Колебания в инженерном деле - Тимошенко С.П.
Скачать (прямая ссылка):
109. Y1 - Y(1-2) ¦ 2*Z(1-1)*0
no. GO TO 118
111. A - YO ¦ Z0*D/2
112. В = XO ¦ Y0"D/2
113. Y1 > (0 t Z0*D
114. CO TO 118
115. A " Y(1) ¦ Z( 1)*0/2
116. В • X(l) ¦ Y(l).n/2
117. Y1 - YO ¦ 2*Z(l)*n
118. J ¦ 1
119. GO TO 123
120. J " J ¦ 1
121. X( 1) " XI
122. Y1 - A ¦ Zl"D/2
123. XI - В ¦ Yl"D/2
124. Z1 - (01 - C"Y1 -K*(X1 ¦ S"X1*X1*X1))/M
125. IF J • 10 THEN GO TO 127
126. IF ABS(X1 - X(1 )) >- F1*ARS(X1) THEN CP TO 120
127. X(1) = XI
128. Y(1) = Y1
129. Z(1) - Z1
130. PRINT T(1),J,X(1),Y(1)
131. NEXT 1
132. PRINT
133. STOP
134. DATA 100,0,400,2,0,10,0.5,20,0.0001,0
135. END
COMMAND 7
459
COMPUTER PROGRAM
1. REM -VIBRATIONS PROGRAM--AVAC2A
2. REM (AVERACE-ACCELERATION METHOD)
3. REM •-NOTATION
i*. RCM T " TIME; D * TIME INTERVAL
5. REM X,Y,Z ¦ 01SPLACEMENT, VELOCITY, AND ACCELERATION
6. REM Kl - P**2 " G/L FOR A SIMPLE PENDULUM
7. RFM XO,YO - INITIAL VALUES OF X AND Y AT TIME 1*0
8. RCM TI * TIME RANGE OF INTEREST
9. REM N1 * NUMBER OF TIMF INTERVALS
10. REM El * ALLOWABLE ERROR RATIO
11. DIM T(100),X(100),Y(1QQ),Z(190)
1 2. READ Kl ,X0,Y0,T1,N1,E1
13. D * Tl/Nl
1(". PRINT •• AVAC2A TIME INTERVAI - D
15. PRINT
16. PRINT
17. PRINT 1 TIME ITERS. APPROX. X APPROX
18. PRINT
19. PRINT 1 ¦ о i i X о -< о
101. REM---------.-INITIALIZE ZO AND ITERATE Y(I>,X(I>,Z(I )
102. ZO " - K1"SIN(X0)
103.- FOR I * 1 TO N1
10Ц. 'T(I) - l*D
105. IF I - 1 THEN- GO TO HI
106. IF I * 2 THEN GO TO 115
107. .A - Y( I -1) ¦ Z(l-l)"D/f
108. В - X(1-1) ¦ Y(I-1)*0/2
109. Y1 - Y(I-2) ¦ 2"Z(I-1)*D
110. GO TO 118
111. A " YO ¦ Z0*D/2
112. В * XO ¦ Y0*D/2
113. Y1 " YO ¦ ZD*D
lilt. GO TO 118
115. A * Y(l) + Z(1)*0/2
11S. В • XU) + Y(l)*0/2
117. Y1 ¦ YO ¦ 2*Z(1)*0
118. .1*1
119. GO TO 123
120. J " J + 1
121. X(l) = XI
122. Y1 - A + Zl*D/2
123. XI " В ¦ Yl*D/2
12U. Z1 - - K1*SIN(X1)
125. IF J " 10 THEN GO TO 127
126. IF ABSCX1 - X(I)) >" E1*ABS(X1) THFN GO TO 120
127. X(l) * XI
128. Y(I) - Y1
123. ZCI> - Z1
1J°. PRINT T(I),J,X(I),Y(|)
131. NEXT I
132. PRINT
133. STOP
139. DATA 3.937687,1.570796,0,2,20,0.0001
135. END
COMMAND ?
460
COMPUTER PROGRAM
1. REM VIBRATIONS PR0GRAM--AVAC1A
2. REM (AVERAGE-ACCELERATION METHOD)
3. REM NOTATION
9. REM T => TIME; D = TIME INTERVAL
5. REM X,Y,Z = DISPLACEMENT, VELOCITY, AND ACCELERATION
6. REM M,С,К = MASS, DAMPING, AND SPRING CONSTANTS
7. REM XO,YO - INITIAL VALUES OF X AND Y AT TIME T = 0
S. REM TI " TIME RANGE OF INTEREST
9. REM N1 " NUMBER OF TIME INTERVALS
10. REM El • ALLOWABLE ERROR RATIO
11. REM QI - MAGNITUDE OF STEP FUNCTION
12. DIM T(100),X(100),Y(100),Z(100)
13. READ M,C,K,X0,Y0,T1,N1,E1,Q1
11). N > C/(2*M)
15. P =>. SQR(K/M - N*N)
16. D =¦ Tl/Nl
17. PRINT 'AVAC1A TIME INTERVAL * *, D
18. PRINT
19. PRINT
20. PRINT 'TIME ITERS. APPROX. X EXACT X'
21. PRINT
22. PRINT ' 0 - ',XO,XO
101. REM INITIALIZE ZO AND I TERATE- Y(I),X(I),Z(I)
102. ZO ¦= (01 - C*Y0 - K"X0)/M
105. FOR I - 1 TO N1
ION. TCI) = I*D
105. IF I = 1 THEN GO TO 111
lot-. IF I = 2 THEN GO TO 115
107. A - Y(I - 1) ¦ Z(I-1)*D/2
108. В ¦= X(l-l) ¦ Y(l-l)*D/2
109. Y1 = Y(I - 2) ¦ 2*Z(t-l)*D
11U. GO TO 118
111. A = YO + Z0*D/2
112. В " XO ¦ Y0*D/2
113. Y1 = YO ¦ Z0*D
11 A. CO TO 118
115. A = Y(1) ¦ Z(l)*D/2
116. В " X(l) ¦ Y(l)*D/2
117. Y1 * YO * 2*Z(1)*D
118. J = 1
119. CO TO 123
120. J * J + 1
121. X(I) = XI
122. Y1 = A + Zl*0/2
123. XI = В + Yl*D/2
12 N. Z1 = (QI - С * Y1 - K*X1)/M
125. IF J = 10 THEN GO TO 127
126. IF ABS(XI -'X(I)) >- El*ABS(XI) THEN GO TO 120
127. X(I) " XI
128. Y(I) = Y1
129. Z(I) = Z1
130. E = EXPt-N"T(I))*(XO"COS(P*T(I)) +
(YC+N*XO)*SIN(P*T(I))/P)
151. E = EXP(-N*T(I))*(COS(P"T(I)) + N*SIN(P*T(I))/P)
132. E " E ¦ (Ql/K)*(1 - F)
133. PRINT T(I ),U,X(I),E
139. NEXT I
135. PRINT
136. STOP
137. DATA 1,1.2,9,0,0,2,20,0.0001,9
138. END COMMAND ?
461
COMPUTER PROGRAM
1, REM. Vi&ftATlONS PROGRAM'-E t G 1 T 3
с , REM (EIGENVALUES AND VECTORS BY ITERATION)
3. REM NOTATION
ц. REM A - COEFFICIENT MATRIX (OF ORDER N)
5. REM M " MASS VECTOR
6. REM X,Y,Z ¦ EIGENVECTORS
7. REM E • EIGENVALUE
8 . REM S - SWEEPING MATRIX
9. REM El - ALLOWABLE ERROR
10. DIMA(10,10),M(10),X(10),Y(10),Z(10,2).S(10,10)
U. READ N, E1
12. MAT READ A(N,N),M(N)
13. PRINT 'EIGIT3 THREE EIGENVALUES AND VECTORS BY ITERATION
1U. PRINT
15. 1 " 0
16. REM ITERATE AND PRINT EIGENVALUE AND EIGENVECTOR
17. 1 " 1 ¦ 1
18. MAT X ¦ CON(N)
19. FOR К ¦ 1 TO 20
20. MAT Y " A* X
21. F " Y(N)/X(N)
22. J1 ¦ 0
2 3. FOR J - 1 TO N
2k. Y(J) * Y(J)/Y(N)
25. IF ABS(Y(J) - X(J)) < El THEN J1 " J1 ¦ 1 _
26. X(J) - Y(J)
27. NEXT J
28. IF J1 - N THEN GO TO 30
29. NEXT К
30. PRINT
31. PRINT 1 MODE *;1;'E1GENVALUE ¦ *;E;*NO. OF ITERS. " *; К
32. PRINT 'EIGENVECTOR*
33. MAT PRINT X
3U. IF 1 - 3 THEN GO TO 57
35. REM SET UP AND APPLY SWEEPING MATRIX
36. MAT S - IDN(N,N)
37. IF 1 - 2 THEN CO TO U6
•38. S<1,1) ¦ o
39. Z(l,l) " X(l)
uo. С - M(1)*X(1)
