THIET KE GCfl CACH CHAN DANG GAI DB DAN H6

(1)

KHAO SAT - THIET KE XAY DUNG

THIET KE GCfl CACH CHAN DANG GAI D B DAN H 6 | CHjU DONG DAT

von M O H I N H P H I TUYEN CUA VAT LIEU CHE TAO

KS. L£ XUAN TONG

Trudng Oai hoc Phuong ddng

Tdm tat: Wp; dung eua bai bao la khao sat phan irng eiia bo giam chan trude tae dong ngoai xem nhu tac dong dong dat. Thiet bi each ehan day dang goi tru, CO dac tinh ea hoc cua vat lieu la phi tuyen, viec khao sat nay nham tim ra cac thong so kich thudc eiia goi dd sao eho bien do eiia dao dong tat nhanh trong nhu'ng giay dau tien.

Jii khoa: Dong It/e hoc phi tuyen; tinh chat phi tuyen eua vat lieu; goi each chan dan hoi

1. Md dau

/. /. Nguyen ly each chan day

Su cich ly kdt ci'u nham tich rdi hoac han chd viec truydn luc ddng di't v i o kdt ci'u khi sd dung cic thidt bj dugc dat d chan cdng trinh (mat eich chin - b6n dudi khdi lugng chinh cua kdt ci'u) dugc ggi l i giai phip cich chi'n diy. Hd thdng cich chin diy ed mdt hoac nhieu chdc nang sau:

- Chju tai trgng thang ddng kdt hgp vdi dd deo theo phuong ngang dugc tang cudng v i cd dd cdng Idn theo phuong ddng;

- Tieu t i n ning lugng, tao can nhdt hoac dng xd trd;

- Li'y lai can bang;

- Ting dd mem theo phuong ngang, ting dd bdn dn dinh eho cdng trinh.

Khi cd thidt bj cich chi'n diy, cdng trinh cd thim mdt dang dao ddng mdi. Cich chan diy cd tac dung keo dii chu ky dao ddng eo ban, gid cho chu ky nay ddc lap v i khdng trung vdi ehu ky dao ddng cudng bde do t i c ddng ben ngoii. Trong q u i trinh hoat ddng, ndu can thidt cd thd thay thd cac bd phan cua h6 each chi'n mdt cich d§ ding.

Nguyen ly cua giai phip cich chi'n diy dugc thi hien nhu hinh 1:

rn n

a) b) Hinh 1. Cach chan day trong bao ve cong trinh chiu dong dat

a) Ket cau thong thuang, b) Ket cau c6 cdch chan diy 1.2. Cac loai gdi each chan dan hoi difdc sCfdung

trong ky thuat

Gdi each chin cd eau tao bdi cic Idp eao su die biet v i cic Idp chi xen ke nhau, mat tren v i dudi cd

hai ti'm thep dd lien kdt v i o cdng trinh v i mdng. H6 thdng niy dugc dat tai mat eich chan, chju luc theo phuong ddng v i cd t i c dung ngan cich tai trpng ddng da't t i c dung true tidp ngay tai thdi didm truydn ldi

30

Tgp chi KHCN Xdy difng - sd4/2010

(2)

KHAO SAT - THIET KE XAY DUNG

cdng trinh. Djch chuydn ciia nen da't lim cho he thdng ldp cao su v i chi ma mdt phan ning lugng cua ddng each chan diy bidn dang v i djch chuydn, nhd cd luc dat bi hap thu, n6n luc tic ddng vio cdng trinh se nhd ma sat trong cac Idp ci'u tao v i luc ma sit giUa cic di [3].

B i n Ih^p mdt tren

Lai chi / C^c dia chi Bin Otip m^t duAi

a)

Hinh 2. Goi cdch chan dan hoi

a) Goi cao su c6 loi chi - LRD, b) Goi cao su c6 do can cao - HDR 1.3. Thiei kehe thdng each ehan day trong ky thuat

- Xic djnh kich thudc du kidn va vj tri ciia cich chan day dudi trpng lugng ciia kdt ci'u ben tr6n;

- Tinh toin chpn lua kich thudc ciia gdi cich chan thoa man y§u cau thay ddi chu ky mong mudn giam tai trpng ddng dat;

- Xac djnh ty sd can nhdt ciia gdi cich chan sao cho chuydn vj cCia kdt ci'u nam trong gidi han thidt kd dudi tac dung cua tai trpng gid v i dpng di't;

- Kilm tra kha nang lim vide cua gdi cich chi'n dudi tac dung ciia trpng luc, ddng di't v i cic tai trpng CO thi xay ra khic [3].

1.4. Cae eong trinh nghien eiAi va ngi dung khao sat bai toan each ehan day

Dinu BRATOSIN v i Tudor SIRETEANU (2002) [1], da nghien cdu md hinh Kelvin - Voigt (hinh 3) khi dd cdng k va dd can c la ham phi tuydn ddi vdi gdc xoay 6 thdng qua mddun chdng cat G{0) va h6 sd can nhdt £)(^)cua gdi each cha'n (hinh 4). Nghi6n cdu chi ra rang md hinh Kenlvin - Voigt cd thd md hinh hda bang cac vdng trd.

M = A/o sill (0/

1

A- = A-(e) - ^ W c = c(e)

I — ^

Hinh 3. Mb hinh phi tuyen Kelvin-Voigt

01%|

Hinh 4. Ham phi tuySn dSc tinh v$t li^u rvi

Tap chi KHCN Xdy dimg - sd 4/2010 31

(3)

KHAO SAT - THIET KE XAY DUNG

Phuong trinh dao ddng cua he ed dang:

J^.0 + c{0).0 + k{0\0 = M^.sincot (1)

trong dd: J^ia mdmen quan tinh cua gdi tru;

M Q la bien dd va co l i tan sd vdng cua luc kich ddng.

c{0) = 2J,(o,.D{0) [Nms];ki0) = -^.G{0) [Nm]

h .. , n.d'

VOI:

/„ =

" 32

- mdmen quin tinh cue; d, h l i duOng kinh v i chidu cao cua gdi tru cich chin din hdi.

JQ - mdmen quin tinh ciia gdi tru:

, 1

^{( ri\}

v^y

= ~md^

8

vdi: m- khdi lugng phan edng trinh t i c dung len tren gdi cich chin;

&)Q - tan sd vdng dao ddng tu nhidn eiia he khi khdng cd can:

fi>o = yJkiO)/J^ , tdc li khi 0 = 0, thay sd ta 8860.023^/

dugc: co^ = r=—

^fmh Mddun chdng cat [1]:

G(^) = 25 + 75exp(-1.12^) (MPa) H& sd can nhdt [1]:

£)(^) = 15.39-13.44exp(-1.2^)(%)

2. Thiet lap bai toan va thiet ke go! each chan dan hoi Trong bii bio niy, t i c gia sd dung kdt qua nghign cdu vd md hinh v i t Ii6u da cdng bd trong cdng trinh [1]

v i giai true tidp phuong trinh vi phan dao ddng (1) d l khao sit lua chpn kich thudc hgp ly cCia gdi each chi'n.

2.1. Thiet lap bai toan

- Thay cic bidu thdc bdn tren dd xic djnh dd cdng k(0)va dd can c(0)kh\ chi'p nhin kdt qua nghien cdu ve md hinh vat lieu theo [1], ta dugc:

c(^) = 2/o<yo.D(^) = 22.15J%|—[15.39-13.44exp(-1.26')] (Nms)

V h

^ ^ ) = ^ . G ( ^ ) = ^ — [ 2 5 + 75exp(-1.12^)Jl0'=98125 —[25-^75exp(-1.12^)](Nm)

h 32h h

Thay vio phuang trinh (1) ta dugc:

Tvid lift {i

.^ + 22.15J\-[15.39-13.44exp(-1.2^)]^ + 98125^[25 + 75exp(-1.12^)]^-MoSin6* (2) 8 V A h

- Hoac cd thd chuydn him D{0) va G(^)bieu didn dudi dang him mu co sd e sang dang ham bic 2 theo phuong phip binh phuong tdi thidu. Tde l i tren dd thi ham mu co sd e, ta li'y vd sd didm (trong bii bio niy lay 10000 didm), sau dd ndi cic didm bang dudng cong cua him bic hai v i xac djnh dugc him bac hai dd, cac budc dugc thuc hien bang chuong trinh Mathematica 7.

Hinh 5. Do thi D{0) dudi dang ham bac 2 Hinh 6. Do thi, G{0) dudi dang ham bac 2

Z)(^) = 15.39-13.44exp(-1.2^) = 4.14065+ 7.70921^-1.3024^' 0(0) = 25 + 75 exp(-l. 120) = 89.0475 - 42.6115^ + 7.07391^' Khi dd, phuang trinh (2) cdn dugc bidu didn nhu sau:

32 Tgp chi KHCN Xdy dimg - sd412010

(4)

KHAO SAT - THIET KE X A Y D U N G

md' .^ + 22.15J\|^[4.14065+7.70921^-1.3024^']^ +

. 4

+ 98125—[89.0475-42.6115^ + 7.07391^-].^ = A/„sin6;r

₍₃₎

Vi6c bidu didn niy cdn l i co sd de giai phuong trinh (3) bang phuong phip nda giai tich. Phuong trinh (2) va (3) d day la nhdng phuong trinh phi tuydn manh, vi vay phai giai true tidp bang sd - bang chuang trinh chuyen dung Mathematica 7.

2.2. Thie't kegdl each chan dan hdi a. Gia thiet vdi bo tham so

Khdi lugng ciia phan kdt ci'u bdn tren tap trung tai gdi each cha'n: m = 100000 kg;

Oieu kien dau: 0^ = 0.3 [rad]; 0^ = -0.01 [rad/s]

Tie ddng ngoai: M^ = 40000 [Nm]; o) = 0.4 [rad]

Thdi gian khao sit dao dpng la 20 giay.

Vdi bd tham sd nay, cd the tinh vdi nhieu cap tham sd d, h chpn bat ky, qua so sanh kdt qua cho tha'y chpn tham sd cua gdi each chin dang tru vdi: d = 0,4m; h - 0,2m thi phan dng cua cdng trinh tat nhanh trong 3 giay dau tidn, sau dd dieu hda vdi bien dp rat nhd (hinh 7 va 8).

l y i

0.10

0.05

0.10

.Ti^

0.3 1

0.2

0.1

0.2

Hinh 7. Do thi 0{t) trong 20s - giai phuang trinh (2)

!

/ n A

\' A \\ \ \ [\

\\ W \\ \ \

I ^{! i ! I ;}

A / \ r^

-i~

li 'I I ' " "

\-lA-- - -\4- \ I ti.

'v/

tUL

5 V 3.0

Hinh 8. Do thi 0{t) trong 3s - giai phuang trinh (2)

Nhan xet: ket qua cho thay tai thdi diem t^O, bien do la 0,3rad; tai thdi diem t > 5s thi bien do chi con 0,05 rad, sau dd dao dong se dieu hda theo tan so eua lue kich dong.

Phuong trinh (3) cho kdt qua d hinh 9 v i 10:

Tap chi KHCN Xuy dimg - sd4/2010

³³

(5)

0.10

0.3 i

0.2]

0.1 I

• 1 | \ A

^ n A A A A A A . ^ -

! i

UJ_/4X.V/A/-Az.-^^

VA \f \ ^

^2.0 ^2.5

0 . 2 ^

i V

Nhan xet Phuang trinh (2) va (3) eho nghiem co quy luat va hinh dang gan nhu nhau, nen viec giai (3) hoan toan cd the ehap nhan duge.

b. Giit nguyen bo tham so nhu tren, nhung cho fie dpng ngoai thay doi - Tang kich ddng ngoii td M ^ = 40000 [Nm] len M^ = 80000 [Nm]

feww

P ' -

20

Hinh 11. Do thi 0(t) trong 20s - giai phuang trinh (2)

34

A

! i

0.1;

0.2

I

/\ f\

-i -'—t

1 D-M I

i M i i A A A A A A A

1-4.-1-4^ i..J ._L..L-.U.-._vX 1 i . o U

! i \ TT5l7"'"T>rt/

/ \ \ / v .

2.5 3.0

V

Tgp chi KHCN Xdy dung - so 412010

(6)

KHAO SAT - THIET KE XAY DUNG

Nhan xet: Vdi mot bd tham so thiet ke, khi kich dong ngoai thay doi thi dao dong van theo quy luat la bien do giam nhanh trong vai giay dau, trudng hgp nay cho kich dong ngoai tang len thi bien do dao dong se tat cham han.

- Tang tan sd vdng cCia luc kich ddng ngoii [(i CD = 0.4 [rad/s] len (o = \5 [rad/s]

0.1

0-'

nn fm

0.2'

0.3.

0.2

0.1

Hinh 13. Do thi0{t) trong 20s - giai phuang trinh (2)

0.1

0.2

A A A A A, A A

11 lAil/ AiA Ur^-

• Gid nguyen luc kich ddng ngoii nhung tan sd vdng cua kich dpng ngoai bang tan sd cua dao ddng tu nhi§n ciia he khi khdng cd can. (0 = 0)^= 25.0599 [rad/s]

Hinh 15. Do thi0{t) trong 20s - giai phuang trinh (2)

Tap chi KHCN Xdy dimg - sd4/2010 35

(7)

KHAO SAT - THIET KE XAY DUNG

0.6

0.4 A

A ! I \ A \

0.2

11 / \

A 11

A M i ! A

M 1 !

4.-L4J_

- 1 — 2.5 U

0.2 ;•

0.4

ly

/ ^^' '-' V? 11 M A !-i I

Hinh 16. Dd thi0{t) trong 3s - giai phuang tnnh (2)

ao

/ , , ^ , , , 9 8 1 2 5 c / ' . 1 0 0 , / W r f ' ^ c n c n n r ^ , i Chii thich: a, = V ^ ( 0 ) / J Q = J ; / - ^ = 25.0599 [rad/s]

V « • 8

Nhan xet: Bien do tang nhanh trong khoang thdi gian tir 0,5 den 3 giay sau dd dieu hda vdi bien do 0,6 rad, nhu vay da xay ra hien tugng khueeh dai bien do dao dong khi tan so vdng cua kich dgng ngoai bang tan so vdng cua dao dgng tt/ nhien khi khong ed can.

e. GiU nguyen tham so dau vao, thay doi kich thudc cua gdi trij

- Tang dudng kinh gdi td rf = 0.4m len d = 0.6/w v i gid nguydn h = 0.2m

0.02 1

0.01

"m^

0.01

0.02

%. V 10 20

tLslL

mi\

Hinh 17. Do thi0{t) trong 20s - giai phuang trinh (2) 0.3 i

0.2

0.1

ii !

0,1

0.2'

ll

1 !i j M i

i

1 A P ''

ii[iA4/V/VAA/ ^^

i i 2.o\/ / W.sV V M.o

I 11 1/

i I.Ol ! 1 ; i 1.5! i ! I \ 2 . 0 \ / \ / \1

A A M M / y y "

Hinh 18. Do thi 0{t) trong 3s - giai phuang trinh (2) - Tang chidu cao gdi \ij h = 0.2m len h = 0.4m va giu nguyen d = 0.4m

36 Tgp chi KHCN Xdy dung - so •(41201^

(8)

*f - •

11- 0.3

0.2

0.1 ||i

0.1

il».v

\ ^

5 V 10 ^- tLS:

20

0.2 I

U.

0.3 >

0.2

0.1 !

0.1

0.2

Hinh 19. Do thi 0(t) trong 20s - giai phuang trinh (2)

11 ,A

:1 Al

^{\ A}^{\ A}

\ i\ l\ l\ A A -.

• • i \ I \ !

\ I

! i

\ \ I \ i

tr^ V ^

2.5 '-' 3.0

li •''

Hinh 20. Do thi 0(t) trong 3s - giai phuang trinh (2) Nhan xet: - Ndu gid nguydn h=0,2m v i tang d=0,6m

thi bi6n dd dao ddng tat nhanh hon (hinh 17,18) so vdi trudng hgp h=0,2m v i d=0,4m.

- Ndu giU nguyin d=0,4m v i tang h=0,4 thi bi6n dd dao ddng tat chim hon (hinh 19, 20) so vdi trudng hgp h=0,2m v i d=0,4m.

3. Ket luan

Bang vi6c chi'p nhan mdt md hinh vat lidu phi tuydn sin cd theo [1] dd cd duge phuong trinh dao ddng cua h& - day la phuong trinh vi phan phi tuydn manh. Thuc hien giai sd true tidp cd thd khao sit su thay ddi ciia nhiiu tham sd td tie ddng ngoai cho den kich thudc cua gdi each chi'n, nit ra:

Hoan toan chd ngu dugc dao ddng theo mong mudn;

- Nghifen cdu dugc hien tugng cdng hudng;

- Khao sit dugc nhiiu bd tham sd mdt cich dd ding;

- Kilm tra tinh chat dao ddng theo thdi gian bi't ky.

*. Hudng phat trien

Nhu tren da thay, giai true tidp bang sd cac phuang trinh (2) va (3) khd khao sat dugc tinh chat nghiem phu thudc vao cac tham sd cQng nhu didu kidn dau, thudng la phai tinh vdi nhieu cap tham sd d, h bat ky rdi so sanh kdt qua dd chpn dugc cap tham sd hgp ly. Chinh vi the ma hudng phat triln tidp theo la giai phuong trinh (3) khdng dung phuang phap sd true tidp ma bang phuang phap giai tich gan dung, de cd thd khao sat su phu thudc tinh chat nghiem vao cac tham sd v i dieu kifn dau bang bidu thdc giai tich rd ring.

TAI LIEU THAI^ KHAO

1. Dinu Bratosin, Tudor Sireteanu. Hysteretic damping modelling by nonlinear Kelvin - Voigt model.

Proceedings of the Romanian Academy, 3/2002.

2. L E X U A N H U V N H , NGUYEN HLTU BiNH. Nghien cUu cong nghe che ngu dao dong ket cau cong trinh nha cao tang phu hgp dieu kien xay dung d Ha Ngi. Bao cao tdng k^t d6 tai ma s6 01C-04/09-2007-3. Vien KHCN Kinh ieXay dung - Viet Nam, 2008.

Ngdy nh$n bdi: 22/11/2010

^gp chi KHCN Xdy dimg - sd 4/2010

³⁷