《桥梁结构振动与抗震》动力电算分析

静力分析程序计算

一、 斜拉桥模型基本信息：

计算模型

1、 结构体系：半漂浮体系； 2、 主梁：单元号1-23

（1） 跨径：中跨：100m；边跨：50m； （2） 截面参数：

换算截面：A=58.8m2, 惯性矩：I=2.20m4,

每延米重：BRO=-180.00KN/m

3、 塔墩：双塔，单元号24-37

（1）索塔高30m，塔跨比为1/3.33，墩高20m （2）截面参数：

换算截面：A=12.00m2, 惯性矩：I=4.58m4,

每延米重：BRO=-335.46KN/m

4、 斜拉索：单元号38-57

（1）竖琴形单索面形式，索距：主梁8m，索塔6m； （2）截面参数：

换算截面：A=0.200m2,

每延米重：BRO=-10.00KN/m

二、 程序修改部分： （1）结构参数

NJ=40,NE=57,N=111,UBW1=12,NB1=9,NJX=120,M=6

DATA IO/20,17,14,11,8,5,4,7,10,13,16,19,22,25,28,31,34,37,36,33,

第 1 页 共 28 页

$ 30,27,24,1,2,3,6,9,12,15,40,39,38,35,32,29,26,

$ 17,14,11,8,5,19,16,13,10,7,24,27,30,33,36,22,25,28,31,34/ DATA JO/17,14,11,8,5,4,7,10,13,16,19,22,25,28,31,34,37,36,33,30, $ 27,24,21,2,3,6,9,12,15,18,39,38,35,32,29,26,23,

$ 18,15,12,9,6,18,15,12,9,6,23,26,29,32,35,23,26,29,32,35/ DATA RL1/1,2,3,58,59,62,118,119,120/ DATA X/-50,-50,-50,-50,-58,-50,-42,-66,-50,-34,-74,-50,-26, $ -82,-50,-18,-90,-50,-10,-100,100,10,50,90,18,50,82, $ 26,50,74,34,50,66,42,50,58,50,50,50,50/ DATA Y/-20,-10,0,0,0,6,0,0,12,0,0,18,0,0,24,0,0,30,0,0,0, $ 0,30,0,0,24,0,0,18,0,0,12,0,0,6,0,0,0,-10,-20/ （3） 修改对应的截面参数，并前后统一； （4） 子程序

1) 平面梁单元和铰接杆单元刚度矩阵BEMK、ROADK：REAL X(40) Y(40) 2) 自重荷载作用下的等价集中力BEMLOAD：

SUBROUTINE BEMLOD(BRO,L,XM,XN,PF1,PF2,IAA) 其中梁单元IAA=1.0，铰接杆单元IAA=0.0; （5）主程序

1）整体刚度矩阵和荷载等价集中力列阵: 塔墩：IZ=4.58 AX=12.00 BRO=-335.46 CALL BEMK(IO,JO,KE,I1,J1,YE,AX,IZ,NE,F,L,LX,LY,X,Y,XM,XN) CALL BEMR(LX,LY,L,R,RT)

CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,1) CALL AAXA(RT,PF1,PF2,M) CALL AAXAA(KE,R,KR,M) CALL AAXAA(RT,KR,KS,M) 斜拉索：AX=0.20 BRO=-10.0 DO 170 I=1,6 DO 170 J=1,6 KS(I,J)=0.0

170 CONTINUE

CALL RODK(IO,JO,KE,I1,J1,YE,AX,NE,F,L,LX,LY,X,Y,XM,XN) CALL BEMR(LX,LY,L,R,RT) CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,0) CALL AAXA(RT,PF1,PF2,M) CALL AAXAA(KE,R,KR,M) CALL AAXAA(RT,KR,KS,M) 2）计算单元力

塔墩：AX=12.00

第 2 页 共 28 页

IZ=4.58 BRO=-335.46 CALL BEMK(IO,JO,KE,I1,J1,YE,AX,IZ,NE,F,L,LX,LY,X,Y,XM,XN) CALL BEMR(LX,LY,L,R,RT)

CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,1) CALL ELMFOC(F,NE,R,XV,A,PF1,KE,I1,J1,M,NJX) 斜拉索：AX=0.200 BRO=-10.00

CALL RODK(IO,JO,KE,I1,J1,YE,AX,NE,F,L,LX,LY,X,Y,XM,XN) CALL BEMR(LX,LY,L,R,RT) CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,0) CALL ELMFOC(F,NE,R,XV,A,PF1,KE,I1,J1,M,NJX)

三、计算主程序：

PLANE ANALYSIS OF Cable-Stayed BRIDGE PROGRAM Cable_Stayed BRIDGE integer ubw,f,ubw1 real l,iz,lx,ly

PARAMETER (NJ=40,NE=57,N=111,UBW1=12,NB1=9,NJX=120,M=6) integer io(NE),jo(NE),rl1(NB1),RLS(NJX),CRL(NJX),NIJ(M) REAL KO(N,UBW1),R(M,M),RT(M,M),KE(M,M),KR(M,M),KS(M,M) REAL A(NE,7),XU(N),p(N),xv(NJX),pij(M),pij2(M),fij(M) REAL PF1(M),PF2(M),X(NJ),Y(NJ) C READING ARRAYS DATA IO/20,17,14,11,8,5,4,7,10,13,16,19,22,25,28,31,34,37,36,33, $ 30,27,24,1,2,3,6,9,12,15,40,39,38,35,32,29,26,

$ 17,14,11,8,5,19,16,13,10,7,24,27,30,33,36,22,25,28,31,34/ DATA JO/17,14,11,8,5,4,7,10,13,16,19,22,25,28,31,34,37,36,33,30, $ 27,24,21,2,3,6,9,12,15,18,39,38,35,32,29,26,23,

$ 18,15,12,9,6,18,15,12,9,6,23,26,29,32,35,23,26,29,32,35/ DATA RL1/1,2,3,58,59,62,118,119,120/ DATA X/-50,-50,-50,-50,-58,-50,-42,-66,-50,-34,-74,-50,-26, $ -82,-50,-18,-90,-50,-10,-100,100,10,50,90,18,50,82, $ 26,50,74,34,50,66,42,50,58,50,50,50,50/ DATA Y/-20,-10,0,0,0,6,0,0,12,0,0,18,0,0,24,0,0,30,0,0,0, $ 0,30,0,0,24,0,0,18,0,0,12,0,0,6,0,0,0,-10,-20/ C BEGIN THE CALCULATION DO 10 I=1,NB1 J=RL1(I) RLS(J)=1 10 CONTINUE WRITE(*,20)

20 FORMAT(1X,18H开始计算约束表rls=) WRITE(*,40) RLS

第 3 页 共 28 页

40 FORMAT(1X,/24I3) do 60 I=1,njx K=0 DO 50 J=1,I K=K+RLS(J) 50 CONTINUE CRL(I)=K 60 CONTINUE WRITE(*,70)

70 FORMAT(1X,4HCRL=) WRITE(*,40) CRL WRITE(*,100)

100 FORMAT(1X,12H开始计算总刚) F=0 UBW=0 WW=0 YE=2.5E+07 110 F=F+1 IF(F.GT.23) GOTO 150 IZ=2.20 AX=63.1 BRO=-180.00

115 CALL BEMK(io,jo,ke,I1,J1,YE,AX,IZ,NE,F,L,LX,LY,X,Y,XM,XN) DO 120 I=1,6 DO 120 J=1,6 KS(I,J)=0.0 KS(I,J)=KE(I,J) 120 CONTINUE CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,1) DO 140 I=1,6 PF2(I)=PF1(I) 140 CONTINUE GOTO 270

150 IF(F.GT.37) GOTO 160 IZ=4.58 AX=12.00 BRO=-335.46 CALL BEMK(IO,JO,KE,I1,J1,YE,AX,IZ,NE,F,L,LX,LY,X,Y,XM,XN) CALL BEMR(LX,LY,L,R,RT)

CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,1) CALL AAXA(RT,PF1,PF2,M) CALL AAXAA(KE,R,KR,M) CALL AAXAA(RT,KR,KS,M) GOTO 270 160 AX=0.20 BRO=-10.0 DO 170 I=1,6 DO 170 J=1,6

第 4 页 共 28 页

KS(I,J)=0.0 170 CONTINUE 180 CALL RODK(IO,JO,KE,I1,J1,YE,AX,NE,F,L,LX,LY,X,Y,XM,XN) CALL BEMR(LX,LY,L,R,RT) CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,0) CALL AAXA(RT,PF1,PF2,M) CALL AAXAA(KE,R,KR,M) CALL AAXAA(RT,KR,KS,M) 270 DO 280 J=1,3 NIJ(J)=I1+J-1 NIJ(J+3)=J1+J-1 280 CONTINUE CALL COMBK(NJ,N,UBW,NIJ,CRL,RLS,KO,KS,P,PF2,M,NJX,ubw1) WRITE(*,285) F,UBW 285 FORMAT(1X,2HF=,I3,4HUBW=,I3) WW=WW+L*BRO IF (F.LT.NE) GOTO 110 CALL CHOLS(N,UBW,KO) CALL CHOLEJ(N,UBW,P,XU,KO) C DEVELOPMENT OF U DO 320 I=1,3*NJ IF (RLS(I).NE.1) GOTO 310 XV(I)=0.0 GOTO 320 310 XV(I)=XU(I-CRL(I)) 320 CONTINUE WRITE(*,325) 325 FORMAT(25X,14H节点位移xv(i)=) DO 330 I=1,NJ WRITE(*,335) I,(XV(3*(I-1)+J),J=1,3) 330 CONTINUE 335 FORMAT(1X,I3,3(8X,F11.7)) C SULUTION OF ELEMENT FORCE WRITE(*,395) 395 FORMAT(1X,14H开始计算单元力) f=0 400 f=f+1 IF(F.GT.23) GOTO 425 IZ=2.2 AX=58.8 BRO=-180.00

402 CALL BEMK(IO,JO,KE,I1,J1,YE,AX,IZ,NE,F,L,LX,LY,X,Y,XM,XN) DO 405 J=1,3 PIJ(J)=XV(I1+J-1) PIJ(J+3)=XV(J1+J-1) 405 CONTINUE A(F,1)=F CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,1)

第 5 页 共 28 页

CALL AAXA(KE,PIJ,FIJ,M) DO 407 I=1,6 A(F,I+1)=FIJ(I)-PF1(I) 407 CONTINUE GOTO 445 425 IF (F.GT.37) GOTO 437 AX=12.00 IZ=4.58 BRO=-335.46 CALL BEMK(IO,JO,KE,I1,J1,YE,AX,IZ,NE,F,L,LX,LY,X,Y,XM,XN) CALL BEMR(LX,LY,L,R,RT)

CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,1) CALL ELMFOC(F,NE,R,XV,A,PF1,KE,I1,J1,M,NJX) 420 CONTINUE GOTO 445 437 AX=0.200 BRO=-10.00 CALL RODK(IO,JO,KE,I1,J1,YE,AX,NE,F,L,LX,LY,X,Y,XM,XN) CALL BEMR(LX,LY,L,R,RT) CALL BEMLOD(BRO,L,XM,XN,PF1,PF2,0) CALL ELMFOC(F,NE,R,XV,A,PF1,KE,I1,J1,M,NJX) 445 IF (F.LT.NE) GOTO 400 WRITE(*,450) 450 FORMAT(25X,13H单元力a(I,J)=) DO 460 I=1,NE WRITE(*,465) (A(I,J),J=1,7) 460 CONTINUE 465 FORMAT(1X,f4.0,3(8X,F15.5)/12X,F15.5,2(8X,F15.5)) C OPEN (6,FILE='OUT.txt') WRITE(*,466) WW 466 FORMAT(1X,F18.4) END

四、运行结果：

开始计算约束表rls=

1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 CRL=

1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 8 9 开始计算总刚

第 6 页 共 28 页

F= 1UBW= 8 F= 2UBW= 10 F= 3UBW= 10 F= 4UBW= 10 F= 5UBW= 10 F= 6UBW= 10 F= 7UBW= 12 F= 8UBW= 12 F= 9UBW= 12 F= 10UBW= 12 F= 11UBW= 12 F= 12UBW= 12 F= 13UBW= 12 F= 14UBW= 12 F= 15UBW= 12 F= 16UBW= 12 F= 17UBW= 12 F= 18UBW= 12 F= 19UBW= 12 F= 20UBW= 12 F= 21UBW= 12 F= 22UBW= 12 F= 23UBW= 12 F= 24UBW= 12 F= 25UBW= 12 F= 26UBW= 12 F= 27UBW= 12 F= 28UBW= 12 F= 29UBW= 12 F= 30UBW= 12 F= 31UBW= 12 F= 32UBW= 12 F= 33UBW= 12 F= 34UBW= 12 F= 35UBW= 12 F= 36UBW= 12 F= 37UBW= 12 F= 38UBW= 12 F= 39UBW= 12 F= 40UBW= 12 F= 41UBW= 12 F= 42UBW= 12 F= 43UBW= 12 F= 44UBW= 12 F= 45UBW= 12 F= 46UBW= 12 F= 47UBW= 12 F= 48UBW= 12 F= 49UBW= 12 F= 50UBW= 12 F= 51UBW= 12 F= 52UBW= 12 F= 53UBW= 12 F= 54UBW= 12 F= 55UBW= 12 F= 56UBW= 12 F= 57UBW= 12 节点位移xv(i)=

1 0.0000000 0.0000000 0.0000000 2 0.0025195 -0.0011915 -0.0005210 3 0.0107661 -0.0022712 -0.0011454 4 -0.0001902 -0.0148611 -0.0028911 5 -0.0001244 0.0065998 -0.0022557 6 0.0188943 -0.0028653 -0.0015702 7 -0.0002560 -0.0384054 -0.0030558 8 -0.0000779 0.0198689 -0.0011090 9 0.0292416 -0.0033239 -0.0018110 10 -0.0003097 -0.0642556 -0.0034072 11 -0.0000411 0.0249372 -0.0001844 12 0.0400289 -0.0036709 -0.0017523 13 -0.0003502 -0.0923223 -0.0035329 14 -0.0000144 0.0230835 0.0006411 15 0.0501347 -0.0039001 -0.0016258 16 -0.0003964 -0.1340584 -0.0022193 17 0.0000002 0.0150259 0.0013366 18 0.0596950 -0.0040129 -0.0015770 19 -0.0003999 -0.1383182 -0.0020371 20 0.0000000 0.0000000 0.0015173 21 -0.0008017 0.0000000 -0.0015156 22 -0.0004010 -0.1382917 0.0020403 23 -0.0605021 -0.0040129 0.0015790 24 -0.0008017 0.0150059 -0.0013340 25 -0.0004044 -0.1340251 0.0022228 26 -0.0509291 -0.0039002 0.0016282 27 -0.0007870 0.0230359 -0.0006368 28 -0.0004506 -0.0922293 0.0035373

第 7 页 共 28 页

29 -0.0408036 -0.0036709 0.0017567 30 -0.0007601 0.0248511 0.0001894 31 -0.0004911 -0.0641349 0.0034088 32 -0.0299759 -0.0033239 0.0018209 33 -0.0007231 0.0197509 0.0011111 34 -0.0005447 -0.0383049 0.0030478 35 -0.0195393 -0.0028653 0.0015913 36 -0.0006764 0.0064991 0.0022479 37 -0.0006106 -0.0148617 0.0028762 38 -0.0112488 -0.0022712 0.0011768 39 -0.0026823 -0.0011915 0.0005494 40 0.0000000 0.0000000 0.0000000 开始计算单元力 单元力a(I,J)=

1. -28.93215 400.72119 -0.00171 28.93215 1399.27881 -4986.50977 2. 2877.67090 530.67322 4986.50098 -2877.67090 909.32678 -6495.67188 3. 5270.57715 685.35114 6495.66846 -5270.57715 754.64886 -6771.60107 4. 7256.05859 584.46387 6771.59961 -7256.05859 855.53613 -7859.44580 5. 9164.03125 475.45593 7859.45020 -9164.03125 964.54407 -9825.05273 6. 12978.41113 1846.24072 9825.06543 -12978.41113 -406.24072 -829.28906 7. 12978.40723 406.23758 829.32111 -12978.40723 1033.76245 -3355.76172 8. 10576.90625 717.37811 3355.75830 -10576.90625 722.62189 -3394.49365 9. 7993.31641 1115.07861 3394.44458 -7993.31641 324.92145 -252.87531 10. 5208.30615 1613.81909 252.84082 -5208.30615 906.18091 4691.56934 11. 2689.44531 461.28223 -4691.27490 -2689.44531 -101.28223 5206.42334 12. 88.86657 1800.45007 -5206.22754 -88.86657 1799.54993 5215.23730 13. 2687.74927 -99.80148 -5214.02832 -2687.74927 459.80148 4700.86865 14. 5205.50391 905.30182 -4701.48584 -5205.50391 1614.69824 -255.23047 15. 7985.83154 320.54352 255.21814 -7985.83154 1119.45654 -3431.77295 16. 10565.60352 715.36249 3431.68530 -10565.60352 724.63751 -3451.03296 17. 12992.79297 1045.78076 3451.05029 -12992.79297 394.21918 -828.50745

第 8 页 共 28 页

18. 12992.79980 -394.21631 828.49707 -12992.79980 1834.21631 -9728.13477 19. 9204.16016 957.28094 9728.12402 -9204.16016 482.71906 -7820.63965 20. 7292.67969 850.87030 7820.63770 -7292.67969 589.12970 -6770.09229 21. 5303.12891 753.01569 6770.08789 -5303.12891 686.98431 -6507.19824 22. 2907.93335 909.41510 6507.19873 -2907.93335 530.58490 -4997.29639 23. -0.00676 1400.35559 4997.29395 0.00676 399.64438 0.00293 24. 37422.12109 -117.78848 5374.62207 -34067.51953 117.78848 -6554.89160 25. 34067.53125 -117.78899 6554.89600 -30712.93164 117.78899 -7740.41943 26. 30712.92578 -117.79594 7740.39893 -28700.16406 117.79594 -8467.93848 27. 23938.27734 1295.09399 8467.90527 -21925.51562 -1295.09399 -723.23242 28. 18356.83203 619.46649 723.27936 -16344.07129 -619.46649 2966.28955 29. 12466.17480 -180.00641 -2966.17725 -10453.41504 180.00641 1860.29736 30. 6643.14990 -306.03296 -1860.48303 -4630.39014 306.03296 -0.20698 31. 37422.08203 88.82239 -5843.95215 -34067.48047 -88.82239 6734.69434 32. 34067.47266 88.82223 -6734.69385 -30712.87305 -88.82223 7630.82080 33. 30712.86914 88.81074 -7630.82520 -28700.10742 -88.81074 8184.88086 34. 23938.22852 -1272.62048 -8184.82910 -21925.46680 1272.62048 575.22009 35. 18357.04102 -604.34418 -575.13354 -16344.28027 604.34418 -3023.67529 36. 12466.90137 186.46631 3023.63916 -10454.14160 -186.46631 -1878.98108 37. 6642.93604 309.08929 1878.95837 -4630.17627 -309.08929 0.08079 38. -3483.25537 200.00000 0.00000 3783.25537 200.00000 0.00000 39. -2871.13330 160.00000 0.00000 3111.13330 160.00000 0.00000 40. -2391.85376 120.00000 0.00000 2571.85376 120.00000 0.00000 41. -2324.97363 80.00000 0.00000 2444.97363 80.00000 0.00000

第 9 页 共 28 页

42. -4737.97363 40.00000 0.00000 4797.97363 40.00000 0.00000 43. -3100.73706 -200.00000 0.00000 3400.73706 -200.00000 0.00000 44. -2859.24854 -190.00000 0.00000 3099.24854 -190.00000 0.00000 45. -3391.25928 -120.00000 0.00000 3571.25928 -120.00000 0.00000 46. -3169.49341 -80.00000 0.00000 3289.49341 -80.00000 0.00000 47. -2971.87988 -40.00000 0.00000 3031.87988 -40.00000 0.00000 48. -3484.90405 -200.00000 0.00000 3784.90405 -200.00000 0.00000 49. -2874.00830 -160.00000 0.00000 3114.00830 -160.00000 0.00000 50. -2396.92896 -120.00000 0.00000 2576.92896 -120.00000 0.00000 51. -2329.32446 -80.00000 0.00000 2449.32446 -80.00000 0.00000 52. -4705.83691 -40.00000 0.00000 4765.83691 -40.00000 0.00000 53. -3098.63550 200.00000 0.00000 3398.63550 200.00000 0.00000 54. -2857.87329 190.00000 0.00000 3097.87329 190.00000 0.00000 55. -3385.43359 120.00000 0.00000 3565.43359 120.00000 0.00000 56. -3164.68262 80.00000 0.00000 3284.68262 80.00000 0.00000 57. -3004.01050 40.00000 0.00000 3064.01050 40.00000 0.00000 WW= -75644.9062

五、结果分析：

1、 位移的对称性

由以上运行结果可以发现，位移的对称性符合的很好，详相见下表列举：

节点 1 2 3 20 21 31 10 9 U 0.0000000 -0.0008017 -0.0004911 -0.0003097 0.0292416 V 0.0000000 0.0000000 -0.0641349 -0.0642556 -0.0033239 θ 0.0015173 -0.0015156 0.0034088 -0.0034072 -0.0018110 第 10 页 共 28 页

32 4

2、 单元对称性

2 39 -0.0299759 0.0025195 -0.0026823 -0.0033239 -0.0011915 -0.0011915 0.0018209 -0.0005210 0.0005494 由以上运行结果可以发现，位移的对称性符合的很好，详相见列举： （1）47号单元和57号单元

47. -2971.87988 -40.00000 0.00000 3031.87988 -40.00000 0.00000 57. -3004.01050 40.00000 0.00000 3064.01050 40.00000 0.00000 （2）25号单元和32号单元

25. 34067.53125 -117.78899 6554.89600 -30712.93164 117.78899 -7740.41943

32. 34067.47266 88.82223 -6734.69385 -30712.87305 -88.82223 7630.82080 （3）2号单元和22号单元

2. 2877.67090 530.67322 4986.50098 -2877.67090 909.32678 -6495.67188 22. 2907.93335 909.41510 6507.19873 -2907.93335 530.58490 -4997.29639 （4）27号单元和34号单元

27. 23938.27734 1295.09399 8467.90527 -21925.51562 -1295.09399 -723.23242

34. 23938.22852 -1272.62048 -8184.82910 -21925.46680 1272.62048 575.22009 3、 支反力之和与重力平衡 整体坐标下Y方向的支座反力：

20号节点为：400.72119KN 21号节点为：399.64438KN 1号节点为：37422.12109KN 40号节点为：37422.08203KN

第 11 页 共 28 页

桥梁自重WW= -75644.9062KN

F+G=400.72119+399.64438+37422.12109+37422.08203-75644.9062 = -0.3375KN

可见误差很小，在允许范围内。

动力分析程序计算

一、程序修改部分：

（1）结构参数

NJ=40,NE=57,N=111,UBW=12,NB1=9,NJX=120,M=6,NV=3

DATA IO/20,17,14,11,8,5,4,7,10,13,16,19,22,25,28,31,34,37,36,33,30,27,24,1,2,3,6, 9,12,15,40,39,38,35,32,29,26,17,14,11,8,5,19,16,13,10,7,24,27,30,33,36,22,25,28,31,34/

DATA JO/17,14,11,8,5,4,7,10,13,16,19,22,25,28,31,34,37,36,33,30,27,24,21,2,3,6, 9,12,15,18,39,38,35,32,29,26,23,18,15,12,9,6,18,15,12,9,6,23,26,29,32,35,23,26,29,32,35/

DATA RL1/1,2,3,58,59,62,118,119,120/

DATA X/-50,-50,-50,-50,-58,-50,-42,-66,-50,-34,-74,-50,-26,-82,-50,-18,-90,-50, -10,-100,100,10,50,90,18,50,82,26,50,74,34,50,66,42,50,58,50,50,50,50/

DATAY/-20,-10,0,0,0,6,0,0,12,0,0,18,0,0,24,0,0,30,0,0,0,0,30,0,0,24,0,0,18,0,0,12,0,0,6,0,0,0,-10,-20/

DATA IZ/2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2, 2.2,2.2,2.2,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0/

DATA AX/58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8,58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8, 58.8,58.8,12,12,12,12,12,12,12,12,12,12,12,12,

12,12,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2/ DATA YE/2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07, 2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07, 2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07, 2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07, 2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+08,2.6E+08, 2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08, 2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,

第 12 页 共 28 页

2.6E+08,2.6E+08/ （2）子程序修改部分

1）bemke、bemr、aaxaa、combk参照静力程序的子程序 2）bemme子程序修改如下：

SUBROUTINE BEMME(ME,IZ,AX,L,IE,NE) REAL L,ME(6,6),IZ(NE),AX(NE) DO 1 I=1,6 DO 1 J=1,6 1 ME(I,J)=0.0

AA=6.0*IZ(IE)/(5.0*AX(IE)*L*L) BB=IZ(IE)/(10.0*AX(IE)*L) CC=2.0*IZ(IE)/(15.0*AX(IE)) DD=IZ(IE)/(30.0*AX(IE)) ME(1,1)=1.0/3.0

ME(2,2)=13.0/15.0+AA ME(3,3)=L*L/105+CC ME(4,4)= ME(1,1) ME(5,5)= ME(2,2) ME(6,6)= ME(3,3)

ME(3,2)=11.0*L/210.0+BB ME(4,1)=1/6

ME(5,2)=9.0/70.0-AA ME(5,3)=13.0*L/420.0-BB ME(6,2)=-13*L/420+BB ME(6,3)= -L*L/140.0-DD ME(6,5)=-11*L/210-BB DO 2 I=1, 6 DO 2 J=1, 6

ME(I,J)=ME(I,J)*25*L*AX(IE)/9.8 ME(J,I)=ME(I,J) 2 CONTINUE RETURN END

二、计算主程序：

vebration of power method

program cable stayed Bridge integer UBW real l,lx,ly

parameter (NJ=40,NE=57,N=111,UBW=12,NB1=9,NJX=120,M=6,NV=3)

第 13 页 共 28 页

integer io(ne),jo(ne),rl1(nb1),rls(njx),crl(njx),nij(m)

real ko(n,UBW),mo(n,UBW),r(m,m),rt(m,m),ke(m,m),kr(m,m) real ks(m,m)

real me(m,m),ms(m,m),f(n),v(n),vk(n),sg(n),egv(n,nv),vo(n), $ egv1(njx,nv+1)

real x(nj),y(nj),ax(ne),iz(ne),YE(NE) DATA IO/20,17,14,11,8,5,4,7,10,13,16,19,22,25,28,31,34,37,36,33, $ 30,27,24,1,2,3,6,9,12,15,40,39,38,35,32,29,26,

$ 17,14,11,8,5,19,16,13,10,7,24,27,30,33,36,22,25,28,31,34/ DATA JO/17,14,11,8,5,4,7,10,13,16,19,22,25,28,31,34,37,36,33,30, $ 27,24,21,2,3,6,9,12,15,18,39,38,35,32,29,26,23,

$ 18,15,12,9,6,18,15,12,9,6,23,26,29,32,35,23,26,29,32,35/ DATA RL1/1,2,3,58,59,62,118,119,120/ DATA X/-50,-50,-50,-50,-58,-50,-42,-66,-50,-34,-74,-50,-26, $ -82,-50,-18,-90,-50,-10,-100,100,10,50,90,12,50,82, $ 26,50,74,34,50,66,42,50,58,50,50,50,50/ DATA Y/-20,-10,0,0,0,6,0,0,12,0,0,18,0,0,24,0,0,30,0,0,0, $ 0,30,0,0,24,0,0,18,0,0,12,0,0,6,0,0,0,-10,-20/ DATA IZ/2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2, $2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,2.2,4.58,4.58,4.58,4.58, $4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,4.58,0,0,0,0,0, $0,0,0,0,0,0,0,0,0,0,0,0,0,0,0/

DATA AX/63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1, $ 63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1,63.1, $12,12,12,12,12,12,12,12,12,12,12,12,12,12, $0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2, $0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2/

DATA YE/2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07, $2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07, $2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07, $2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07, $2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+07,2.6E+08,2.6E+08, $2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08, $2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08,2.6E+08, $2.6E+08,2.6E+08/

open(5,file='output.dat',status='old') c begin the calculations do 15 i=1,nb1 j=rl1(i)

第 14 页 共 28 页

rls(j)=1 15 continue

write(*,40) rls 40 format(1x/24i3) do 60 i=1,njx k=0

do 50 j=1,i k=k+rls(j) 50 continue crl(i)=k 60 continue write(*,70)

70 format(1x,4hcrl=) write(*,40) crl ie=0 10 ie=ie+1

if(ie.gt.ne) goto 30 CONTINUE

call bemke(IO,JO,KE,I1,J1,YE,AX,IZ,NE,NJ,L,LX,LY,X,Y,XM,IE) call bemr(x,y,r,rt,l,ie,ne,nj,i1,j1,io,jo) call bemme(me,iz,ax,l,ie,ne) call aaxaa(ke,r,kr,6) call aaxaa(rt,kr,ks,6) call aaxaa(me,r,kr,6) call aaxaa(rt,kr,ms,6) DO 11 I=1,3 NIJ(I)=I1-1+I

NIJ(I+3)=J1-1+I 11 CONTINUE

call combk(NIJ,ko,ks,n,UBW,crl,rls,njx) call combk(NIJ,MO,MS,n,UBW,crl,rls,njx) goto 10 30 continue eps=0.01

call chols(n,UBW,ko) do 34 i=1,n f(i)=0.0

第 15 页 共 28 页

34 v(i)=1.0 ind=1 38 iter=0

do 42 i=1,n 42 vo(i)=1.0 46 iter=iter+1 do 52 i=1,n

call single(sg,mo,n,UBW,i) f(i)=0.0 do 51 j=1,n if(ind.gt.1) then f(i)=f(i)+sg(j)*vk(j) else

f(i)=f(i)+sg(j)*v(j) end if 51 continue 52 continue do 56 i=1,n 56 vk(i)=0.0

call cholej(n,UBW,f,vk,ko) call norm1(vk,n,vmax) do 61 j=1,n

61 if(abs(v(j)-vk(j)).gt.eps) goto 64 goto 72 64 continue do 68 j=1,n 68 v(j)=vk(j)

if(ind.gt.1) then

call norm2(vk,nv,ind,n,UBW,sg,mo,egv,a1,b1,beta) call norm1(vk,n,vmax) end if goto 46 72 continue do 76 j=1,n 76 egv(j,ind)=vk(j) ab=1/abs(vmax) qm=sqrt(ab)

第 16 页 共 28 页

hz=qm/6.2832

write(5,80) ind,vmax,ab,qm,hz write(*,80) ind,vmax,ab,qm,hz

80 format(1x,i2,2x,e8.3,2x,e8.3,2x,e8.3,2x,e8.3) ind=ind+1 eps=eps+0.03

if(ind.gt.nv) goto 92

call norm2(vo,nv,ind,n,UBW,sg,mo,egv,a1,b1,beta) call norm1(vo,n,vmax) do 84 i=1,n vk(i)=0.0 84 v(i)=0.0 do 88 i=1,n vk(i)=vo(i) 88 v(i)=vo(i) goto 38 92 continue do 96 i=1,njx if(rls(i).ne.1) goto 94 do 93 j=1,nv 93 egv1(i,j)=0.0 goto 96 94 continue do 95 j=1,nv 95 egv1(i,j)=egv((i-crl(i)),j) 96 continue do 97 i=0,nj-1 97 egv1(1+3*i,nv+1)=i+1 do 98 i=1,njx

write(5,99) i,(egv1(i,j),j=1,nv+1) 98 write(*,99) i,(egv1(i,j),j=1,nv+1) 99 format(1x,i4,4(3x,f8.5)/) stop end

subroutine cholej(n,UBW,p,xu,ko) integer UBW

real p(n),xu(n),ko(n,UBW)

第 17 页 共 28 页

do 620 i=1,n if(i.lt.UBW) then j=1 else

j=i-UBW+1 endif sum=p(i)

do 610 k=j,i-1

sum=sum-ko(k,i-k+1)*xu(k) 610 continue

xu(i)=sum*ko(i,1) 620 continue

do 640 i=n,1,-1

if((n-i+1).lt.UBW) then j=n else

j=i+UBW-1 endif

sum=xu(i) do 630 k=i+1,j

sum=sum-ko(i,k-i+1)*xu(k) 630 continue

xu(i)=sum*ko(i,1) 640 continue return end

subroutine norm1(z1,n,vmax) real z1(n) vmax=0.0 do 1 i=1,n

1 if(abs(z1(i)).gt.abs(vmax)) vmax=z1(i) do 2 i=1,n

2 z1(i)=z1(i)/vmax return end

subroutine norm2(w,nv,ind,n,UBW,sg,ko,egv,a1,b1,beta) INTEGER UBW

第 18 页 共 28 页

real w(n),sg(n),ko(n,UBW),egv(n,nv) real a1(nv),b1(nv),beta(nv) do 2 k=1,ind-1 a1(k)=0.0 b1(k)=0.0 do 1 i=1,n

call single(sg,ko,n,UBW,i) do 1 j=1,n

a1(k)=a1(k)+sg(j)*egv(i,k)*w(j) 1 b1(k)=b1(k)+egv(j,k)*sg(j)*egv(i,k) 2 beta(k)=a1(k)/b1(k) do 3 j=1,n do 3 i=1,ind-1

3 w(j)=w(j)-beta(i)*egv(j,i) return end

subroutine bemr(x,y,r,rt,l,ie,ne,nj,i1,j1,io,jo) real r(6,6),rt(6,6),x(nj),y(nj),l,lx,ly integer io(ne),jo(ne) ii=io(ie) jj=jo(ie) i1=3*ii-2 j1=3*jj-2 lx=x(jj)-x(ii) ly=y(jj)-y(ii)

l=sqrt(lx*lx+ly*ly) XN=LX/L XM=LY/L do 1 i=1,6 do 1 j=1,6 r(i,j)=0.0 1 rt(i,j)=0.0 R(1,1)=XN R(2,2)=R(1,1) R(4,4)=R(1,1) R(5,5)=R(1,1) R(1,2)=XM

第 19 页 共 28 页

R(2,1)=-R(1,2) R(3,3)=1.0 R(4,5)=R(1,2) R(5,4)=R(2,1) R(6,6)=1.0 GOTO 5 5 CONTINUE do 10 i=1,6 do 10 j=1,6 10 rt(j,i)=r(i,j) return end

subroutine single(mg,mo,n,UBW,i) INTEGER UBW

real mg(n),mo(n,UBW) do 1 j=1,n 1 mg(i)=0

do 2 j=1,UBW-1

2 if((i-j).gt.0) mg(i-j)=mo(i-j,j+1) do 3 j=0,UBW-1

3 if((i+j).le.n) mg(i+j)=mo(i,j+1) return

end

subroutine bemke(IO,JO,KE,I1,J1,YE,AX,IZ,NE,NJ,L,LX,LY,X,Y,XM,IE) INTEGER IO(NE),JO(NE)

real ke(6,6),iz(ne),ax(ne),YE(NE),X(NJ),Y(NJ),lx,ly,L II=IO(ie) JJ=JO(ie) I1=3*II-2 J1=3*JJ-2 LX=X(JJ)-X(II) LY=Y(JJ)-Y(II) L=Sqrt(LX*LX+LY*LY) XM=LY/L do 10000 i=1,6 do 10000 j=1,6 10000 ke(i,j)=0

第 20 页 共 28 页

W1=12*YE(IE)*IZ(IE) W2=YE(IE)*AX(IE) KE(1,1)=W2/L KE(4,4)=kE(1,1) KE(4,1)=-KE(1,1) KE(2,2)=W1/L/L/L KE(5,5)=KE(2,2) KE(3,2)=KE(2,2)*L*0.5 KE(6,2)=KE(3,2) KE(5,3)=-KE(3,2) KE(6,5)=KE(5,3) KE(3,3)=W1/L/3.0 KE(6,6)=KE(3,3) KE(5,2)=-KE(2,2) KE(6,3)=0.1667*W1/L do 10 i=2,6 do 10 j=1,i-1 10 ke(j,i)=ke(i,j) return end SUBROUTINE BEMME(ME,IZ,AX,L,IE,NE) REAL L,ME(6,6),IZ(NE),AX(NE) DO 1 I=1,6 DO 1 J=1,6 1 ME(I,J)=0.0 AA=6.0*IZ(IE)/(5.0*AX(IE)*L*L) BB=IZ(IE)/(10.0*AX(IE)*L) CC=2.0*IZ(IE)/(15.0*AX(IE)) DD=IZ(IE)/(30.0*AX(IE)) ME(1,1)=1.0/3.0 ME(2,2)=13.0/15.0+AA ME(3,3)=L*L/105+CC ME(4,4)=ME(1,1) ME(5,5)=ME(2,2) ME(6,6)=ME(3,3) ME(3,2)=11.0*L/210.0+BB ME(4,1)=1/6

第 21 页 共 28 页

ME(5,2)=9.0/70.0-AA ME(5,3)=13.0*L/420.0-BB ME(6,2)=-13*L/420+BB ME(6,3)=-L*L/140.0-DD ME(6,5)=-11*L/210-BB DO 2 I=1,6 DO 2 J=1,6 ME(I,J)=ME(I,J)*25*L*AX(IE)/9.8 ME(J,I)=ME(I,J) 2 CONTINUE RETURN END

subroutine combk(NIJ,ko,ks,n,UBW,crl,rls,njx) integer UBW,nij(6),crl(njx),rls(njx),row,col real ko(n,UBW),ks(6,6) do 1030 i=1,6 mu=nij(i)

if(rls(mu).eq.1) goto 1020 row=mu-crl(mu)

ko(row,1)=ko(row,1)+ks(i,i) do 1010 j=i+1,6 nu=nij(j)

if(rls(nu).eq.1) goto 1010 if(nu.lt.mu) then row=nu-crl(nu)

col=mu-row+1-crl(mu) else

row=mu-crl(mu)

col=nu-row+1-crl(nu) end if

ko(row,col)=ko(row,col)+ks(i,j) 1010 continue

1020 write(*,1025) col

1025 format(1x,8hUBW=col=,i2) 1030 continue return end

第 22 页 共 28 页

subroutine aaxaa(a,b,c,k1) real a(k1,k1),b(k1,k1),c(k1,k1) do 3 i=1,k1 do 3 j=1,k1 c(i,j)=0 do 3 k=1,k1

c(i,j)=c(i,j)+a(i,k)*b(k,j) 3 continue return end

c cholesky factorization

subroutine chols(n,UBW,ko) integer p,q,UBW real ko(n,UBW) ic=n-UBW+1 do 560 i=1,n if(i.lt.ic) then p=UBW else p=n-i+1 end if

do 550 j=1,p q=UBW-j

if((i-1).le.q) q=i-1 sum=ko(i,j) if(q.ge.1) then do 510 k=1,q

sum=sum-ko(i-k,1+k)*ko(i-k,j+k) 510 continue end if

520 if(j.ne.1) goto 540

if(sum.le.0.0) write(*,530) i

530 format(1x,13hHave Wrong i=,i3) temp=1/sqrt(sum) ko(i,j)=temp goto 550

540 ko(i,j)=sum*temp

第 23 页 共 28 页

550 continue 560 continue return end

三、运行结果：

计算振型 位移列阵最大值 圆频率平方 自振圆频率 频率 1 .232E+00 .431E+01 .208E+01 .330E+00 2 .165E+00 .607E+01 .246E+01 .392E+00 3 .240E-01 .417E+02 .646E+01 .103E+01 自由度 第一主振型 第二主振型 第三主振型 节点号 1 0.00000 0.00000 0.00000 1.00000 2 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 4 -0.03973 -0.05581 0.13550 2.00000 5 0.00156 0.00019 0.00718 0.00000 6 0.00857 0.01149 -0.02307 0.00000 7 -0.18423 -0.23645 0.38556 3.00000 8 0.00313 0.00037 0.01434 0.00000 9 0.02097 0.02498 -0.02339 0.00000 10 0.00097 -0.00046 0.00425 4.00000 11 0.00534 0.00052 0.02509 0.00000 12 0.05848 0.07205 -0.09413 0.00000 13 0.00078 -0.00042 0.00338 5.00000 14 -0.43059 -0.53024 0.66329 0.00000 15 0.04647 0.05494 -0.05182 0.00000 16 -0.33738 -0.41345 0.50183 6.00000 17 0.00406 0.00048 0.01862 0.00000 18 0.03033 0.03417 -0.01445 0.00000 19 0.00116 -0.00050 0.00513 7.00000 20 0.44058 0.53114 -0.61785 0.00000 21 0.04630 0.05492 -0.05242 0.00000 22 0.00080 -0.00011 0.00224 8.00000 23 -0.72471 -0.85301 0.77635 0.00000 24 0.02941 0.02828 0.01951 0.00000 25 -0.52793 -0.61850 0.51571 9.00000 26 0.00495 0.00059 0.02269 0.00000 27 0.02955 0.02935 0.01613 0.00000 28 0.00155 -0.00028 0.00566 10.00000 29 0.72908 0.85378 -0.73453 0.00000 30 0.02771 0.02828 0.01880 0.00000 31 0.00066 0.00000 0.00155 11.00000 32 -0.91403 -0.99862 0.42068 0.00000 33 0.01717 0.00759 0.06486 0.00000 34 -0.66479 -0.72996 0.29010 12.00000 35 0.00596 0.00070 0.02688 0.00000 36 0.01517 0.00669 0.05581 0.00000

第 24 页 共 28 页

37 0.00182 -0.00025 0.00669 13.00000 38 0.89852 1.00000 -0.37346 0.00000 39 0.01458 0.00780 0.06898 0.00000 40 0.00038 0.00000 0.00089 14.00000 41 -0.96915 -0.96049 -0.13856 0.00000 42 -0.00642 -0.01832 0.06443 0.00000 43 -0.70863 -0.69891 -0.10536 15.00000 44 0.00732 0.00081 0.03123 0.00000 45 0.00012 -0.01589 0.07120 0.00000 46 0.00207 -0.00034 0.00782 16.00000 47 0.96959 0.96544 0.30201 0.00000 48 0.00417 -0.01761 0.09431 0.00000 49 0.00000 -0.00010 0.00014 17.00000 50 -0.75404 -0.68382 -0.43401 0.00000 51 -0.05148 -0.05235 -0.00175 0.00000 52 -0.68329 -0.56530 -0.53446 18.00000 53 0.00882 0.00088 0.03473 0.00000 54 -0.00639 -0.02546 0.07172 0.00000 55 0.00227 -0.00053 0.00855 19.00000 56 0.98369 0.69482 1.00000 0.00000 57 0.00067 -0.05182 0.06933 0.00000 58 0.00000 0.00000 0.00000 20.00000 59 0.00000 0.00000 0.00000 0.00000 60 -0.08738 -0.07642 -0.06437 0.00000 61 0.00467 -0.00095 0.01638 21.00000 62 0.00000 0.00000 0.00000 0.00000 63 0.08918 -0.07373 0.05623 0.00000 64 0.00238 -0.00063 0.00879 22.00000 65 1.00000 -0.66553 0.92551 0.00000 66 0.00057 -0.05168 -0.07154 0.00000 67 0.70121 -0.54495 0.49683 23.00000 68 0.00885 -0.00051 0.03328 0.00000 69 0.00699 -0.02511 -0.06713 0.00000 70 0.00467 -0.00095 0.01637 24.00000 71 -0.77010 0.66041 -0.37377 0.00000 72 0.05271 -0.05070 -0.00003 0.00000 73 0.00258 -0.00052 0.00952 25.00000 74 0.99228 -0.93514 0.24977 0.00000 75 -0.00377 -0.01755 -0.08788 0.00000 76 0.72964 -0.67693 0.09685 26.00000 77 0.00734 -0.00049 0.02985 0.00000 78 0.00025 -0.01576 -0.06579 0.00000 79 0.00428 -0.00078 0.01575 27.00000 80 -0.99167 0.92967 -0.09728 0.00000 81 0.00684 -0.01800 -0.05883 0.00000 82 0.00283 -0.00050 0.01057 28.00000 83 0.92188 -0.97066 -0.36568 0.00000 84 -0.01479 0.00747 -0.06150 0.00000

第 25 页 共 28 页

85 0.68647 -0.70864 -0.26403 29.00000 86 0.00598 -0.00043 0.02565 0.00000 87 -0.01534 0.00631 -0.05016 0.00000 88 0.00399 -0.00070 0.01519 30.00000 89 -0.93732 0.96859 0.40759 0.00000 90 -0.01737 0.00715 -0.05791 0.00000 91 0.00310 -0.00061 0.01151 31.00000 92 0.74871 -0.82915 -0.68127 0.00000 93 -0.02842 0.02743 -0.01547 0.00000 94 0.54687 -0.60113 -0.46271 32.00000 95 0.00497 -0.00035 0.02161 0.00000 96 -0.03026 0.02843 -0.01334 0.00000 97 0.00385 -0.00074 0.01457 33.00000 98 -0.74430 0.82843 0.72024 0.00000 99 -0.03012 0.02737 -0.01631 0.00000 100 0.00349 -0.00089 0.01199 34.00000 101 0.45248 -0.51588 -0.56540 0.00000 102 -0.04757 0.05335 0.04847 0.00000 103 0.35119 -0.40219 -0.44329 35.00000 104 0.00408 -0.00028 0.01772 0.00000 105 -0.03123 0.03318 0.01390 0.00000 106 0.00388 -0.00096 0.01355 36.00000 107 -0.44243 0.51530 0.60801 0.00000 108 -0.04774 0.05335 0.04798 0.00000 109 0.00368 -0.00093 0.01277 37.00000 110 0.00539 -0.00030 0.02320 0.00000 111 -0.06007 0.07000 0.08598 0.00000 112 0.19296 -0.23025 -0.33614 38.00000 113 0.00314 -0.00022 0.01363 0.00000 114 -0.02175 0.02428 0.02102 0.00000 115 0.04214 -0.05448 -0.11635 39.00000 116 0.00157 -0.00011 0.00682 0.00000 117 -0.00903 0.01120 0.01996 0.00000 118 0.00000 0.00000 0.00000 40.00000 119 0.00000 0.00000 0.00000 0.00000 120 0.00000 0.00000 0.00000 0.00000

四、结果分析：

（1）自振圆频率分析

计算振型 自振圆频率 频率 1 2.08 0.330 2 2.46 0.392 3 6.46 1.030

桥梁的自振圆频率逐渐增加，属柔性体系，振动周期较小。 （2）振型分析

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1）对称性：满足对称性，不同振型出现不同的正对称或是反对称 节点号 18 偏移方向 第一振型 x y θ x 23 y θ x 16 y θ x 25 2）绘制振型图 第一主振型：

y θ -0.68107 0.00882 -0.00639 0.70216 0.00885 0.00699 0.00207 0.96959 0.00417 0.00258 0.99228 -0.00377 第二振型 -0.56413 0.00088 -0.02546 -0.54267 -0.00051 -0.02511 -0.00034 0.96544 -0.01761 -0.00052 -0.93514 -0.01755 第三振型 -0.54356 0.03473 0.07172 0.49521 0.03328 -0.06713 0.00782 0.30201 0.09431 0.00952 0.24977 -0.08788

第一主振型为桥梁的主要振型，相比其他振型出现较大的偏移量。主梁最大竖向偏移14、27号节点-0.96915、-0.99167；主塔18、23号节点出现最大水平偏移量-0.68107，0.70216

第二主振型：

第 27 页 共 28 页

主梁的最大竖向偏移出现在14、27号节点：-0.96027、0.92896 主塔，18号、23号节点最大水平偏移：-0.56413、-0.54267 第三主振型：

主梁的曲线呈四阶波形；

最大竖向偏移出现在19、22号节点：0.9998、0.92541 主塔，18号、23号节点最大水平偏移：-0.54356、0.49521 致谢：

《桥梁结构振动与抗震》这门课给了我非常大的启示，它使我对桥梁程序电算有了初步的认识和了解，在张教授严格的要求下我的收获非常之大，不仅对桥梁的电算程序有了深刻的了解，而且对以前的基础知识也进行了一次充分的复习和提高。感谢张教授对我严格的要求，我对张教授深厚的理论功底感到由衷的钦佩，祝张教授万事如意、身体健康。

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