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A 15 3 Ser. A , V o l. 15, N o. 3 2000 9 JOU RNAL O F H YDROD YNAM ICS Sep. , 2000

: 1000 24874 (2000 ) 03 20366 214

1 , 1 , A S T IJSSEL IN G 2(1. 137 , 150001;

2. Eindhoven U niversity of Technology , P. O. Box 513, 5600 MB Eindhoven , NL )

: ,, ,

,

: ; ; ;: O 353. 1 : A

1

19 , , :

c0 =K f (1)

H elm holtz , c0 , Young [ 1 ]

:

c1 =E f D (2)

, Kor tew eg [ 2 ]

:

1c2 f

= 1c20

+ 1c21

c f =K f (1 +

D K E )

- 1 (3)

, K ; E ; D ; (1) (2) (3) : ( E ) ( E > >

: 1999 209 225

: (SZ 9830 ) ;

(97E 0003 G) ; SERC (GR J 54857 ): (1959 ) , , , ,

1995-2004 Tsinghua Tongfang Optical Disc Co., Ltd. All rights reserved.

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K ) , (3) (1) ; (K > > E ) , (3) 1, (3) (2) H alliw ell [3 ] , Kor tew eg

, (3) 7 :

cF =K f (1 + 7

D K E )

- 1 (4)

, 7 = 1 ( ) ; , , 7 = 1- 2 ( ) ; , ( ,

) , 7 = 1 - 2Kor tew eg 1878 : , Poisson

, ,

Kor tew eg Grom eka [4 ]

, L am b [5 ] L am b :

; , :

c p =E p (5)

, p , ,,

, Kor tew eg Joukow sky

M o scow , Joukow sky [6 ]

2

1956 , Skalak [7 ] L am b , ,

: , Young ;

, L am b L in &M o rgan [ 8 ] Skalak H errm ann

& M irsky [ 9 ] Spllier [10] Tang [11]

M OC H errm ann & M irsky L in & M o rgan , K ing & F rederick [12]

L in & M o rgan Skalak Thorley[13]

L am b ,L am b Skalak

70 , (FS I) DeA romond &

Rouleau [14] FS I , L in &M o rgan R ubinow &

Keller [15] FS I Kuiken [16- 19]

Kalkw ijk [20- 21] , Ko t [22] , Streeter [23] , W ylie [24] , T ijsseling [25]

1[26]

, :

2. 1

,

, , ,

, B row n [27- 28] D Souza and O ldenbruge [29] Ho lm boe [30]

763:


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1 FS I

, Tentarelli [31] Bessel[32] 2 , 1

; 2 ; ; 0. 02 ; R e ;Im 2 , , ,

2

2. 2

,

3 :

V , p ; ( ) , p ,

c f , c p ,,

, ,

[33] Po isson 4

2. 3

863 2000 3


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3 Poisson 4 Poisson

, 5 ,

, c f , Poisson c p ,

1 2 2 3

Regetz [34] , ,

, ,

B lade [35] Regetz ,

Davidson & Sm ith [36] T imo shenko FS I , Wood

& Chao [37] Jones &W ood [38]

E llis [39] T ijsseling & V ardy [40, 41] T 2

90 , [42]

R PV 6 ,

5 6

2. 4 Bourdon, ,

, Bourdon Clark [43, 44]

, W atham [45, 46] Bourdon ,

Tentarelli [31] J 2 L 2 , 7

963:


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7 J 2 Bourdon

3

42 ( Skalak [ 7 ] D Souza &O ldenbruger [29] Budny [47] L in & M o rgan [8 ] , H erm ann & M irsky [ 9 ] , Bu rm ann [48] Barez [49]

W iggert [ 6 ] T ijsseling [25] ) 42 (W iggert [50, 51] V ardy [5254 ] O bradovic [55]

T ijsseling [25] ) 42 ,

: 42

, [56 ], [57] H am ilton Gurtin , 22

Tentarelli [31] Hovgaard [58] V igness [59] Clark [43, 44] W ilk in son [60] ,

Buordon 42 , 82 12 2

14 2 , [42] :

[ A ]5 < 5 t

+ [ B ]5 < 5 z

+ [C ]< = r (6), [ A ] [ B ] [C ] , [C ] ; < ; r

, [42][42, 61 67 ]

4

, , Paidoussis [68]

[69]

V an de Pol :

q

- q(1 - q

2

) + 2

0q = 0 (7), q ; 0 ,

, ,

,

1939 Bourrieres , :

m u + 2m f v f u + m f v 2 f u - E I (u w w + u w w

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- u w w - w 2u ) - ( p u ) - 2 EA p u u = 0

m w + 2m f v f w + m f v 2 f w - E I (u 2w + u u w

- u w w - u w u ) - ( pw ) - 2 EA pw w = 0 (8a, b ), m + ; m f ; v f ; u

; w ; p ; ; ,

Pa idoussis & Issid [70] , : E

3 Iw + E Iw + {m f v 2 f - T + pA f (1 - 2) - (m g - m f v f ) ( L - z ) }w

+ 2m f v f w + m gw + E k w + C d w+ m w = 0 (9), E

3 Kelvin 2Voigt ; E k ; C d

; T ; 0 1,(9) ( ) , :

, , , ,

; (ar ticu lated p ipe )[71, 72] ; , ,

, v f 0 , [73] ;

60% , , 60%, ; , ,

, [74] ; T imo shenko Euler 2Bernoulli[75] ; [76, 77]

T hurm an & M ote [77, 78] :

w + (v 2 f - # )w + 21 2v f w

+ w

= (- # ) [ 32 w 2w + u w + u w ] (10a b)

(1 - ) u

- u = (- # )w + w , u , w ; v f ; ; # ; = A p L 2 I

, L indstedt K rylov 2Bogoliulov ,

,

Paidoussis [80] , (p itchfork

bifurcation ) , , Paidoussis(post 2divergence ) , Ho lm es [75, 76] Paidoussis :

w + (v 2 f 2

1

0

(w ) 2d )w + 21 2v f w

+ w

+ w

= 0 (11 )

, Ho lm es [75, 76] i = i2 ,

, ,

Galerk in (11 )

q1 = p 1 , q2 = p 2

173:


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p 1 = - 2 (2 - v 2 f ) q1 - c p 1 + 163 1 2v f p 2 - 12

2 (q21 + 4q22) q1

p 1 = - 42 (42 - v 2 f ) q2 - c p 2 - 163 1 2v f p 1 - 22 (q21 + 4q22) q2 (12 )

, 4 , ,

Paidoussis [81]

Bajaj [82] Paidoussis [72] L undgren [83] , ,:

u

+ 2v 01 2 u

+ v 20u + u = - u [ 1 2 (1 - ) v

f + 2v 0v f + v f ]

- 21 2v f u

- 32

{u [ (u ) 2 + (w ) 2 ]} - [u 1

(u u

+ w w

) d ] (13a )

[ 1 2 v

f + 2 v 0v f + v 2 f + 1

0

(w w

+ u u

) d = 0 (13b )

, ,

, : ( ) v 0; ; ( ) , ; ( ) ,

; Hopf ,Bajaj & Sethna [84, 85] , ,

, , , ,,

Rousselet & H errm ann [86] K rylov 2Bogoliubov ,, S L i

& Paidoussis [87] , Hopf Ch ng & Dow ell [88] , = 0. 5 , Hopf ,

, ; ,

5

, Bourrieres Sem ler& Paiduossis [89] :

m u + m f v f + 2m f v f u + m f v 2 f u + m f v f u

- EA p u - E I (w w + w w ) + (T 0 - P 0 - EA )w w - m g = 0 (14a )

m w + m f v f w + 2m f v f w + m f v 2 f w - (T 0 - P 0 )w + E Iw

- E I (3u w + 4u w + 2u w + w u + 2w 2w + 8w w w + 2w 3 )

(T 0 - P 0 - EA p ) (u w + u w + 32 w2w ) = 0 (14b )

273 2000 3


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,

, ,

, , ,

L ee 2Pak 2Hong [90] N ew ton 42

:

:

EA p u - ( pA f ) - m f (v f + v f v f ) - m g z - m p u = 0 (15a ):

E Iw + ( pA f w ) + m f (v f w + 2v f w + v 2 f w + v f v f w ) + m g w - m w = 0 (15b ):

( pA f )3

+ m f c2F (v f - 2u ) = 0 (15c ):

( pA f ) + m f (g ww + g z + v f + v f v f + f 2 D v f v f ) = 0 (15d )

, c2F ( ) ; g z , g w ; f

, (

, ) , , ,

, L ee 2Pak 2

Hong , 42 M athieu 2H ill

,

[91] H am ilton N S 42 :

m u + m f [ v f (1 + u ) + 2v f u + v 2 f u + wv f ] + 1c2F

P(v f + u)

- [ (1 - 2) 1 (1 + u ) ] + 4 f

D K P v2 f - gm f (1 - 2) (1 + u )w

- E I (7w w + w w ) - 12 EA p (2u + 6u u + 2w w ) = 0 (16a )

m w + m f [ (1 + w ) v f + 2wv f + v 2 f w ] + 1c2F

P(w+ v f ) - [ (1 - 2) 1 w ] - gm

+ E Iw - E I (u w + 6u w + 9u w + 4u w ) - EA p (u w + u w ) = 0 (16b )

1c2F

P+ m f [ (1 - 2) (u+ v f ) u - (u + v f ) ]

- m f (1 - 2) (u + u u + w w ) = 0 (16c )

373:


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1 + m f (u + v f ) + m f w w + gm f w + 12 D f f v2 f = 0 (16d )

8 9 ,

, ,

8

9

6

,[79] , Tang & Dow ell [92]

, , ,

Paidoussis &M oon [93] ,

, Paidoussis and L i [94]

, , Hopf

H ein sbroek & T ijsseling [95] ,

, , Paidoussis &M oon H ein sbroek & T ijsseling ,

, , , ,

Pa idoussis and Cu sum ano [96] (fractal d im ension )

, d c = 1. 03 ; d c = 1. 53 ;

d c = 3. 20 ,

Paidoussis and Sem ler [97] :

473 2000 3


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w

+ 2v f 12w

+ cw

+ v 2 f w + w + w + ( v

f 12 - ) (1 - )w + 2v f 12w

w 2

+ w w 2

[ v 2 f +

32 ( v

f 1

2 - ) (1 - ) ] +12 w

3+ w w

2+ 4w w w + w

3

+ w

0

(w

2 + w w

) d - w [1

0

(w

2 + w w

) d d ]

+ w 1

( 1

2v

f 12w 2 + 2v f 12w w

+ v 2 f w w ) d = 0 (17 )

, ,

,(post 2chaotic ) ,

7

,

, ,

, ,

,

:

[1 ] T YOUN G . H ydraulic investigat ion s , subservient to an in tended croonian lecture on the mo tion of theblood [J ]. Ph ilo soph ical T ran saction of the Ro yal Society . 1808, 98, Part 2, Paper 13: 164 2186.

[ 2 ] D. J. KOR T EW EG . O n the velocity of p ropagation of sound in elast ic pipes ( in Germ an ) [J ]. A nnalen de rphysik und Chem ie , N ew Ser ies . 1878, 5, (12 ) : 525 2542.

[ 3 ] A R HALL IW ELL . V elocity of w aterhamm er w ave in an elast ic p ipe [J ]. A SCE Jou rnal of the Hyd raulicsD ivision , 1963, 89 (H Y 4) : 1221.

[ 4 ] I S GROM EKA . O n the V elocity of P ropagat ion of W ave 2like M o tion of F luids in E lastic T ubes ( inRussian ) [M ]. Phy sicalM athem at ical Section of the Scient ific Society o f the Impe rial U niversity of Kazan ,Kazan , Russia , M ay 1883: 1 219.

[ 5 ] H LAMB . On the velocity of sound in a tube , as affected by the elast icity of the w alls [J ]. M emo irs of theM anchester L iterary and Ph ilo soph ical Society , M anchester , 1898, 42 (9) : 1216.

[ 6 ] N JOU KOW SKY . O n the hyd raulic hamm er in w ater supp ly p ipes [A ]. 1898, Eng lish translat ion by OSim in : W ater hamm er . P roceedings of the Am erican W ater W o rks A ssociat ion [C ]. 1904. 24: 341 2424.

[ 7 ] R SKALA K . A n extension of the theo ry of w aterhamm er [J ]. T ran saction s of the A SM E . 1956, 78 (1) :105 2116.

[ 8 ] T C L IN and G W M OR GAN . W ave propagation th rough fluid contained in a cy lind rical elastic she ll [J ].Jou rnal of A cou stical Society of A m erica , 1956, 28 (6) : 1165 21176.

[ 9 ] G H ERRM ANN and IM IR K . Three 2dim ensiona l and shell 2theo ry analysis of axially symm etr icmo tion of cylinders [J ]. A SM E Jou rnal of A pp liedM echan ics , 1956, 23 (4) : 563 2568.

[10] W R SP ILL ERS . W ave p ropagation in a th in cy lind rical she ll [J ]. A SM E Jou rnal of A pp lied M echan ics ,1965, 32 (2) : 346 2350.

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[15] S I RUB INOW and J B KELL ER . W ave p ropagation in a viscoelast ic tube containing a viscou s fluid [J ].Journal of F luid M echanics , 1978, 88, Part 1: 181 2203.

[ 16 ] G D C KU IKEN . A pp rox im ate dispersion equation s fo r thin w alled liquid 2filled tubes [ J ]. AppliedScientific Research , 1984, 41: 37 253.

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120.[60] D H W IL K IN SON . A cou stic and m echan ical vibrat ion in liquid 2filled p ipewo rk system s [A ]. P roceeding s

BN ES In ternat iona l Conference on V ibrat ion in N uclear P lant [C ], Kesw ick , M ay 1978, Paper 8. 5: 863 2

878.[61 ] C R FULL ER and F J FAH Y . Cha racteristics of w ave p ropagating and energy distribut ion in cylind rical

773:


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elastic shells filled w ith fluid [J ]. Jou rnal of Sound and V ibrat ion . 1982, 81 (4) : 501 2518.[ 6 2 ] C R FULLER . T he effect of w all discon tinuities on the p ropagation of flexual w aves in cylind rical shell

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Review of FSIanalysis of fluid -conveying p ipesZHAN G L i 2xiang 1 , HUAN G W en 2hu 1 , A S T IJSSEL IN G 2

(1. H arb in In stitute of T echnology , P. O. Box 137, Harbin 150001;2. E indhoven U n iversity of T echno logy , P. O. Box 513, 5600 MB Eindhoven , NL )

Abstract : P ipes are w idely used in industry and p lay a quite important ro le . A Coupling v ib rat ion inducedby a fluid su rgem ay at tack a wo rking p ipe w h ich exh ibits comp licated dynam ical behavio r . Form any years , thissubject ha s been exten sively studied in bo th the linear and the non 2linear analysis in the academ ic and the

engineering comm un ities , and a lot of results have been reported . In this paper , the typ ical ach ievem ent s in theresearch f ield w ere in troduced and review ed .

Key words : p ipes; f lu id structu re in teraction ; surge ; non 2linear vibration

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