Колебания в инженерном деле - Тимошенко С.П.
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kl. FOR J ¦ 2 TO N
U 2. S(1,J) • - M(J)*X(J)/C
63. Z(J,1) ¦ X(J)
uu. NEXT J
65 • GO TO 56
66. S(2,2 ) ¦ 0
k7. Z (1, 2 ) ¦ X(l)
68. Z(2,2) ¦ X(2)
49. С ¦ M(2)*(Z(1,1)*Z(2,2) - Z(1,2)*Z(2#1))
50. FOR J - 3 TD N
51. Z(J,2) • X(J)
52. S(2,J) - - M(J)*(Z(1,1)*Z(J,2) - Z(1,2)"Z(J, 1))/C
53. NEXT J
5*". MAT В " A*S
55. MAT A - В
5b. GO TO 17
57. PRINT
58. STOP
59. DATA 3, 0.0001
60. DATA 1,1,1, 1,2,2, 1,2,3
61. DATA 1,1,1
62. END
COMMAND ?
462
COMPUTER PROGRAM
1. REM--------VIBRATIONS PROGRAM -DYNAC0N3
2. REM (DYNAMIC RESPONSE OF MULTI-DEGREE SYSTEM
3. REM TO PIECEWISE-CONSTANT FORCING FUNCTION)
It. REM--------NOTATION
5. REM N - NUMBER OF DEGREES OF FREEDOM
6. REM N1 - NUMBER OF TIME STEPS
7. REM El - ALLOWABLE ERROR FOR EIGENVECTORS
8. REM G1 ¦ MODAL DAMPING RATIO (GAMMA)
9. REM II * TYPE INDICATOR (O-STIFFNESS; 1-FLEX I В ILITY)
10. REM A ¦ STIFFNESS OR FLEXIBILITY MATRIX
11. RFM M - MASS VECTOR
12. REM B,C - INITIAL DISPLACEMENTS AND VELOCITIES
13. REM P - VECTOR OF LOAD FACTORS
16. REM T - TIME; D - TIME INTERVAL
15. REM F - FORCING FUNCTION (PIECEK!SE-CONSTANT)
16. REM E - EIGENVALUES; X,Y,Z - EIGENVECTORS
17. REM S - SWEEPING MATRIX
18. REM G,H - INITIAL DISPLS. AND VELS. IN NORMAL COORDS.
19. REM 0 - NORMAL-MODE LOADS
20. REM P1.P2 ¦ UNDAMPED AND DAMPED ANGULAR FREQUENCIES
21. REM U,V * NORMAL-MODE DISPLACEMENTS AND VELOCITIES
22. REM R " RESPONSE IN ORIGINAL COORDINATES
23. REM W,L " WORKING STORAGE
26. DIM
A(10,10),M(10),B(10),C(10),P(10),T<100),0(100),F(100),E(3),X(10)
25. DIM
Y(10),Z(10,3),Q(3,100),U(3,100),V(3,100),R(1,10),W(10,10),L(10)
26. READ N,N1,E1,G1,I 1
27. MAT READ A(N,N),M(N),B(N),C(N),P(N),T(N1),F(N1)
28. IF II - 0 THEN MAT A - INV(A)
29. FOR К - 1 TO N
30. FOR J " 1 TO N
31. A(J,K) - A(J,K)*M(K)
32. NEXT J
33. NEXT К
36. D(1) - T(l)
35. FOR J - 2 TO N1
36. D(J) - T(J) - T(J-l)
37. NEXT J
38. PRINT 'DYNACON3--DYNAMIС RESPONSE OF FIRST THREE MODES OF
DAMPED'
39. PRINT 'MULTI-DEGEE SYSTEM TO PIECEWISE-CONSTANT
FORCING FUNCTION'
60. PRINT
61. PRINT
62. PRINT 'THREE EIGENVALUES AND VECTORS BY ITERATION'
63. MAT Z - ZER(N,3)
66. I - 0
65. REM-------ITERATE AND PRINT EIGENVALUE AND ANGULAR
FREQUENCY
66. 1=1+1
67. MAT X * CON(N)
68. FOR К = 1 TO 20
69. MAT Y ¦ A"X
50. E(I) * Y(N)/X(N)
51. J1 - 0
52. FOR J " 1 TO N
53. Y(J) - Y(J)/Y(N)
56. IF ABS(Y(J) - X(J)) < El THEN J1 - J1 ¦ 1
55. X(J) - Y(J)
56. NEXT J
57. IF J1 * N THEN GO TO 59
58. NEXT К
59. FOR J ¦ 1 TO N
60. ' Z( J, I ). - X(J)
61. NEXT J
62. PI • 1/SQR(E(I))
463
63. PRINT
64. PRINT 'MODE '; I ; 'E-VAL. - ';E(I);'ANG. FREQ. - ';P1;'ITERS. -
';K
65. IF I - 3 THEN GO TO 84
66. REM SET UP AND APPLY SWEEPING MATRIX
67. MAT S - IDN(N.N)
68. IF I • 2 THEN GO TO 75
69. S(l.l) * 0
70. Cl - M(1)*X(1)
71. FOR J - 2 TO N
72. S(1,J) - - M(J)*X(J)/C1
73. NEXT J
74. GO TO 81
75. IF N - 2 THEN GO TO 81"
76. S(2,2) - 0
77. C2 - M(2)*(ZO,l)*Z(2,2) - Z(1.2)*Z(2,1))
78. FOR J " 3 TO N
79. S(2,J) = - M( J)*(ZO,l)"Z( J,2) - ZC1,2)*Z(J,1))/C2
80. NEXT J
81. MAT W - A*S
82. MAT A " W
83. GO TO 46
81". PRINT
85. PRINT 'MODAL MATRIX'
86. PRINT
87. MAT PRINT Z
88. REM NORMALIZE MODAL MATRIX WITH RESPECT TO M
89. FOR I ¦ 1 TO 3
90. Cl ¦ 0
91. FOR J - 1 TO N
92. Cl - Cl ¦ M(J)*Z(J,I)*Z(J,I)
93. NEXT J
99. IF Cl - 0 THEN GO TO 100
95. Cl - SQR(Cl)
96. FOR J * 1 TO N
97. Z(J,I) - Z(J,I)/C1
98. NEXT J
99. NEXT I
100. REM-------TRANSFORM INFORMATION TO NORMAL COORDINATES
101. FOR I - 1 TO 3
102. G(I) - H(I) - L(I) - 0
103. FOR X * 1 TO N
104. G(I) - G(I) ¦ Z(X,I)*M(X)*B(X)
105. H(l) - HO) ¦ Z(X,I )*M(X)*C(X)
106. LO) - L(l) ¦ Z(X,I)*P(X)
107. NEXT X
108. FOR J - 1 TO N1
109. QO.J) " LO)*F(J)
110. NEXT J
111. NEXT I
112. REM.......COMPUTE RESPONSE IN NORMAL COORDINATES
113. FOR I - 1 TO 3
114. UI - GO )
115. VI * HO )
116. IF Ed ) - 0 THEN GO TO 134
117. PI - 1/SQR(E С I))
118. P2 ¦ P1*SQR(1 - G1*G1)
119. FOR J • 1 TO N1
120. IF J - 1 THEN GO TO 123
121. UI " U(l,J-l)
122. VI - VO.J-l)
123. Cl " EXP( - P1*G1*D(J))
124. C2 - COS(P2*D(J))
464
125. C3 ¦ S1H(P2"D(J))
126. C6 • (VI ¦ P1*G1*U1)/P2
127. C5 " P1*G1/P2
128. C6 - Q(I,J)/(P1*P1)
129. U(I,J) ¦ C1*(U1*C2 ¦ C6*C3) ¦ C6*(l - C1*(C2 ¦ C5*C3) )
110. V(I,J) ¦ Cl*( - U1*C3 ¦ C6*C2 - C5*(U1*C2 +C6"C3))"P2
111. V(I,J) - V(I,J) ¦ C6"C1"(1 ¦ C5"C5)*C3*P2
132. NEXT J
111. NEXT 1
136. REM TRANSFORM AND PRINT RESPONSE
135. PRINT
136. PRINT 'RESPONSE IN ORIGINAL COORDINATES (PRINTED COLUMN-WISE)'
137. PRINT
138. FOR J - 1 TO N1
139. MAT R • ZER(1,N)
160. FOR К • 1 TO N
161. FOR 1 - 1 TO 3
162. R(1,Ю - R(l.K) ¦ Z(K,I)*U(I,J)
163. NEXT 1
166. NEXT К
165. MAT PRINT R
166. NEXT J
167. PRINT
168. STOP
169. DATA 3,10,0.00001,0.05,0
150. DATA 2,-1,0, -1,2,-1, 0,-1,1
151. OATA 1,1,1, 0,0,0, 0,0,0, 0,0,1
152. DATA 1,2,3,6,5,6,7,8,9,10
153. DATA 1,1,1,1,1,1,1,1,1,1
156. END
COMMAND 7 ко
OYNACONJ--DYNAMIC RESPONSE OF FIRST THREE MODES OF DAMPED HULTI-DEGEE
