinh vi phan ehuyen dgng Flutter 55

4.4.2 Chuan hoa theo khoi lugng 56

4.4.3 Nghiem cua phuang trinh (4.4.2.2) 57

4.5 Ma Iran phan tucua lire khf dgng 59

4.6 Phuang phap chong limg cap dang dao dgng 60

4.7 Vf du tfnh loan 63 4.7.1 Dal bai loan 63 4.7.2 Tfnh loan van toe gio tai han phuong phap giai Ifeh cho he 2 bae tir do 63

4.7.3 Tfnh loan van toe gio tai han theo phuong phap chong dang dao dgng 66

4.8 Kel luan euoi chuang 73

CHUONG 5 CAC H U O N G KIEM SOAT F L U T T E R CHO CAU DAY VANG

5.1 Giai thieu chung 74 5.2 Kiem soal cau tao khf dgng lire 75

5.3 Kiem soat co hgc bi dgng 77

5.3.1 Thiet bi eiam chan khoi krone ludieu ehinh (PTMD) 78

5.3.2 Phiromg trinh ea ban eiia kiem soal Flutter dung PTMD 78

5.4 Kiem soal co hgc ehii dgng 80

5.4.1 Kiem soat ehii dgng kel cau cau day \ang 81

5.4.2 Phutmg trinh vi phan ehuye'n dgng eua kie'm soat kel eau ehiidgng 81

5.5 Vai tro eiia cac hien phap kiem soat Flutter eho eau day \ang 83

5.6 Ket luan euoi ehuang 84 KET LI AN

T.AI L I E l THAM KHAO

MO DAU

1 Gioi thieu chung

Ket cau cau treo va cau day vane da khane dinh duac tfnh uu viei so vai cac dang ket cau cau khac do kha nang vugt khau do Ion va kien true dep Loai hinh ket cau ciu treo va cau day vang dugc ap dung rat rgng rai tai nhieu nuac tren the giai, cac eong trinh cfiu quy mo Ian va ky thuat lieu bieu tren the giai cung da phan ap dung cac loai hinh ket cau cau nay Tuy nhien dang ket cau cau treo va ciu day vang nay la cac eong trinh co ky thuat dae biet, rat phuc 'ap trong phan ifch va thiet

ke Han nua, ket cau nay co xu huang ngay cang thanh manh va nhe do vay bien dane Idn, do cixne neane va xodn giam va nhav cam dao done vai kfeh done neoai Danh eia cac lac done eiia hoal lai eio va done dat luon co vai tro quan trone irone thiet ke vai cac loai hinh ket cau nay Dae biet cac lac dgng khi done lire eiia gio can phai dugc nghien ei'ru va danh giii

Cho tai thai diem 10/1940, cau Tacoma Narrow a Hoa ky bi do hoan loan do gio thi Uie done khi done luc ciia eio duoc dat van di va quan tam nehien CIJTJ voi doi tugng la kel can dan dung noi chung va cone trinh cau noi rieng Cung ke tu sir co nay va cac nghien ciai sau do v^ cac hien tucrng khf dgng lire dae biet eua gio da lam ihav doi cac quan niem \ e thiet ke eau khau do Ian hie nay cac phan tieh \'e dong lire khf done lire va dia chan anh huane quvet dinh tai quan niem \e thiet ke eau chir khong phai la cac phan ifeh iTnh do tTnh tai va hoal tai nhu cac kel cau cau thong thuane Cune nho \ao cae ket qua nehien ciru \ i tac done eio noi ehune (Iv thu\ei

va thue nghiem) nia nhieu eong trinh eau Mrgt bien qu\ mo Ion da dugc xa\ dimg ihanh eong lai nhieu niroe tren the gidi trong nhung nam gan day

Trong cae lac dgng eiia gio len eong trinh eau thi nghien cuu \e mat 6n dinh khf dong lire luon dirge uu tien ehii irgng \i mat 6n dinh khf dgng liJc thULvng dien ra nhanh dot nedt, khd ludne eav hu hai nehiem trone Phan ifeh on dinh khi dgng lire elu) cone trinh ciiu la iiioi bai loan khd va dugc nude ngoai nghien cuu nhieu lir

nhune nam 60 Kho khan d ehd lae dong eiia eio vao eong trinh vdi nhieu hien

tugng, dae biet cac tac dgng dgng luc cua gio gay ra cac phan ung phuc lap , kho ludng cua eong trinh han nua nghien cuu gio can phai co sir ket hgp giua Iv thuyei

va thue nghiem, khong co mot phuang phap so hay giai tfch \an nang nao mo la duac ddy dii cac hien tuone Bai loan on dinh khf done nav van tiep tuc duac nehien cuu va phai trie'n, gan day nhd vice ap dung ky thuat 16 hgp cac dang dao dgng va bai loan tri rieng trong vice giai phuang trinh khf dgng lire da lam tang do chfnh xae cua phan tfch ly thuyei, ddng thai gan doi lugng nghien cuu vdi ket eau cau day vang va cau treo quy mo Idn

0 Viet Nam hien nay mot so eong trinh ciu day vang quy mo Idn dang va se dugc xay dung Cau day vang quy mo Idn dau lien dugc xay dung d trong nude la

cau My Thuan (Long An), cac d\X an can day viing Idn khac dang dugc xay dung

nhu cau Bai Chay (Quang Ninh), cau Kien (Hai Phong), eau Bfnh (Hai Phong), cau Can They (Can Th(t), eau Raeh Mieu (Song Fie) Phan tfch on dinh khf dgng lire luon dugc dat ra va la mot bg phan rat quan trong trong phan tfch, tfnh loan ket cau cac

eong trinh nay Vdi cac eong trinh eau Idn dang dugc xay dung trong nude deu do

nude ngoai phan lieh \a thiet ke kel effu viec phan tfch on dinh khf dong hay danh eia tac dons cua cid noi ehune khdne duoc eiai thfeh va ehuven eiao Viec eiai qu\et bai loan phan tieh on dinh khf dgng lire trong nude con mdi chi bude dau \a rat han che, dae biet khi gan nghien eiiii \di doi tugng la eong trinh cau Hien na\' nhu eau \ e nehien cuu on dinh khf done lue ndi riene ha\ cae phan tfch done luc duac dat ra de dap irng doi hoi eiia thue tien la trong nude lu kha nang phan tfch \'a thiet ke cae cone trinh cau dav vane va cau treo qu\' mo Idn

2 Bai hoc tii sy co pha huy cau lacoma Narrow

Can Taeoma Narrou ihiige bang Washington Hoa Ky bi sup do hoan loan nam 1940 do uie done khi dgng lire eua gio Phan tieh nguyen nhan pha huy cau la

do lae ilimg khi ddng lire lam eau dao ddng vdi hai dang udn va xoan ddng thdi dudi eune n'\o\ tan so Sir tuong lae dgng lire giua ddng khi \a eong trinh gay phai sinh

lue khi done bo \ung cung cap them nang lirong cho dao dgng eua ket eau lam bien

d(^ [>han kv ga\ mat on dinli kel eau Hien tugng khf dgng lire ga\ mat ow dinh eau

J

-Taeoma Narrow dugc biet den la hien tugng Flutter c6 dien (gidng phan ting dgng luc ciia canh may bay trong ddng khf da dugc nghien cuu irudc do) Tai bien dot nggl cua eong trinh eau Tacoma Narrow da lam cac ky su thiet ke cau ehii trgng danh gia dung vai tro cua cac hieu ung dgng lire cua gio len eong trinh dan dung ndi chung va eong trinh cau ndi rieng Pha hoai do tac dung dgng lire cua gio thudng di^n bien nhanh, dot nggt va khd ludng

't^K^^ :< — - ^ • • ; ^ —

Hinh 1 FTmh anh dao dgng manh cua eau Taeoma Narrow trirde qua huy

3, Hien tirgng mat on dinh khi dong luc Flutter

Khi nghien eiru phan ling eiia ket eau phan bd theo chieu dai dat n^m ngang trong ddng khi ed phai sinh cae lue khf dgng tac dung len ket eau theo hudng gio (phuirne neang ciia ket eairi lh-?o phuoiig vuong gdc (phuong dung) \a lam xoan ket cau Cae lue khi dgng na> lam kel cau ed hai dang phan I'mg nhu sau :

- l)afv.l phiin lOi;^ ihi'r nln'il: Do lieh ehal hdn loan eua dong khi va phan ung

ciia done khi qua kel cau cae lire khi dgng nay ed the la cac liic bien ddi theo thdi eian hoae bieti dien llieo cac ham xae sual Trong irudne hgp dau cae lire

khf done eav kfeh ddng lam kel eau dao dgng eudng bue eon d trudng hop

sau lam kel eau dao dgng ng;Ui nhien Da\ la eae hien tuong ma cae kieh

dgng dang nay chi don thuan lam kel cau dao dgng phii thuge vao eudng do, tinh chat ciia ban than dong khf ma khong cd sir tuong tac giua ddng khf va kd't cau Dae diem chung ciia cac hien tugng dang nay la lam ket cau dao done vdi bien do eidi han

* *— i—

- Dang phan Ung thi( hai: 0 trudng hgp eij the cac luc khf dgng khong nhung

chi phu thugc vao dae trung ban than ciia dong khf ma con phu thuge vao ehuyen dgng ciia kel ciu trong ddng khf tuc la cd sir tuong tac giua ket cau

va ddng khf Nhu vay cae lire khf dgng tu kfeh phu thuge vao ddng khf va ehuye'n dgng cua ket cau Cae hien tugng nay ggi chung la hien tugng khf dan hoi Trong mot so dieu kien, cac lire khf dgng tu kfeh bd xung them nang lugng eho ehuyen dgng lam lire can ciia he thong chu>en sang bi dgng, bien do ehuyen dgng ciia ket eau pha n ky dan t-di ket cau mat 6n dinh

Cae hien tuong khf ddng lue lac dune len kel eau ndi ehune ha\ cone trmh can ndi rieng bao gdm hien tugng Flutter Buffeiing \'ortex-shedding va Galloping Hien tugng mat on dinh do dao dgng udn-xoan ddng thdi con ggi la hien tuctng Flutter Tac dgng gay dao dgng ngaii nhien theo hudng gid ggi la hien tugng Buffeiine Hien tuctne Vortex-sheddine eav dao done eirdne bue theo huc^e

\udng gid \a\ hudng gid do cac xoay khf hinh thanh sau eong irinh Cae uie ddng

dao dgng lir kfeh thfeh nhu hien tugng dgng lue dae trung eiia gid khi qua eae \ai the dang hinh iru, iron, ehu nhat ha\ day cap ggi la hien tugng Galopping Vdi mot ket can ed the ddng thdi phai xem xei lae dgng eiia ca bdn hien lucmg tren tu> nhien \ ai tro quan trgng \a mire do eiia eae hien tuctng lac dgng len eong irinh la khac nhau Theo [5J, vdi eae eong trinh dang egi eao thi thudng phai ehu trgng xem xei uie done ciia hien luane Galoppine \a hien tuone \'onex-sheddine, con \di ciic cone trinh eau phan ho itieo ehieii dai can phai ehii trgng xem xei hien tugng Flutter \a

hien tuong Buffeing do \\\ ra d \an ide gid Idn ga> hu hai eong trinh Cae tac dgng

khf done lire eua done khf ed the tae done len ket eau ed the lom tat trone so do

i i n h

5

-Dao dong ihco

phi/ong cua dong khi

Dao dong ngau nhien

^ ' Hinh 1 So do phan nhanh cac hien tuone khf done luc cua eid

Cae hien tugng gay mat dn dinh ehuyen ddng ket cau thudng ditoc dae biet

ehii trong, irong dd hien tuetng mat on dinh khf dan hoi Flutter ed the ga\ ra eae hu hai cho diim eau, tham ehi cd the dan tdi pha hoai eau Nehien ei'ru hien tuone nav

se la ndi dune nehien eiini ciia luan van Co nhieu each dinh nehla hien lUtme

Flutter Theo each dinh nghia ed dien thi hien tugiig Flutter la mot hien tugng mat 6n dinh khf dan hoi trong dd d trang thai tdi han dau lien ed su kel hgp ddng thdi dao dgng udn \a dao dgng xoan eiia ket cau Dinh nghia nay xuat phat tu nghien eiru

thue nghiem canh ma\ bay tuy nhien khi nghien cCru vdi cdng trinh can co nhieu

Irucmg lio[t do cau tao eiia eau d trang thai tdi han ed su ket hgp eiia dang dao dgng bai k\ h(K)e nhieu dang dao dgng ddng thdi Cae dinh nghTa gan da\ xem hien lugng

I'lutier la mot dang mai on dinh ehuye'n dgng \'a ap dung dinh ly Liapuno\ noi lieng

de dd lim trang thai tdi han, tu dae diem eiia he dao dgng do lue tu kfeh eae tri rieng

dugc bieu dien duo\ dang eae cap sd phue lien hop nhau trong trudng hop nao dd do

tuong uie giua kei eaii va ddng khf xuat hien eae gia tri phan thue eua cae cap tri

rieng bat kv duong ihi hien do dao dong se phan k\ \a he thong mat on dinh ehu\en

done Trang thai tdi han bat liau \a\ ra mat on dmh khi phan thue eua cap tri rieng

cdn phai xac dinh dugc van toe gid d trang thai tdi han dau tien he bit dau mat 6n dinh, con goi la van tdc gid tdi han Cd 2 hudne xac dinh van ide eid tdi han trone bai toan 6n dinh khf dgng luc :

- Hi((/ng thi( nhdt (phuang phap ly thiiyet) : Xac dinh van tdc gid tdi han thong

qua viec giai true tiep phuang trinh vi phan ehuyen ddng cua cdng trinh dudi tac dune ciia cac lue khf ddng tu kfeh Flutter d trane thai xav ra mat on dinh

de tim ra van tdc gid tdi han

- Huc'/ng ihi'f hai (phiamg phap ihi/c nghiem) : Xae dinh van tdc gid tdi han

thong qua ihf nghiem md hinh vat ly ket cau Ciiu trong thf nghiem ham gid HucVng xac dinh van tdc tdi han theo phuang phap ly thuyei ggi la phan tfch dn dinh khf done lire Trone tructne hop van tdc eid tdi han xav ra mai dn dinh nani trong vimg riii ro eao thi huge phai tien hanh sua ddi cau tao ket cau hoae ap dung cac bien phap kiem soat dn dinh khf dgng lue So dd ung xii vdi bai loan dn dinh khf dgng cho cau ndi chung va eau day vang ndi rieng md la tren hinh 2:

Bai loan 6n dinh khi doni: lire

Mo hinh loan hoc

C6ne ihuc ihirc nshiCink

Mo hinh vai

i Phiin ii'ch 6n dinh

khi done tuc

Thi nghiem mo hinh irone ham eio

BiCn phap cau lao

lans cuCme On dinh I

b • - — ~ — ^ ^ — — '

BiCn phap co hoc

(FtC ihong bi dOng)

DitHi khic^n kOi ciVu

(He ihoiie ehu done)

\'an loe gio tir nhien

on nhJl tai cone irmh

Hinh 2 Svv diS une xueiia bai loan on dmh khi done lue eho eau

- 7

4 Tmh hinh nghien ciiu bai toan on dinh khi dgng lire cho cau d nirdc ngoai

Cac nghien cuu hien tugng Flutter eho cau dau lien phai ke' tdi cae nghien cuu CLia tac gia Theodorsen, Roeard, Bleich, Scanlan Bleieh[19] gidi thieu cdng thiJe thue nghiem ndi lieng de" tfnh loan van tdc gid tdi han eho liet dien dam cau dang ban mdng thoat khf, Cong thue nay dugc Selberg[19] sua doi va bd xung he sd hinh dang mat cdt eho phep tfnh loan vdi dang mat cat cau bat ky, hien nay eong thiic thue nghiem Selberg van dugc su dung rgng rai Ldi giai giai tfch cung dugc Roeard [ 10] gidi thieu nam 1950 ap dung cho phan tfch cau treo vdi md hinh hai bae

lu do Ve phan minh Theodorsen da phat trie'n cae nghien eiai trude dd cho canh may bay de xay dung phuang trinh khf ddng lire Flutter ap dung cho cdng trinh cau

cd liet dien ban mdng, dua ra cae ham luan hoan Theodorsen de' thiet lap tfnh loan cac lire khf dgng tu kfeh trong phucmg trinh \i phan ehuyen dgng, cac luc khf ddng dugc tfnh loan theo giai tfch Seanlan[5] [7] da x^y dung cae lire khi dgng tu kfeh nhd dua vao eae he sd khf dgng Scanlan hay edn ggi he sd phat sinh Flutter ed ngudn gdc thue nghiem Cach xay dimg ifnh loan eae lire khf dgng theo thue nghiem ciia Scanlan vin edn dugc ap dung rgng rai hien nay do cd the ap dung eho eae mat cat bai ky theo dae trimg eiia eau Theo dd eae he sd Scanlan dugc xae dinh thong qua thf nghiem md hinh hoae su dung cae kei qua ed sSn theo dang mat cdt

Bai loan dn dinh khf dgng co dien eiia eau dugc xei tdi la phan ung eiia phan

to chieu dai dam eau trong ddng khf dn dinh, ehuyen ddng phan id dam theo 2 bae

tu do: ehuyen vi thang dung h \ a ehuyen vi gdc xoay a (sau na> ed xet them thanh phan ehuye'n vi ngang p) (hinh 3)

- ^ l _ ^ - >

J), ( j c lh.inh ph.in c h u u n \'\

i h ; l h i n ^ {liriiL; p: irj-iiiL; a :''**< \ t ) n i

b i C J C luc khi doni; I n n

inol (JMTI \ i c l i i i u daj d j r n [linh 3 Dieh ehu\en eua dam trong ddng khf \a eae lire khf ddng phat sinh

Phuang trinh vi phan ehuyen dgng ciia phan id dam cau bieu diln biine phuang trinh dao dgng udn xoan ket hgp sau :

md hinh thue nghiem eiia Scanlan TTieo md hinh Tlieodorsen [5], [7] eae lire khf dgng tfnh tren mot phan id chieu dai dam dugc tfnh theo cdng thue sau:

U, b, p U3 Ian lugi la van tdc gid, mot nija chieu rgng mat eau mat

do khong khf \a tan sd goe ciia dao ddng

A' = — hi tan so ehiei eiam (thone so khone thu neu\en) L: ^

Theo mo hinh Scanlan | 5 | , [7| eae lire khf ddng dirge xae dinh nhu sau:

L=]-pU'2B Kf!'{K ) ~ + Kff'AK )—^K-f!'{ K )a

U =-pi'2R K.l' (K)— + K.4l (K)~ + K-.i{K )a

U ' U

la xet tdi su lam viec khong gian eiia ket cau cau Vice giai bai loan dn dinh khf done lire eho loan kei cau eau la bai loan khd eiai qu\ei do he nhieu bae tu do luc khf dgng phu ihugc vao van tdc gid, utn sd dao dgng kei cau \a ehu>en \i kei eau va dao ham eiia ehiing, xae lap lieu ehuan on dinh va do lim trang thai mat dn dinh

Phuong phap sd giai phui^g trinh khf dgng hre Flutter da phat trien kha manh tu dau nhung nam 90 nhd ap dung phuemg phap phan tu huu han(PTHH) va to hop dang dao ddng ricMig eho phep tiep can long quat ldi giai md hinh kei can hat

ky va cd the to hgp nhieu dang dao dgng trong mot phan ung lieu bieu la eae nghien ei'ru eua Seanlan[21 ] |22] Agar [24J Naminil24] Chcn[24] Thu tue lap va each

thue Id hgp eae dang dao dgng van tiep tue d\iac nghien ei'ai \a phai trien \i no anh

hudng tdi tdc do xu ly va su ehfnh xae eiia ldi giai Gan day cd hudng xae dinh he sd Scanlan iheo thuan tuy ly ihuyet nhd phuong phap kich dong ngau nhien tham sd

Nhir \'ay bai loan on dinh khf dgng lire eua ket eau eau ndi chung hay ket cau eau da\ \ang noi rieng la mot bai loan phue tap thu tuc giai bai loan na\ \an edn

wcp tue dirge nghien eiru va phat trien Gan da\ trong ihue tien phan tfch \a thiei ke ehdne eio eho eau dav vane da ehu wonsi tdi huone kiem soat khi done lue \ a kiem soat co hoc kei eau bang each them \ao liei dien eae thiei hi thoat khf hudng

ilone \a thiei bi giam chan nham lam giam eae uie dung eua eid \a kiem soat phan

ixn^i eiia eone irinh

5 Tmh hinh nghien curu bai toan dn dinh khi dong lire d trong nude

Nghien ciru trong nude ve tac dgng ciia cac hien tugng khi dgng lire gio ndi chung hay hien tugng mat dn dinh Flutter ndi rieng gid len cdng trinh dan dung va cdng trinh cau con rat ban che Ve ket qua nghien cuu tac dgng cua gid len ket cau xay dung phai ke ldi cac nghien cuu cua Vien KHCN Xay dung tren ca sd tfnh loan cac thanh phan lue iTnh va thanh phan lire dgng cua gid tu nhien eho cdng trinh dan dung va da xay dung dugc lieu chuan nganh ve tai trgng gid mot sd nghien cuu ciia irudne DH Xay dune v6 lue tac dune len cone trinh eiia gid Ide, nehien cuu ciia trudng DH Quan sir ve hien tugng Flutter cho kel cau ban mdng V.Q.Tru [13] da nghien cuu mot sd phuong phap giai bai loan dn dinh khf dgng luc cho he dan hoi Nhdm nghien cuu do GS.TSKFL Nguyen Van Khang (Dai hgc Bach Khoa) dimg dau (GS.TSKH NguytMi Van Khang, TS Dd Xuan Thg, TS Hoang Ha, TS VQ Van

Khiem) da nehien cuu \'6 dao done uon ciia cau dav vane dudi tac dune eiia doan tai trone di don<i- Mot so nehien cuu ciia mot sd Uie eia lien quan tdi eae uie dune

dgng lire eiia gid va dn dinh khf dgng dugc trinh bay trong [26], [27], [28], [29], [30],|3IM321.[33J,[34]

Hien nay, cae nghien cuu trong nude ve cae hien tugng khf ddng lire edn bi han che nhieu \e mat thue nehiem do ihieu phone thf nehiem md hinh ham eid Hgc vien Phdng khong- Khong quan (Bd Qude phdng) ed phdng thf nghiem ham gid

\an ide thap quy md nhd phue vu cho nghien eiru \a giang day ve khf cu bav \'ien Khoa hgc Cdng nghe Xay dimg (Bg Xay dimg) dang dau tu xay dimg niot phong thf nghiem ham gid qu\ md nhd phue vu nghien cuu \ a phat trien danh gia uie dgng eua gid len ket eau dan dung, lu kinh nghiem ciia nude ngoai vice xa\ dimg \a khai ihae phdng thf nghiem thdi gid deu phai dua tren mot ddi ngu can bg nghien cuu ed hieu biei sau rgng ve mat ly ihuyet v a ihire nghiem Chae chan nghien cuu \e tac ddng (long lue eiia gid se lang len nhanh trone thdi gian tdi khi irong nude tir thiet

ke cae eong irinh dan dung \a eau khau do Idn cd de cap ldi phan ifeh khf dgng lire

va \ iee nlia nUiVe dau lu mgl phdng ihi nghiem mo hinh gid ijuoe eia

CHUONG 1 TAC D O N G CUA GIO LEN CONG TRINH CAU

LL Gidi thieu chung

Tac dgng cua gid len cdng trinh cau ndi chung hay dang ket eau cau treo va cdu day vang ndi rieng chia lam 2 nhdm : tac dijng iTnh va tac dijng dgng lire Tu dae diem cua dang ket cau cau treo va cau day vang cd ket cau dam manh, m6m deo do su lam \ iee ddng thai cua dam , cot thap va cae day vang, do cung udn va do cung xodn kha yeu so vdi cac dang ket cau cau thong thudng nen rat nhay dao dgng dudi tac dune cua cac kfeh ddno ddng luc cua eid Vai ird ciia eae hien tuone khf dgng luc eiia gid la rai quan trgng trong thiet ke cau day vang trong nhieu trudng hctp anh hudng quyet dinh tdi lira chgn phuang an kei cau cau

Dudi tac dune ciia done khf hdn loan eae lue khf done bien ddi la ham ciia thdi gian Cae lire nay tae dung vao kei eau lam cho ket cau dao dgng eudng bue Day la nhiem \u nghien eiai cac hien tugng Buffeting va Vortex-Shedding Cac dao dgng eudng bue ed tfnh ehai tat dan do hao tan nang lugng eo hoe Nhung Irong nhieu tructne hop khi nehien cuu dao done ket cau d van tdc eid Idn thav rane ban than dao done ket cau lai phat sinh ra lire khf done bd sune tao them nane krone mdi ehi^ dao ddng lir than dan tdi bien do dao dgng dot nggt tang nhanh ga> hu hai

va tham ehf hu\ kel eau Cac dao done tu kfeh thfeh do cae lire khf done duoc phat sinh tu ban than dao ddng ban dau eiia cdng trinh ha_\ do tucfng tae co hgc giua ket cau va done khf ehu khdne phai ed neudn ede tu tae done ddne khf Giai thfeh hien luttne nav d van tdc eid Idn tuone lac ddne khf \a kei eau dane dao ddne eav ra eae lue khf ddng bd sung ket hgp vdi cac lire san cd lam cho dao dgng eiia ket cau eo lue

can khf ddng lire lien ldi bi ddng, lue na_\ bien do dao dgng dot nggt phan ky gay

mat dn dinh ddng lire eho kei eau va pha hu\ ket eau mat dn dinh na\ ggi chung la mai dn dinh khf dan hoi ma nghien cuu nd d eae hien tugng Flutter \a Galloping

Cac anh hirdne do tac dune ddne lue ciia eid vao kei eau ed the eav mdi ddne

-lue ea> hu hai eae bd pluin ehiu lire eua kei eau hay ga> anh huoiig lam ly tdi ngudi qua eau tham ehf gay pha hiiy kel eau trong trudng hgp mat on dinh khf ddng neu tren Cae anh hudng loi lam ly xual phai ur \iee kei eau hi eong huong nga> vdi van

ide gid thong thudng lam dao ddng cua ket cau phue tap Cac tac ddng va anh

hudng ciia gid tdi ket cau cau ndi chung va dang kel cau cau day vang ndi rieng cd

the' tdm tat trone bane 1.1

Bang 1.1 Tdm tat tac dgng cua gid len ket cau cau

- Theo huong g i o u'ti

A p luc g i o va ciic lire k h i dong

H i e n tuong phan ky do xoan

Dao dong b.d phan k y

- Dao dong t u kfeh thfeh

- Van toe gio eao

Dao dong b.d giai han

- Dao dong cuong hue

- \ ' a n toe gio eao

Trong ehmmg nay se trinh bay long quat eae tae ddng eua gid len cdng trinh

cau ndi chung va kei eau cau day vang ndi rieng, xae dinh van tdc gid tu nhien, cac

thanh phan lire khf dgng linh, eae dae irung xac dinh phan ung ciia ddng khf vao

cdng trinh eau, so luge eae hien tircmg khi done lire \a \'ai ird eiia cac hien tucTng

khf dgng luc trong thiet ke cau day vang

1.2 Xac dinh van tdc gid tu nhien

Gid tu nhien ed linh chat hdn loan, bien ddi eudng do va hudng lien lue, tac

dong mang tfnh ngau nhien Tai mot dia hinh va thdi gian nhai dinh \an toe eiia gid

tang trong khoang \ai tram met chieu eao theo ly ilui\et Idp bien do tfnh chat hdn

loan \a lire can eua mM irai dat Dia hinh anh hudng tdi bieu do bien thien \an toe

\a ehieu eao \an tdc gan mat dat, dia hinh cang trdng trai van tdc cang tang nhanh

thei^ chieu eao va cang giam ehani khi gan mat dai nguge lai \di dia hinh thanh phd

\-;'m ide lang eham lio'n khi len eao \a giani nhanh khi gfin dat Theo \\ thu>ei Idp

bien cone thue tfnh \an tdc eid bieu dien nhu sau (hinh 1 h : t_ *—

u,,., (z, t) = u (/) + u iz, I) (1.2-1) Trone do : u, „ I /.t» la \an tdc eid idne cone (van ioc eio eiai)

0

-il (z) la van tdc gid trung binh (phu thuge chieu eao z)

u (z, l) la van tdc gid chenh lech do tfnh chat hdn loan

Tfnh loan van tdc gid trung binh u iz) theo cdng thiic Davenport nhu sau:

U/

u

Tron" dd : a, z Ian luot la he sd dia hinh va chieu eao tfnh van tdc eid

Ug, z^ la van tdc va eao do so sanh Thong thudng van tdc trung binh ca sd lay tai eao do 10m tren mat dat thien

nhien nen van tdc trune binh tao chi^u eao z vie lai nhu sau :

0

(1.2.3)

Trong dd : Lay a = 0.16 vdi dia hinh trdng trai; a - 0.28 vdi riing ihua ddi

thap, thi Iran nhd, a = 0.4 \di thanh phd Idn nha eao tang

Ap luc gid iTnh xae dinh lu van tdc gid trung binh theo cdng thue BecnuUi:

Trong dd : p la mat do khdng khf (p = 1.2 kg/m' d dieu kien thong thudng)

Thanh phan \'an tdc gid chenh lech u(z.t) bieu di^n tfnh chat hdn loan cua gio tu

nhien Tfnh loan van tdc gid giat \\i \an ide gid trung binh iheo he sd gid giat Vf- :

L3 Cac thanh phan lire khi dgng tinh

Ddng khf khi vugt qua cdng trinh tac dung luc true tiep vao cdng trinh Lire

nay phu thugc kfeh thude, hinh dang vat can, van tdc va hudng tdi cua gid Khi xet

tdng quat uic dung cua ddng khf hdn loan vao vat the khdng gian se phat sinh 6

thanh phan lire: 3 thanh phiin lire dgc true va 3 thanh phan md men xodn Tuy nhien

vdi ket cau eau thi lue khf dgng gdm 3 thanh phan lire tinh la lire chdn (F^), lire nane

a V^t the khong gian b Vat the 2 chieu (Dam cau)

Hinh 1.2 Cae thanh phan lire khf ddng tinh (hi) va md men xoan (Mp) Day la eae thanh phan lire gid linh trung hinh dirge ke

tdi trong phan tfch cau (hinh 1.2)

De dae trung cho do Idn eiia cae lire khf dgng F^, FL, MR dua vao cac he sd

hinh dang la he sd chan gid (C^)- he sd nang (CL) he sd mdmen (Cv.,) xae dinh nhd

thf nehiem md hinh hay sir dune lai lieu siin ed Cae luc khf ddne tae dune len cone

trinh cd the' xac dinh theo cone thue :

F„ = C „ c ] H L (l.?.l)

FL = C L q H L

M, = C „ q H L B

Trofii! <\6: H L B Ian lirol la chitju eao chieu dai \ a rone cua ket cau cau

t] la ap lire gio \ac dinh iheo \oi vdi \an toe gio thiet ke u^

Hay F o = - / i » : C y / / / (l.-^.i) :; -)

F, = -.p.ir.C.H.l

Mp= -.p.ii:.C„.U L.B

1 5

-Cac he sd C^, C^, C\i theo cac dang mat cat liet dien cau sfin cd trong cac tai

lieu tham khao hoae xae dinh trong thf nghiem ham gid vdi md hinh doan ket cau

L4 Dae trirng xac dinh phan ung cua dong khi khi qua eong trinh

L4.L Sd Reynold va sir hinh thanh xoay khi, vung trdng

De xac dinh phan ijmg cua dong khf khi qua vat can sii dung cae sd khdng thu

nguyen Reynold va Strouhal Sir lien quan giiia lue nhdt (tfnh can) va luc quan tfnh

the hien ung xu eiia ddng ihuy khf qua vat can phu thugc vao hinh dang, kfeh thude

va tfnh nhdt, sir nham mat cua vat lieu mat eua vat the Dinh nghia sd Reynold nhu

Trons dd : U,L,7 Ian luot la van tdc cua ddne khf, kfeh thude bao mat

tiep xue ddng khf \'a he sd nhdl ddng S(>' Reynold se cho biei dae diem ciia ddng khf va mdi trudng phfa sau \at the la

ddng dn dinh done hon kxm, eo xoay khf, \ung trdng \a tfnh ehai uieh ha} dfnh ird

lai ciia ddne khf Khi sd Revnold be ean nhu khdne ed su uieh phfa sau \'at the cua

ddne khf va neu ddne phfa trude la dn dinh thi ra khdi \ai the cune van la ddne on

dinh Vdi cae dang mat cat dae biet nhu canh may bay, hay mat cat mdng ed chieu

rgng Idn dang ihoai khf dgng lire thi ung xu eiia dong khf d (Jang lien Vdi sd

Reynold dii nhd ddng khf qua vat the se bi taeh qua bien dong thdi phfa sau tao

thanh eae xoa\ khf xuai hien ed ehu ky goi la eae xoa> khf Kamian Cae dang mat

cat cau ihdne ihudne cd cau lao thoat khf ddne luc nam d pham w irne xii nav Khi

SO Re\nold Idn img xiiddng khi phfa sau eong irinh kho doan trude \a can xae dinh

qua lln' nghiem mo hinh Tu\ nhien hie na\ ddng khf phfa sau hon loan, khdng ddi

xung, xuai hien xoa\ khf dan xeii kieh thude \a tan sd xuat hien eae xoa\ khf khae

nhau (hinh 1.3)

Ntici (tunciiiniK Im (SaR^aidnJi ihjf^

QL viiy KiTTwaii f»^ihj)tiiik> T

N tl ail &c> rhim(SS RjvaiJ r i ci>)

Hinh 1.3 Pluin ung eiia ddng khf qua vat can theo sd Reynold

L4.2 Sd Strouhal va tan sd xuat hien xoay khi sau cdng trinh

Hien tucmg tao ra eae xexiy gid va \iing trdng edn dirge md la bo\ mdi sd

khdng thu ngu>en khae la sd Strouhal Sd Strouhal lien quan tdi tan sd hinh thanh cac xoay khf ciia vung trdng Vdi viec hinh thanh cac xoay gid sau vat lam phan bd lai van tdc va ap lire gid len \at the Sir taeh \a dfnh eiia eae xoa\ khf quanh \at the phu thude vao sd Reynold, kfeh thude vat va dae trung hdn loan eua ddng khf

Trong trudng hgp ddng khf tao ra cac xoay khf \ a viing trdng sau \at ean thi tan sd xiKii hien eiia eae xoa\ khf edn duoc xac dinh theo sd Stroutral nhu sau:

Dang m^i cat

Tici JiOn 171 j i c j i iron v j c j p J J ^ vjng

T I C I diifn n ij i cjr hinh ehu nhat

1.5 Dao dgng tif kich theo hudng vuong gdc gio tdi do hien tuoTig Flutter

Hien tugng Flutter la mot dang tac ddng tu kfeh xay ra dudi \ an tdc gid Idn cae luc khf ddne bd sune phat sinh tu ban than dao ddne ciia cone trinh do tucfne tae giua ddng gid va kei eau Trong iruimg hop, sir ket hgp eiia lire khf dgng ho sung na_\' lam lire can am, liie nay bien do ket cau tang nhanh khdng ngimg dan tdi pha luiy cdng trinh Hien tugng dugc nghien cuu dau lien eho canh ma\ ba\' sau dd la cac phat trien eho cdng trinh eau nen edn ggi la Flutter eho eau ha_\ Flutter ed dien

0 day, hien iue)*ng Flutter xay ra khi cd sir ket hgp dao ddng udn va dao dgng xoan eiia kei eau dudi citing mot tan sd dao dgng (hinh 1.4)

Cone dmmi; Cons am

HiivVru; «.hu\cn Joni: b Do loch pha bani: 90' - Toriii com: uuoiit:

Hinh 1.4 Dang dao ddng udn - xofm ddng thdi [12].[I6]

Hien tugng Flutter cd the xem la hien tugng dao dgng tur kfeh co bien do

phan ky Van de dat ra la can xac dinh van tdc xay ra hien tugng mat dn dinh

Flutter, ggi la van tdc gid tdi han xay ra Flutter Cae cdng thue thue nghiem de' xac

dinh van tdc gid cue ban dugc trinh bay trong [17], [20], [ 29], [39], [41] Viec

xac dinh van tdc gid gidi han edn dugc tien hanh trong thf nghiem md hinh loan kei

cau [41] Cach tiep can ly Ihuyet de xac dinh van tdc cue ban la giai phuang trinh

khi ddng lue ciia hien tuone Flutter d trang thai tdi han Cach thue xav dune phuerne

trinh vi phan ehuyen dgng eiia hien tugng Flutter va each giai se dugc nghien cuu

va trinh bay d cae chuang 3, 4

1.6 Cac hien tucrn^ khi dgng lire khac cua gid len eong trinh cau

1.6.1 Dao ddng eudng hire theo hudng vudng goc gid tdi do hien tugng \

ortex-Shedding

Vdi phan Idn dang kei cau dam eau thoat khi cd sd Reynold kha be ddng

khf qua cdng irinh lao thanh eae xoay khf Ian toa sau eong trinh \di tan sd Ian toa

xae djnh iheo sd Strouhal:

Cac xoay khf nay lao thanh lire nang uic dung \ao ket eau theo hudng thang

dune lam kei eau dao done cudne bue theo cac dane dao ddne udn vdi tan sd Ian ida

xexiy khf Nhu \'ay neu tan sd Ian toa xoay khf bang Ian sd dao dgng rieng ciia eong

trinh thi kei eau xay ra cdng huemg Van tdc tdi han ga\ cdng hudng do Ian toa

xoa\ khi x;ie dmh theo:

//,, = (1.6.1.2)

S,

Trong dd: U^^ , 1^ Ian luett la van ide tdi han gay cdng hudng \a tan sd dao

dong rieng dau tien eiia eau

Thue nghiem ihay rang, khi \an toe gio iir nhien {rong dai \an ide trirde \a

sau \an Ide ldi hvUi se xuat hien hien tuone dao ddng eua cdng irinh do xoa> khf ed

Ian sd ddne nhai \di lan sd dao ddne riene ciia eo ne trinh (hinh 1 "^)

19-Hien tugng nay con ggi la trang thai "khoa" tan sd nhu vay trong vung "khda" nay d tai dai van tdc nhat dinh da xay ra cdng hudng do xoay khf lam tang bien do ciia dao ddng cdng trinh Nhung do ket cau cd luc can nen dao dgng la tat dan nen con ggi dao dgng do lan Ida xoay khf con ggi la dao ddng eudng bue vdi bien do gidi han Thudng hien tugng nay xay ra vdi van tdc gid thap, hien tugng eong hudng lai xay ra tren mgl dai van toe quanh van tdc cue ban

Vune khoa

- t^n so

Lur khi done xuat hien theo ehu kv

i '

Hinh 1.5 Vung "khoa'' tan so va tae ddng lire do cae xoay khf

Tae done ddne lire ciia hien tuone nav ihudne khone eav pha hoai kei cau

nhung gay hu hai mdi va dae biet la gay hieu ung \i\xn ly vdi ngudi qua cau do dao

dgng manh eiia kei eau d mien cdng hudng Cae cdng thue thue nghiem xae dinh bien do dao dgng Idn nhat va eudng do luc nang Idn nhai d trang thai eong hudng dugc neu trong [17] [26], [39] [40] Lire kfeh dgng va phuang trinh dao dgng eiia cdng trinh d trang thai "khda" duge trinh ba\ trong [5] [6]

1.6.2 Dao ddng tir kich theo hudiig vuong gdc gid tdi do hien tugng Galloping

Khi ddne khf tac ddne xien ede len kei eau mat eat khdne phai hinh iron, se

phai sinh lire nang khf ddng lam ket cau elui\en dieh quanh \\ trf can bang ban dau

Tii\ nhien iir sir dao dgng ban ctfiii eiia kei eaii lam tha\ ddi gdc tdi eiia eio va se

dan \o\ iha\ ddi tuong irng lire nang khf ddng (hinh 1.6) Neu lue nang na\ tang len

Cling hudng \di dieh ehu\en eua kei e:Vu se lam lang dieh ehu\en len nua eho ldi khi

dd eirne eiia kei eau khae phue duoc lue nane na\ hoae hre nane bat dau eiam irone

khi gdc tdi cua gid van dang tang Do tac ddng cua hien tugng nay phat sinh tu dao ddng cua ket cau ehu khdng phai tir ban than ddng khf nen nd la hien tugng dao dgng tu kich Mat dn dinh khf dgng luc do hien tugng Galloping cung dugc xem la mgl dang dao dgng tu kich cd bien do phan ky

Vi t r i c.-in b.-^ntr

linh 1.6 Tae dung do Galloping

Vat r a n

'-'one khi hon loan

a Tac dong Buffeting

do dong hon loan

U o n e khi hnn loan

b Tac dong Buffeting khi qua vat c.in

Cone

Hinh 1.7 Tae dune do ButTetin:

Cdng thue thue nghiem tfnh van tdc cue han gay mat dn dinh Galloping dugc trinh bay irong [39], [40], [41], xae lap phuang trinh ddng luc ciia hien tuctiig Galloping dugc neu trong [5] [ 6], [7]

1.6.3 Dao dgng ngau nhien theo hudng gid tdi do hien tugng BufTeting

Do tfnh chat hdn loan ciia ddng khf se phat sinh ra lire bien ddi ma bien do eiia lire nay la ham eiia mat do va eudng do eua hdn loan lam eong trinh bi dao dgng neau nhien doc theo huctne eid dudi lac dune eiia cae lire bien ddi nav Dav duoc xem nhu la hien tugng Buffeting do su hdn loan eua ddng khf Mgl hien tugng khae

Cling do lire gio phat sinh tu sir hdn loan ciia ddng khf ga>* dao dong eudng hue ciia

cone irinh nhune su hdn loan na\ khdne phai tu than tu ddne khf ma do dong khf

khi \Uol qua cac vat can phfa irude lao ra sir hdn loan khi tdi eong trinh nam phfa sau (hinh 1.7) Day duac xem la hien luong Buffeiing trong \ung trdng (hien tugng

Buffeiing do vai can) Hien lugng sau ed the lam don gian hda hon hien tugng irudc khi eae lue bien ddi la ham eiia ehi tan sd lan toa xoa\ khi sau \al ean Cong ihue

llure nghiem tfnh ehu\en \i Idn nhat do hien tuong Buffeiing trinh bay trong [39]

va Galloping) lai can thiei phai kiem tra \a gidi ban van tdc gid ldi ban

Cae hien tugng khf dan hdi eiia gid ndi chung lae dung va anh hudng theo eae vai tro khae nhau vdi cae bd phan kei cau: dam cung, cot thap va cac day vang Kei

eau dam eirng trong can day \'ang thudng duoc ehu trong xem xei tae dune eiia eae

hien luone Vortex-sheddine Buffeiine va Flutter \a lien quan tdi tfnh loan tone the kei cau eau Con vdi kei eau edl thap thudne xem xet dudi tae dune eua eae hien tugng Buffeting Fluller \a Galloping, cung lien quan tdi tfnh loan long the kei can cau Vdi eae day vang thudng dirge xem xet cue bg dirdi tae dung eiia hien lugng Vortex-shedding \a Galloping Tdm lai trong thiei ke va tfnh toan tdng the kei eau eau da\ \ a n e eae hien tuone Fluller \a Buffeiine can phai duoc ehii trone xem xet

khi van tdc eid thiei ke Idn nham danh eia ket cau ed bi neu\ hai do mai dn dinh

ddng lue \a hu hai kei can d xan toe gid eao ha> khdng edn hien tugng shedtling can ehii trong khi \an tdc gid thiei ke trung binh \a thap nham danh eia kel eau eo kha nang b| eong huong \di dai \an ide gid thong thudng ea\ ngu> hai moi \a anh huong tam ly lia\ khdng \'ai iro eua eae hien tugng khf dgng lire trong

\*onex-thiet ke eau da\ vane duac tdm lai irone sadd 1.8

Tac done khi don? luc

- Phan ung cua ket cau

- Kiem ira : Cng suat - chu)cn vi Moi, hieu tmg tam ly

Thiol ke dam

1

Hien iL/ong Flutter

- Van IOC gio toi han

- Kiem tra : Van toe gio ihiot ko

1

Thiet ke day vang

Hinh 1.8 So dd vai ird eiia cac hien tucme trone thiet ke eau dav vane

1.8 Ket luan cudi chuong

Trong chuang nay da trinh bay each xae dinh van tdc gid thiei ke va van tdc gid Idn nhai, tfnh loan cac thanh phi'in lire khf dgng iTnh, eae dae tnmg xac dinh phan line eiia done khf, eae hien tuane khf ddne lue \ai tro tac dune eiia eae hien tuone khf ddne lue trone thiet ke cau dav \ane Cd the rut ra mot sd nhan xet chfnh

tu kei qua nghien cuu nhu sau:

- Sd Revnold va sd Strouhal la hai thdne so khdne thu neuven quan trone xac dinh phan ling ciia ddng khf khi qua mot liei dien eau bai ky Vdi eae dang liet dien cfiu day vang thoat khf ddng lire se cd sd Reynold be done khf khi quan eong

Irinh se h\o thanh eae xoay khf Karman cd kfeh thude gidng nhau, xuai hien \di

tan sd xae dinh ihdng qua sd Strouhal Mgl trong eae miie tieu lam giam eae lue khf done uie ddne vao kel eau eau da\ \ane la thiei ke mat eat dam eau ed sd Reynold be nhat ed the, lire la mat eat dam eau cang thoat khf cang tot

- Trong ihiei ke eau day vang can thiei phai danh gia lac dgng eiia hien tugng {•lulter xav ra d van tdc eid eao eav mat dn dinh kei cau Han ni'ra eung can phai

kiem tra \o\ hien tugng Buffeting eune eo the ea> hu hai eho eau a \an toe eio eao Mi hien iirgng Vortex-shedding ga\ cdng huong cdng irinh ehi a dai van toe

eid thone thuctng ga> anh huong tam 1_\ \a ga> moi ddng lire

- 2 3

CHUONG 2 MO HINH HOA VA PHAN TICH DAO DONG

2.1 Gidi thieu chung

Trong phan tfch tmh va dgng luc ket cau cfiu day vang, can thiei phai ly tudns hoa ket cau thue te theo mot each thue md hinh nao dd, ggi chung la md hinh hoa ket cau Xay dung md hinh ket cau rdi rac phan nhd ket cau thanh cac phdn lu nhd cae niit, cac phuang trinh can bang luc va ehuyen vi xae dinh tai cae niit phan ehia Trone cac phuang phap md hinh rdi rac hoa thudng dung trong tfnh loan ket cau thi phuang phap phan tu hCrii han (f^HHj duge ap dung pho bien rung rai nhai trong tfnh loan kei eau

do Ihfch hgp vai lap irinh tren may tfnh, thuan Igi va hieu qua trong giai quyet cae bai loan phan tfch iTnh va dgng lire, kel cau Idn vdi nhieu an sd va lam vice phuc lap

Md hinh ket cau cau day vang phai phu hgp vai su lam vice cua ket cau thue te, cii the la can bao ton cac dae diem hinh hgc va ca hgc ciia ket cau thue le Co hai dang

md hinh: md hinh tdng the va md hinh cue bg Vdi mo hinh long the ihdng ihirdng co

hai each xa>' dimg md hinh la md hinh phang va md hinh khdng gian Trong xay dimg

md hinh ket cau cau day vang thudng ap dung cac loai phan tu nhu phan tu thanh khdng gian [•)han tir dam, phan tii dan va phfin lu Uim ban, xac dinh ehu\ en \ i mil \ a luc nut ciia cac loai phan tu tren the hien tren hinh 2.1

Trong ehuong nay se trinh ba\' ve each thue md hinh hoa kei cau can day vang theo phirong phap I^FIH phuc vu phan tfch dao dgng rieng ciia kei eau eau da> vang Vice mo hinh hoa ket cau eau dav \'ang can thiet dua tren nghien emi \e eau tao \a su

lam \'iee eiia eae bd phan kei cau Chirane na\ eune se nehien euu co so Iv ihu\et phan

ifeh dao dong rieng iheo phuong phap PTMH de ed the sir dung eae kel qua dao dgng

rieng trong giai qu\el bai loan phan lieh on dinh khi dgng lire Flutter eua eau da\ vang

2.2 Cau tao so bd cac bd phan cau day vang

Sa do kit cau: Ket cau cau day vang rat da dang ve cau tao tii bd trf so dd ket

cau (hai nhip, ba nhip hay nhieu nhip, ddi xiing hay khong ddi xung), each bd tri dav tren col thap (bd tri day ddng quy, bd trf song song hay bd tri re quat), so lugne mat phang day (bd trf mot mat phang hay hai mat phang day) (hinh 2.2)

Can too dam ci'rng: Dam cung la bg phan cau lao rat quan trgng cua kei cau cau

day vang Cau tao dam cung phu thugc nhieu vao sd lugng mat phdng day, chieu rone mat cau Phan biet cau lao dam cung theo vat lieu be tdng hoae thep hoae vat lieu hdn hgp thep - be tong Theo cau tao cd cac dang dam cirng pho bien nhu sau: dane dam ban dang dam I thep, dang dam ehu n , dang dam dam hop, dang dan ciimg (hinh 2.3)

Cau tao cot thap: Cau tao va hinh dang cua cot thap phu thugc vao sd lugne mat

phang day, eau lao lien kel vdi dam, chi6u eao ciia col thap va anh hudng Kin ldi do cirng chung ciia ca he ihdng Theo cau tao cd cae dang cot thap pho bien nhu sau: dang cot thap dan, dang cot thap hinh chiJ H, dang col thap hinh ehu A va dang egi thap hinh chfr Y ngirgc (hinh 2.4)

Cau tao day rang: Cac bd day vang thudng cau lao d hai dang pho bien sau: bd

cap sai dat sone sone, bd cap tao dat sone sone Ve dae trune co hoc vat lieu, cd the* xem cac bd cap cau day vang chi cd kha nang ehiu keo, khdng ehiu nen \ a udn

Cau tao lien ket va ^oi: Lien ket bien tai vi trf cot thap thudne cd cae dane: lien

ket cirne eiCra cot va dam, edi di ddne, edi cd dinh, khdne cd edi, trone khi lien ket edi eiia dam tai md cau va cac Iru neo thudng la cd cau tao chong nhd

2.3 .Mo hinh ket cau cau day vang theo phu'ong phap PTHH

2.3.1 Md hinh dam ciirng

Md hinh dam cung theo cac phan lir thanh khdng gian dan hdi Cae diem mil tren mo hinh xae dinh phan tu la eae diein dae trung tren dani nhu eae mil treo day

Phan lif ihanh kh6ng gian Phan lii tam

Hinh 2.1 Mdi sd loai phan tu thanh thudne dune trone md hinh boa eau dav \ani:

K c i cau c^u d^y v,ing 3 nhip

d.U dong quy

KOt cau c;Ui da\

dav soni! sonc

KOt cau »;.iu dav \An<2 ?• nhip

d.^y re ijuat

Hinh 2.2 Cae dane so' do kei eau eau da\ van,

O i i i ^ J J in hi'tp J i i n - C l u flJi C h j > | Q u j n g N m h )

I').iiig J.I111 hi^p n h i i i u n g i n - C J U C u n T h ^

ninh 2.3 Cau lao dam eirne eau dav vane

( 0 1 I M i • I '

Hinh 2.4 Caii lao cot lh:ip can da\ \ang

2 7

-cung ph6 bien nhu sau: mo hinh phang chap hay md hinh phdng khdng chap, md hinh khong gian mgl true dam trung tam, md hinh khong gian hai triic dam md hinh khone gian mang dam phdng va mo hinh khdng gian chi tiet (hinh 2.5) [34], [35], [36 ]

Cac dae trung vat lieu va hinh hgc bao gdm md dun dan hdi udn (E), mo dun cat (G) va dae trung hinh hgc cua cac nhdm phan tu gdm dien iich cua liet dien (A), dien

lich cat cd hieu ciia tiet dien(A2, A3), md men quan tfnh udn (L., lyy), hang sd xodn [i)

xac dinh theo cac eong thue thong thudng Tuy nhien su phue tap la viec xac dinh dd ciimg xoan ciia tiet dien Do cung xodn phu thugc cau tao hinh dang ciia mat edl dam va dam ehiu tac diing cua dang xoan nao: xoan thuan tuy (xodn St Vemanl) dang xodn eudng bue hay xoan bien dang Mot sd eong thue riit ggn tfnh loan hdng sd xodn tuong duane (J,,) ) vdi mot so dang mat edl dugc trinh bay trong [34], [36]

N b hinh true dim irupi! lam

F h f i i i /

R u n i a

lien kLi ^citei

Nb hinh lhL"o hu dini

Hinh 2.5 Cach thire mo hinh tone the dam cung

2.3.2 M d hinh cot thap

Cot thap diroe md hinh ihanh nhieu phan lU thanh khdng gian dan hdi eae diem mil xae dinh phan tu la eae diem dae tnmg iren eot lha[^ nlur eae nut treo Ja> vang eae

mil ndi, cae nut cd su thay doi liet dien mat cdt ngang va cac mil bien lien ket Cac dae trung vat lieu gdm md dun dan hdi udn (E), mo dun cat (G) va dae trung hinh hgc eiia cac nhdm phan tu gdm dien tfch (A), dien tfch cdt (A2, A^ ), mo men quan tfnh udn (I I33), hdng sd xodn (J) xac dinh theo cac eong thiic theo dang mat cdt tiet dien

2.3.3, Mo hinh day vang

Mo hinh sir lam viec cua cac day vang nhu phan tu dan dan hdi xac dinh qua hai mil: nut tren cot thap va mil tai dam Cac dae trung ciia cac phan tu day vang gdm md dun dan hdi (E) va dien tfch tiet dien (A) Khi xet tdi anh hudng cua do vong ciia cac day vang va luc cang trong cac day vang tdi mo dun dan hdi Young, cd the dua vao tfnh loan vai md dun dan hdi tuong duang ciia cap vang ( md dun dan hdi Ernst )[]] [3]

Mo dun dan hdi tuong ducmg ciia cap vang phu thugc vao chieu dai day, lire cang trong day, trgng lucmg ban than eiia day vang

Md dun dan hdi luang duong theo tiep luyen

E,j ^, E^j, lan lugt la eae mo dun dan hdi luong duang tfnh loan theo tiep

tuyen va theo cat luyen /^., 1 lan luiTt la mat do trgng lugng eua cap vang va ehieu dai cap vang

a la un<z siiai keo cd dinh irone cap vane

CT^, rr- h'in luol la (mg suai keo thap nhai \ a eac^ nhai trong cap vang

2.3.4 Mo hinh dieu kien bien

29

Mo hinh dieu kien lien ket giiia dam va cot thap la mot trong cac van de khd

khan trong viec xay dung mo hinh kel cau cau day vang theo phuang phap PTHH

Trong mo hinh boa lien kel dam va cot thap dua vao cac phan tu thanh lien ket, vdi cau

tao lien kel kiem che ehuyen vi ciia dam theo phuang thang dung va ngang Dae trung

ca hgc ciia cac thanh lien kel tfnh loan phu hgp vdi cau tao ciia cac goi dung va goi

ngang cua dam tai cot thap

2.4 Phan bd khdi lugng tren ket cau

Mo hinh chfnh xac sir phan bd khdi lugng tren ket cau anh hudng rat Idn tai

phan tfch dao dong rieng cua cau day vang Phan tfch dao dgng cau day vang vdi mo

hinh PTHH can ihiel phai xay dung mo hinh phan bd khdi lugng tren kei cau va lap

trune khdi lucme tai cac mil chfnh, cune nhu phai xet ldi dav dii cac loai khdi krone dai

han ed tren kel eau Do khdi luone ciia dam ehicm iru the va anh hudne quvet dinh tdi

dao ddne ehune eiia ea cau, ncn trone phan tfch dao ddne eiia cau dav vane ihdne

thudng chi xet tdi phan bd khdi lugng tren dam cirng va bd qua khdi lugng ciia col thap

va cac day vang [35] Mo hinh lap trung khdi lugng ve cac mil phai bao loan khdi lugng

va md men quan tfnh khdi lugng theo cae phuong so vdi kei can ihire ic

Diem mil tap trune khdi luone tren mot tiet dien neane dam phu thude vao each

thue xa\' dune md hinh thone thudne la cae diem niit neo da\' \'ane lai dam Khdi

luone va md men quan tfnh khdi lircme tfnh theo:

M.=- (2.4.1)

n

I =y{/ -/;;/•-) (2.4.2)

I

Trong dd : i la chi sd true toa do ( c =X: \: Z)

cl,n lan krot la khoang each cap va so niit khdi lugng tren tici dien 111, L,,, I, lan lugt la eae khoi lugne ireii tiet dien mo men quan tinh ban

than va khoane each loi true irone Uim khdi lucme eua tiet dien

2.5 Phan tieh dao dgng cau day vang theo phuomg phap PTHH

2.5.1 Phuong trinh vi phan ehuyen dgng cua he nhieu bae tu do

Phuang trinh vi phan ehuyen dgng cua he nhieu bae tu do dir di tac ddng ciia lire

gid cd the bieu di^n dudi dang phuang phap PTHH nhu sau:

Trong dd :[-^/l[c],[/r] lan lugt la eae ma Iran khdi lugng, can va do cung ciia he

{A'}, {xj, (jfj lan lugt la cac vecto ehuyen vi mil va dao ham cap 1, dao

ham cap 2 ciia vecto chuydn vi mil

{P{t)] la vecto lire khi dgng

Ma Iran \K\ la ma Iran vudng, ddi xung, xac dinh duong, ma Iran [A/] cung la

ma tran vuone, ddi xirne, xac dinh duone, trone trudne hop khdi krone tap trune lai mil

ihi ma Iran khdi luone lai mdi mil cd dane hinh eheo Ma Iran can [C] xav dune iheo co

che hao tan nane krone trone kel cau, vdi md hinh Revleiuh thi ma tran can [C] eune

vudng, ddi xi'rng 0 bai toan nay lire khi ddng{P(0} la lire tir kich Flutter

2.5.2 Dao ddng rieng va cac dang dao dgng rieng

Phuttne trinh \'i phan ehuven ddne ciia he n bae tir do, dao ddne tu do khdne can

dirge vi el lai nhu sau:

Phuong trinh tren ed phuong trinh dae tnmg dao dgng (bay phuong trinh tan sd)

d dang co ban sau:

DctlK]-oy[M\ = 0 (2.5.2.2)

Trong dd : eo; la tri rieng ciia dang dao dgng thu i (1=1-:- n)

Nghiem ciia phuong trinh (2.5.2.2) se la n tan sd rieng eua he

Tir phuong trinh '[^'1 - r'>"[A/J Jc) I-t) iim duoe n cac vecto rieng [^ { , (i = \^n)

31

-ij.)

Tap hgp cac vecto rieng ^<p^ /, (/ = 1 - n) theo col thanh ma Iran dang rieng [0]:

[ 0 ] = {^, ,^., , <^,, ^ J ; (2.5.2.3)

Cac vec to rieng thudng dugc chuan hoa de thanh cac dang dao done riene [</> }

va cac dang dao dgng rieng nay chi dae trung cho dang ehuyen vi une vdi cac tan so'

rieng Mot trong cac tfnh chat quan trgng ciia ma tran dang rieng [o] phuc vu viec eiai

bai loan dgng luc la tfnh chat true giao va true giao chuan boa

- Tfnh chat true giao ( phep bien doi sang true toa do chfnh)

kYMki-^^A ^ M[KM = [K-'

(2 r2.4)

Trons do : S la so Kronecker, ,1 kill i = j

'' ' 0 A7;/ / ^ j

V 1/ la cac ma Iran dudne eheo

- Tfnh chat true giao ehuan hoa ( phep bien ddi sang true toa do chudn)

A-m

hav M[KM = [K'\

(2.5.2.5

Trong do : [K^ J la ma Iran duang eheo eo eae Iri rieng OJ^ , J = \-^n

[/] la ma tran dirong eheo don vi

2.5.3 (Jiai hai toan don^ lire theo phan tieh dang dao dong

ChiiNcn CO so eua phirong trinh eo ban (2.5.1 h sang true toa do ehi'nh:

{r}=[0]{A'} (2.5.3.11

Ta diroc: [/V/J[o]!r!+ [r][ch]|>-[+ [A-][ct)]lr|= {/>(/)} (2.5.3.2 >

Nhan hai \c [ihiamg trinh (2.5.3.2) \a\ ['t'] va bien doi ve phirong trinh dao

don^i eua he niol IXK lu ilo unu \oi Liam: tlur i nlur sau

m Y+cY-k,Y = p,(t) voi p,(n = kYPit)

y + 2C,co, Y - co: K = ^ ^ vof' ^'^'

2.5.4 Chuan hoa nia tran darn; riens

Do cac sd hang ciia vec to dang rieng {^^} trong ma tran dang rieng [({)] sai khae

nhau mot hane sd nhan, nen luon ed the ebon cac vec to dane riene thfeh hop thoa man:

[ch]'[.\/][(D]=[/] (2.5.4.1) Day la tfnh chat true giao chuan hoa ma Iran khdi lugng Ma tran dang rieng [o]

diro'e true siao ehufin hoa trone irudne hem nav eoi la ma Iran dane riene ehuan hoa

theo khdi krone 4^' Trone tfnh loan ihudne ma Iran dane riene bien ddi odane ehuan

hoa theo khdi lugng

Ma Iran dane riene chuain boa ihco khdi krone O

dane rieng [d>| iheo each llure sau :

Trone dd

*^

6 xac dinh iheo eong ihue 9 = ±\\d \' [ujlt^ \ ^

duoc bien doi tu ma Iran

5.4.2)

- \ ni

33

2.6 Tinh toan vi du

2.6.1 Thong sd cau tao cau day vang

Tfnh loan vf du vdi mot cau day vang cd cac thong sd ket ca'u sau: (hinh 2.6)

- Ket cau cau day vang 3 nhip ddi xung, phan bd nhip:L=40.4+97+40.5=178m Dam cung dang dam ban BTCT, chi6u eao tren tiet dien dam bien thien h=35cm-55em, chi6u rgng mat cau xe chay 12.5m, chieu rgng loan bg la B=14.5m, chieu rgng treo cap 13.4m

Cot thap BTCT hinh ehu H, chi6u eao loan bg 34.5m Cap vang diing loai bd tao 7 sgi, cd 2 loai bd cap vang loai 12 bd T15.2 va 19 bd T15.2

U^

125

^ ^ z z z z z z z ^ ^ / / / / / / / " ak

B - B

Hinh 2.d So do va eau tao eae bd phan eau day vang

- Trgng Iirgng loan bg cac tai trgng dai han tren dam (dam eirng dam ngang, lop mat eau, khdi neo, lan ean lay vin ) la 19.8 Uin/lm ehieii dai dam

Cac dae irirng vai lieu, hinh hoe eiia dam ei'rng cot ihap \a eae da> vang dugc

mh toan iriMie bane 2.1

Bang 2.1 Cac dae trung hinh hoc ciia dam cung, cot thap va cac day vans

T/m-2 Dgc trung hinh hoc

Dinh va than cot thap A=1.14m-;l3,=0.257m' l22=0.118m-*;J=0.223m' Chan cot thap

A = 1 1 4 m - ; I , , = 0 2 5 7 m ' I,, =0.118m^;J=0.223m^

cm-

A^=16.69cm-2.6.2 Phan tieh dao dong rieng ciia cau day vang

Xily dung mo hinh ket cau khong gian mot true dam theo phuang phap F l l l l l

voi cae ehi dan (.]u(.ic trinh hay a eae miie tren Phan tieh 10 dang dao dong rieng dung

chuofns trinh SAP2000 Xet 2 trudnu hop mo hinh hoa eae dav vans: khona xet loi anh

hudne eiia dd vdne ban than (trudne hop 1) va xet ldi anh hinrne do vdne ban than

(trudng hop 2) Kei qua cac dae trung dao dgng rieng duge trinh ba> trong bang 2.2

Being 2.2 Cac dae trung dao dgng rieng ciia eau (trudng hgp 1) Dane

1.05E+02 1.12E+02 1.36E+02

Tan so

(Hz)

Chu k\' (s) 0.6099131 1.639579 0.801663

0.852593 1.194920 1.293130 1.449593 1.581915 1.630459 1.683362

1.247406 1.172893 0.836S76 0.773318 0.689849 0.632145 0.613324 0.594049 1.857597 0.538300

M o ta tfnh ehat dans dao dons S-V-1 A-V-2 S-T-1 A-T-2 S-V-3 A-\-4 S-T-P-3 S-V-5 j A-V-6 i S-V-7 i

(/hi chu :S : Dane ddi xirne

A : Dang phan ddi xung

\ : Dane dae» ddne udn

T : Dane dao ddne xoan

P : Dane dao dgng ngang