Tính toán ổn định khí động flutter của dầm chủ trong kết cấu cầu hệ dây bằng phương pháp bước lặp (tóm tắt)

1







 
 
         

 
1. 
Trong lun án c gng gii quyt ba v 
- Phát trin tc gió flutter ti hn ca cu trên
 ng un xon ca dm ch.
- Xây dng mt s phn mm chuyên dng tính toán vn tc gió ti
hn phc v cho vic kinh thit k và duy tu bng cu
treo.
- u khin th ng vn tc flutter ca cu treo b
ng hc
2. 
 Đối tượng nghiên cứu của luận án
Nghiên cu nh flutter ca mô hình mt ct dm cu 2D. T
u khin th ng nh flutter ca dm ch cu
treo.
 Phạm vi nghiên cứu của luận án
Lun án trình bày áp dng c  c l  tính
toán s mt nh flutter ca mt s cu treo có chiu dài nhp ln.
Phn quan trng ca lun án trình bày ng dc

l u khin th ng flutter ca dm ch
cu treo b    c (lp b    ng
png hc (lp hai cánh vy).
3. 
- c và mô hình
tính toán ca kt cu cu h dây.
- ng s: Phát tric lp ca
Matsumoto tính toán vn tc flutter ti hn ca cu khi có lp b
u chng hc) và khi không lp.
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- c nghim: Tham gia l
          
 
4. 
- Phát tric lp ca M. Matsumoto tính
vn tc gió ti hn ca mt ct cu 3 bc t do [116] sang tính toán
mô hình mt ct cu có lp b u chnh rung 4 bc t do.
- Xây d  g trình tính toán vn tc gió ti hn: Flutter-
BK01 và Flutter-BK02, da trên phn mm MATLAB  tính toán
vn tc flutter ti hn ca ci tác dng ca gió.
-  u t     ca b gim chn khng-cn
(TMD) cho dm ch cu h dây, t    ng nhn xét,
khuyn ngh vic l t b tt ch   t hiu qu
mong mun. Kt qu này có th áp dng trong nhng gii pháp gim
i tác dng ca gió ca mt cu treo bt k.
- Áp dng các kt qu nghiên cu  tính toán cho mt mô hình mt
ct dm cu c th. Các kt qu c là hp lý gia tính toán lý
thuyt và thc nghim.

5. 
Lun án gm  n Kt lun, kin ngh vi 133
trang, 58 hình v  th, 9 bng biu.

1 
1.1  
Hin nay, các kt cu cu h c
xây dng ngày càng nhiu ti Vit Nam vi kh t nhp ln
cùng vm v mt kin trúc m quan. Tuy nhiên, do có dng
kt cu thanh mnh nên các công trình c, dây võng rt
nhy cm vng ca gió bão.
1.2 

 nghiên cu ng cn công trình cu, u tiên ta
phi xây dng ca ci tác dng cn
i ta xây dng hai loi mô hình: mô hình mt ct và mô hình
toàn cu [35, 79, 94, 96, 141, 149, 153, 154].
V mc mô hình mt ct là mô hình h ng hai bc
t ng ung xon) hoc mô hình h ng ba
3


bc t do (dao ng ung xong ngang). Do dao
ng ngang ít có ng lng s dng mô
hình hai bc t do.
Mô hình toàn cc nghiên cu [35, 96, 141, 153, 154].
n t hu hn theo các
d xây dng mô hình và
ng toàn cu.
1.3 

 tính toán vn tc ti hn flutter cng s
d
-  riêng phc
- m s phc
-  dng tiêu chun Routh  Hurwitz
- c lp
1.4 
Do tính phc tp cng ca ci tác
dng ca gió, trong lu s dng mô hình mt c 
nghiên cu tính toán mt  nh flutter ca cu. Trong quá trình
nghiên cu chúng tôi th   c lp ca GS. M.
  i hc Kyoto) là m    
xuu v có th nghiên
cu phát trin. Vi vy trong luu s dng và phát
tric lp tính toán vn tc flutter ca mô hình cu.
Trong lu dng và phát tric l
nghiên cu khin th ng kt cu cu dây s dng các
b gim chn kh ng-cn (TMD) và s dng các cánh vy b
ng.

2 
       

2.1 
2.1.1 
10
/U m s

 




4


2.1.2 
/
d
U m s




10 1
.
d
U U E
(2.3)
2.1.3 



2.2 


2.2.1 
2.2.1.1 Biến dạng và ứng suất tĩnh

g và momen
46, 149]

 
2
1
2
D
D U BC


(2.5)

 
2
1
2
L
L U BC


(2.6)

 
22
1
2
M
M U B C


(2.7)

2.2.1.2 Các hiện tượng mất ổn định tĩnh
a. Mất ổn định uốn ngang

xz
          

y
vuông góc 


]

3
28.3
zT
cr
EI GI
q
L

(2.10)
5


(2.5) [125]

1/2
2
cr
cr

D
q
U
CB





(2.11)
b Mất ổn định xoắn






 V

2
0
2
'
cr
M
k
U
BC




(2.19)
2.2.2 
2.2.2.1 Dao động do xoáy khí (Vortex-induced vibration)
a. Giới thiệu chung - Hiện tượng lock-in
1

các xoáy khí luân phi      
s
f
    
Strouhal [149]

s
fB
St
U

(2.20)
K

             

lock-in.
b. Mô hình phân tích hiện tượng dao động gió cuộn xoáy


           


2
1
sin
2
LS s
F U BC t


(2.21)
       g, p
g [68, 109, 149]
6



 
2
11
2
2
12
2
2
1
( ) 1 ( ) ( )sin
2
L
m y y y
y y y
U B Y K Y K C K t

B U B
  
  





    




 

(2.23)
2.2.2.2 Dao động do gió mưa (Rain-wind-induced vibration)
uchi,

.
  

0
0
yy
y


   
   

  
       
   
   
M C K
 
 
(2.34)
2.2.2.3 Dao động do rối của dòng khí (Buffeting)


g
m

A

k
và
0
c
(hình 2.9)

x


   
0
mx c x kx P x P t   
  
(2.37)

 
D
P x AC Ux



(2.38)
2.2.2.4 Dao động phía cuối gió (Wake-induced vibration)



a. Cộng hưởng luồng gió rối


cr
U
]

2
cr
t
B
U
T

(2.42)
b. Cộng hưởng xoáy khí

cr

U


k
f

]
7



k
cr
t
Hf
U
S

(2.43)
c. Hiệu ứng giao thoa



 
tháp và d].
2.2.2.5 Dao động tự kích khí động học theo phương uốn (Galloping)

. 


0
0
L
D
dC
C
d







(2.57)
2.2.2.6 Hiện tượng dao động tự kích khí động học uốn xoắn (Flutter)
a. Hệ phương trình dao động tự kích khí động học uốn xoắn của
hệ hai bậc tự do

Hình 2.13 Mô hình dao động flutter
 
    
  (hình 2.13) :

( ) ( ) ( )
h h h
mh t c h t k h t L  
 
(2.58)
k

B
U
h
k
h

h
L
M

,mI
h
c

c
8

( ) ( ) ( )I t c t k t M
  
  
  
 
(2.59)
b. Lực nâng và momen khí động

]

2 * *
12
2 * 2 *
34
1
( ) ( )
2
( ) ( )
h
hB
L U B KH K KH K
UU
h
K H K K H K
B














(2.64)

2 2 * *
12
2 * 2 *
34
1
( ) ( )
2
( ) ( )
hB
M U B KA K KA K
UU
h
K A K K A K
B















(2.65)

K
là 
c. Mô hình flutter ba bậc tự do
 [138]

2 * * 2 *
1 2 3
2 * * 2 *
4 5 6
1
2
h
hB
L U B KH KH K H
UU
h p p
K H KH K H
B U B




  



  





(2.66)

2 2 * * 2 *
1 2 3
2 * * 2 *
4 5 6
1
2
hB
M U B KA KA K A
UU
h p p
K A KA K A
B U B





  



  





(2.67)

2 * * 2 *
1 2 3
2 * * 2 *
4 5 6
1
2
p
pB
D U B KP KP K P
UU
p h h
K P KP K P
B U B



  




  





(2.68)

trình chuy]

( ) ( ) ( )
h h h
mh t c h t k h t L  
 
(2.69)

( ) ( ) ( )I t c t k t M
  
  
  
 
(2.70)
9



     

p p p
mp t c p t k p t D  
 
(2.71)
2.3 
2.3.1 












2.3.2 














175]).
2.3.3 

 






50, 108, 134, 160].
2.4 

2.4.1 
 


2 2 2 3
2 2 2 2
2
2
ei
b b L
e
b P t T L
w w w w
m c EI c A
t t x x x t

I c GI M
t t x x
  


   
    
   

   
     
   


   

  


   


(2.160)
2.4.2 -


trình d-

       
11

, sin , , sin
nn
jj
jj
jj
w x t h t x x t t x
LL



   

   
   

(2.163)


( ) ( ) ( )
hL
mh t c h t k h t A

  
 
(2.177)

( ) ( ) ( )
L
I t c t k t M


  
  
 
(2.178)
2.5 




    -      
10


dòng          
---wind-induced
     -      

h

3 
TREO THEO MÔ HÌNH      

  ,       

3.1            



[153]






h
và

. P
]

( ) ( ) ( )
h h h
mh t c h t k h t L  
 
(3.1)

( ) ( ) ( )I t c t k t M
  
  
  
 
(3.2)


ình (2.64), (2.65).
3.1.4 

flutter
 
**

, 1, ,4
ii
A H i 



[143].


.  
11



 
flutter
**
,
ii
AH

 

3.2 Tính toán 





3.       



 

     
K K K  M q D q C q 0
 
(3.17)

 
T
h

q
;
     
;;K K KM D C

(3.17) :
 
t
te

qq

(3.18)
            

 
Bươ

́
c 1: :
0
sin
FF
t
F
et

  


(3.22)
Bươ
́
c 2: 






















Bươ
́
c 3: 

, 
















, 



 











2
20
F F F
     
  
 
(3.67)

 
 
3/2
2 2 * 2 * * 2
1 3 1 2 1 2 1
* * 2 * * 2
1 3 2 4 2 1 1
* * 1/2
4 3 2 2

[ { 1 sin
1 sin 1 (cos sin )
(cos sin )}]
F F F F
F F F
F
A A H
A H A H
AH

     
     
  
     
    

(3.68)
 
 
* * * 2
1 2 1 2 1 2 1 1
* * * * 2 * *
1 3 2 2 4 2 1 4 3 2
2 2 { 1 sin cos
sin cos 1 sin sin }
F F F
F
FF
A A H
A H A H A H



    

     
       
    
(3.69)
12


H(3.68) và (3.69) 

F

và
F


Newton-
,
FF

.
3.3 




.


2
34,8kg, 0,71kgm , 2790N/m, 70,8Nm/rad
0, 2 0,420m, 0.79m
h
h
m I k k
c c B b l


   
    

Hình 3.5 Hình dáng mặt cắt mô hình thí nghiệm (đơn vị: mm)









Hình 3.6 Mô hình thí nghiệm với TMD trong thí nghiệm hầm gió

.
13


-BK01 ta t

:
9.31m/s; 9.42rad/s
FF
U


. 

9.8m/s
F
U 
, %.
vài


 Kết quả tính toán vận tốc flutter
F
U
(m/s)

1
2
3
4


21.78
39.6
74.1
19.4

]
21.5
40.2
73.0
15.5
    
[165]
20.6
41.3
70.2
16.1


21.90
41.73
73.54
23.16

 
]
1.3%
1.49%
1.5%
25.16%

utter-
 :
40.14m/s; 0.978rad/s
FF
U



.    ],
39.2m/s;
F
U 
0.995rad/s
F



[146] là 2.4%.

-

23.75m/s; 0.9671rad/s
FF
U


. 
trong tà] là
23.6 m/s;
F
U 

0.97rad/s
F




n
[153] là 0.64%.

-
:
72.5m/s; 1.2711rad/s
FF
U



],
72.5 / ;
F
U m s

1.28rad/s
F



tro] là 0%.
14



-ó flutter
t :
75.5m/s; 3.1249rad/s

FF
U


.   

48.1m/s
F
U 


hF
f f f


          
 công trình khác.
3.5 

- 
-
 
- 
-BK01.
-              

m-
- -
         
          

er-
-BK01.

4     

         -
(TMD)             

4.1 
 (hình 4.1)
 
 
12
2
12
1 1 1
2 2 2
2
2
0
0
C C C h h h
C C C C C C
C C C C C C
C C C C C C
m m h m y m y c h k h L
I m b m b y m b y c k M
m h m b m y c y k y
m h m b m y c y k y
  

  



     

     


    


    

 
 
 
 


 


 
(4.8)

15

Hình 4.1 Mô hình tính toán


Bươ
́
c 1: 



:
0
sin

FF
t
F
et

  


(4.16)
Bươ
́
c 2: Thay
,,

 
       

   
0 0 10 0
/ , / ,hy


 
20 0
/,y

12
,,
h y y
  

  

,
FF

. V
0 10 20
,,h y y
là

12
,,
h y y
  
  


12
,,h y y

Bươ
́
c 3: 

2
20
F F F
     
  


(4.63)

16




 
 
 
 
2
01
11
0
2
02
22
0
33
**
00
14
00
4
*2
2
1 sin 2 cos
1 sin 2 cos
sin cos sin

22
/ 2 2
2
F C C F F y F y
C C F F y F y
F F h h F h
F C C F
y
mb
y
m b c
hh
BB
AA
B
A I m b

  
  
   

  


  




     



     

      






(4.64)

 
 
 
 
 
2 2 2
01
11
0
22
02
22
0
3
*2
0
1

0
34
2 * 2 * 2
0
43
0
1 cos sin
1 cos sin
sin 1
2
cos sin / 2
22
F C C F F y F y
C C F F y F y
F F h F
F h h F F C C
y
mb
y
m b k
h
B
A
h
BB
A A I m b

  



   

  


  


  



      




      

  

     


(4.65)
 (4.64), (4.65) 

,
FF


.



Phân tích           

Belt.


0.058,0.116,0.174kg; 7N/m; 0.081Ns/m;
0.05,0.10,0.15,0.20m
C C C
C
m k c
b
  


17

Hình 4.4 Mô hình thí nghiệm với TMD trong thí nghiệm hầm gió















Hình 4.5 Bố trí chung của thí nghiệm mặt cắt dầm cầu với TMD






end plates
bridge girder

TMD
damper pot
traverse

18


Bảng so sánh kết quả lý thuyết và thực nghiệm
 
/
F
U m s

C
k
= 2*7 N/m,
C
c
= 2*0.081 Ns/m),
C
m
= 2*0.058; 2*0.116; 2*0.174 kg
 
C
m kg

 
C
bm

0.05

0.1

0.15

0.2

2*0.058

Lý 
9.84
9.8
9.71
9.54

9.9
9.85
9.8
9.9
2*0.116


8.96
9.42
10.07
10.87

9.4
9.8

10.2
10.7
2*0.174


9.04
9.26
9.62
10.07

9.6
9.7
9.9
10
 

4.4 


km/h).


12.4m, 142.4kg, 18.1663Ns/m, 108.5311N/m
C C C C
b m c k   

S-BK02, 

50.7m/s; 0.89rad/s
FF

U



         ]:
49.5m/s; 0.86Hz
FF
U


         
] là 2.42%.
4.

4.5.1 g 
th

, , ,
C C C C
b m c k

min max
0,05m; 0,2m; 0,05m
C C C
b b b   

min max
0,116kg; 9*0,116kg; 0,116kg
C C C
m m m   

19


min max
2*4N/m; 2*10N/m; 2*1N/m
C C C
k k k   

min max
0,081Ns/m; 4*0,081Ns/m; 0,081Ns/m
C C C
c c c   


0,2m; 0,116kg; 2*0,081Ns/m;
Copt Copt Copt
b m c  

2*5N/m; 16.1m/s
Copt F opt
kU

Hiu sut:

16,1 9,31
*100 72,93%
9,31
Fopt F
F

UU
U



  

4.5.2 

, , ,
C C C C
b m c k

min max
3,4m; 12,4 ; 1m
C C C
b b m b   

min max
50kg/m; 200kg/m; 10kg/m
C C C
m m m   

min max
50N/m/m; 150N/m/m; 10N/m/m
C C C
k k k   

min max
2Ns/m/m; 20Ns/m/m; 2Ns/m/m

C C C
c c c   


11,4m
C opt
b 
;
90kg/m
C opt
m 
;
4Ns/m/m
C opt
c 
;
80N/m/m; 73.9m/s
C opt Fopt
kU

Hiu sut:

73,9 40,14
% *100 84,11%
40,14
Fopt F
F
UU
U





  



4.

- 

-

-         
            

-80%.
- 


20


           -


5     
       





Hình 5.1 Mô hình tính toán của hệ dầm cầu-2 cánh vẫy

   
1 2 2 2 1 1 1 2h h h w w
m m m h m e me k h c h L L L

         
 

(5.15)
 
 
   
   
22
2 2 1 1 1 1 2 2 1 1 2 2
1 1 2 2 1 1 2 2
w w w w
w w w w w w
m e me h I m e m e k k k
c c c M e L e L


     
    
         
       



    
(5.16)
   
1
1 1 1 1 1 1
w
w w w w w
I k c M

    
     
  
(5.17)
   
2
2 2 2 2 2 2
w
w w w w w
I k c M

    
     
  
(5.18)

21








và các c


Bươ
́
c 1: 

0
sin
FF
t
F
et

  


(5.35)
Bươ
́
c 2: Thay
,,

 
vào 
 

     
12
0 0 10 0 20 0
/ , / , / , , ,
ww
w w h
h
    
    
  
   
,
FF

. V
0 10 20
,,
ww
h


12
,,
ww
h
    
  
là

12

,,
ww
h


Bươ
́
c 3: 

2
20
F F F
     
  

(5.84)

 
 
 
22
3
2 * * *
0 1 2
2 2 1 1 1 1 11 2 12
0
22
3
2 * 2 * 2 *
0 1 2 0

4 1 41 2 42 1 2
00
4
*
21
1 sin 2 cos
2 2 2
sin cos sin
2 2 2
2
ww
F F F h F h F F F
ww
F h h F F F h w w
F
F
h B B
B
m e m e A e H e H
h B B h
B
A e H e H c c c
B
Ae

   


      




   
  





          






           



 
1
1 1 2
2 2 3 3
2 * 2 * 2 * *
1 2 1 10 1
11 2 12 1 1 31 1 1 21
0
33
2 * *

10 2 20 2
2 2 32 2 2 22
00
20
0
sin
2 2 2 2
sin cos sin
22
w
w w w
w w w w w
F F w F w F
F
w w w w
F w F w F
F
w
B B B B
H e H k e H c e H
BB
k e H c e H

     
    
   

   
  
  



   
        
   
   
   
         
   
   

 
 
22
22
1 1 2 2
sin cos / 2
ww
FF
I m e m e
   



    



(5.85)
22

 
 
 
 
 
22
3
2 2 2 * * *
0 1 2
2 2 1 1 1 1 11 2 12
0
22
3
2 2 * 2 * 2 *
0 1 2 0
4 1 41 2 42 1
00
4
2
2
1 cos sin
2 2 2
sin 1 cos sin
2 2 2
2
ww
F F F h F h F F F
ww

F h F F F F h h F w
wF
h B B
B
m e m e A e H e H
h B B h
B
A e H e H k k
B
kA

   


      



     






           







           



 
 
 
11
1 2 2
2 2 3
* 2 2 * 2 2 * 2 *
1 2 1 10
3 1 41 2 42 1 1 31
0
33
* 2 2 *
1 10 2 20
1 1 21 2 2 32
00
3
2
22
cos sin
2 2 2
sin 1 cos sin
22
2
ww

w w w
w w w w
F F w F F
w w w w
w F F F w F F
w
w
B B B
e H e H k e H
BB
c e H k e H
B
ce
   
     
   
   

   
    




        


   
         
   

   

   
2
* 2 2 2
20
22 1 1 2 2
0
sin 1 /
w
w
F F F
H I m e m e







   






(5.86)
 (5.85), (5.86) 


,
FF

.

 


40.14(m/s)
F
U 


1 2 1 2 1 2
0,1 , 0,5 , 0
w w w w
B B B e e B c c     


3
7850kg/m
w


,

0,02m
.

Hình 5.3 Vận tốc gió flutter tới hạn thay đổi theo
12
,
ww
kk

23


         theo tính
:

58(m/s)
Fopt
U 



58 40,14

*100 44,49%
40,14









            



 
            


 






- 


- 


 


       

24




Flutter-
-
       



- 
-
MATLAB.


           -

-
      
- ng
80%.




    -    




            

ng-
           -


