Users guide and description of CABLE, a PC program to analyze cable vibrations

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Users guide and description of CABLE, a PC program to

analyze cable vibrations

Citation for published version (APA):

Rienstra, S. W. (1988). Users guide and description of CABLE, a PC program to analyze cable vibrations. (WD report; Vol. 8808). Radboud Universiteit Nijmegen.

Document status and date: Published: 01/01/1988

Document Version:

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Report no. WD 88-08

Users guide and description of CABLE, a PC program to analyze cable vibrations

S.W. Rienstra

July 1988

Wiskundige Dienstverlening Faculteit der Wiskunde en N atuurwetenschappen Katholieke Universiteit Toernooiveld

6525 ED Nijmegen

This program is prepared under contract for the NV Provinciale Limburgse Elektriciteits-Maatschappij PLEM, Maastricht.

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Contents 1. Sununa.ry 2. Introduction 2.1 Background 2.2 Scope 3. Applicable documents 4. General description 4.1 Basic theory

4.2 Menu and output overview 4.3 Keys 4.4 Environment 4.5 Memory management 4.6 External interfaces 5. Practical example 6. Computer program 6.1 Functional description 6.2 List of program variables 6.3 Source listing

7. Figures

1. Flow chart of menu and output screens 2. Logo

3. Help screen with brief description of program and keys 4. Main menu

5. Stationary results, some basic parameters 6. Submenu amplitude-mode (for dY - dT) 7. Submenu time-mode (for variation in time)

8. Table of maxima and minima of dY and dT, frequency and energy for varying amplitude 9. Plot of minima and maxima of dY vs. dT

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1. Summary

This report contains a users guide and program description of CABLE, an interactive program for IBM Personal Computers and compatibles to analyse the dynamics of free vibrating suspended elastic cables. Specifically, the program is meant to support interpretation and evaluation of experiments on galloping overhead transmission lines.

Output includes the stationary solution, and the instationary solution for 6 elementary configurations. This solution is presented as: tension and vertical displacement variation in time, and: minima and maxima oftension related to that of vertical displacement, and includes frequency and vibrational energy. The tension considered is either from the cable, or from the suspension chain.

The program is menu-directed, entirely self-explaining, and contains a standard example.

2. Introduction

2.1 Background

Galloping of overhead transmission lines (an aero-elastic instability, occurring regularly but not frequently under certain weather conditions) is a still unresolved problem. Although many sides of it are understood, it appears to be still not possible to design the system of suspended electricity cables free of galloping. One reason is undoubtedly the always rather difficult conditions under which observations have to be done.

Since the main damage from this phenomenon is the short circuit when two cables (or cable bundles) touch each other, a practical approach is to design neighbouring cables sufficiently separated. However, for this it is necessary to know the actual maximum displacement of the cable during galloping. It appears to be difficult to automatically monitor a cable and measure its deflection, since galloping only occurs with bad weather conditions.

It is, however, possible to automatically measure the reaction forces in the supports (fixed connections, or suspension chains). The problem that remains is to relate these measured forces to the corresponding displacement. Very little appeared to be known on that in the literature. Therefore, a new theory was developed, published in (1]. The present program CABLE, based on this theory, provides (among other things) a tool for the above experiments.

2.2 Scope

Galloping is a. motion of the cable very close to a free vibration, since the forces (wind) are only small. Various aspects occurring with galloping are therefore not related to the galloping in particular but are inherent to the free motion the cable is close to. Essential to understand galloping is therefore to understand the dynamics of free vibrating suspended cables. For example, the relation between tension and displacement can be found by studying the equivalent free vibration.

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A study of the free motion of a cable in several elementary configurations, including single and coupled spans, is presented in [1). The scope of the present program is to provide an easy-to-use, interactive, menu-directed, and self-explaining tool to quantify the results of [1]. It is designed to help the analysis and interpretation of experiments, and in particular to make available the relation between measured reaction forces in the cable supports and the corresponding cable deflection.

3. Applicable documents

1. S.W. Rienstra A nonlinear theory of free vibrations of single and coupled suspended elastic cables, KUN Report WD 88-06, 1988

2. Manual "Microsoft QuickBASIC Compiler Version 3.0 for IBM Personal

Computers and Compatibles", Microsoft Corporation, 1987

4. General description

4.1 Basic theory

The essentials of the relevant theory will be given here. Details can be found in [1].

Denote by S the distance between supports (span), L the unstretched cable length, m and mo the mass per length with and without ice, Hand Ho the horizontal component of the stationary tension, T and To the tension, and V and

Vo

its vertical component, at the cable ends, A the cable cross section, E Young's modulus, and g the gravity acceleration. The equation

8= H

+~lnT+V

EA mg

T-V= ~mgL, T

=

(H2

+

V2)t

is first solved without ice, to obtain L. Then, with L known, it is solved for H with ice. All further results are based on the "ice" situation. The sag, with or without ice, is given by

l

2[

2 1]

D= smgL T+H +EA.

The instationary theory can be applied to 6 basic configurations.

1. multispan: any section, apart from the first, from any large number of spans, or any section from any even number of spans.

2. multispan end section: the first section of a large number of spans, with the assumption that this end section is driven by the others and is not, as is possible with an even number of spans, entirely equivalent to the others.

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3. 1-span,1-loop: single span in one loop motion (elasto-gravity wave, with gravity and elasticity equally important, and tension and deflection in phase).

4. 1-span,2-loop: single span in double loop motion (first asymmetric mode).

5. 3-span, middle section: the middle of three coupled sections. This odd number "3" yields a solution, rather different from 1.

6. 3-span, end section.

Certain conditions of symmetry and regularity (no propagating waves, etc.) are supposed to further define the solutions from an otherwise infinite number of possibilities.

The instationary theory is based on the same assumptions as are usual for the well-known parabola approximation of the stationary solution:

- relative sag t = D / L is small.

- relative weight or elasticity w

=

mgL/ EA is very small: O(c:3 ); suitably scaled: w

=

8p.c:3 _with

p.

=

mgL4_/8EAVS

₌

_0(1).

- transversal wave length is of the order of the span (the natural situation).

An immediate result of these assumptions happens to be the fact that the longitudinal ("sound") wave length is very large, or: tension variations propagate very fast, so that the tension is approximately constant along the cable.

Finally, the vibration considered is dependent on a single parameter 6, the (scaled) amplitude of the first harmonic; effectively, it parametrizes the energy of the motion. With angular frequency w

=

Wo

+

62wa

we have vertical displacement dY and tension variation dT given by

dY = (scalingfactor) (6y11 sin(wt)

+

62(y20

+

y22 cos(2wt))

+

63(y31 sin(wt)

+

Y33 sin(3wt))), dT = (scalingfactor)( cru sin(wt)

+

62( r 20

+

r 22 cos(2wt))

+

63( r31 sin(wt)

+

1"33 sin(3wt))).

Note that in all coupled configurations r11 = r31

=

r33

=

0 if dT denotes the cable tension. This is not

necessarily the case if it denotes the suspension chain tension.

The point of the cable considered is always the midpoint, except for the 1-span,2-loop case, in which case the midpoint is almost stationary and the quarter point is taken instead.

4.2 Menu and output overview

A flow chart of the menu and output screens, as they are presented to the user, is given in figure 1, with examples of the different screens in figures 2-10.

After the logo we find the help screen with a brief description of the program and key functions. From this screen we can end the program session. Via the main menu for input of the problem parameters and some switches we arrive at the screen with stationary results (with and without ice) and, if "additional information=yes", some theoretically important parameters c:, tJ,k, Q. These denote:

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c= sag/span ratio

1-1= scaled relative weight or elasticity (0(1))

k= scaled wave number

0= scaled frequency of linear problem (w0 in [1])

Warning messages are provided if 1-' is very small or very large, and, except in the 1-span,l-loop problem, if 0 (=wo) is close to 4. Then the first and second harmonic are in resonance and the present solution with a single first harmonic breaks down.

After this result screen we continue, depending on the presentation mode (a-mode=amplitude variation=

dY- dT, or: t-mode=time variation), to a submenu to input 6 (t-mode) or maximum 6 (a-mode) and

boundaries of the plots. Then we obtain the instationary solution, as selected, by a table and/or plots. During a session the settings for this output are saved for each configuration, with the understanding that two configurations are considered to be equivalent if they differ only in the presented tension (i.e., cable or suspension chain). In that case a change of settings in one is communicated to the other.

4.3 Keys

Forward and backward between screens is with <Tab> and <Esc>. These keys are also active during plots and table calculation. Leaving the program is to be confirmed by ''y". Stepping through the menu is by the cursor

t

and

!

key. To go directly to top or bottom of a menu is possible with <PgUp> and <PgDn>. With <Return> we can select a configuration or switch, or come into input mode where numerical input (to be ended with <Return>) is possible. Configuration selection backwards is with <Backspace>. The cursor positions in the menu's are saved during the session.

4.4 Environment

The program is written in GWBasic, and compiled under Microsoft QuickBasic Version 3.0, [2]. Although Basic cannot always be recommended for the more complex programs, as it does not contain the tools for a natural and flexible structured programming, it was in the present case most convenient with its many input/output, screen, and graphical commands. The program is executable on an IBM Personal Computer or compatible with high resolution graphical screen, at least 128 kB RAM, and (optionally) an Intel 8087 (80287) numerical coprocessor. Without coprocessor the performance will be considerably lower.

Note that it may be necessary to issue the DOS command GRAFTABL before CABLE is executed, to make available to the graphics adapter a table of additional characters, used in the graphical plots.

4.5 Memory management

The size of the source file CABLE.BAS and the executable file CABLE.EXE are

CABLE.BAS CABLE.EXE

26842 B 97724 B

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4.6 External interfaces

There are no external interfaces. Prints of results are most conveniently made by a <PrintScreen> command from the key hoard. Make sure that to enable the printing of plots from a graphical screen the DOS command GRAPHICS is given before CABLE is executed.

5. Practical example

In a practical situation, when we have measurements of tension to be "translated" to vertical displacement, we can do the following steps.

Start the program and go, via an <Enter> at the logo screen, to the help screen. Inspect the con-figurations, the output required, and the functioning of the keys. Then select in the main menu the configuration (tension in cable or in chain?), leave the presentation mode switch at "dY-dT", and enter the geometrical parameters for no-ice conditions, and the mass ratio with/without ice. Then at the results screen we have the details of the stationary solution and the frequency of the vibration if the amplitude is small. If you have no warnings at this screen you can continue to the submenu for "dY-dT". Select a value for max 6 of about .5 (about .1 in 1-span,l-loop) and inspect the table. Compare the table with the measured tension fluctuations (note that the table is always for one cable; measured data are sometimes for bundles!). If max 6 is too small or too big, make another choice. Compare max dT and min dT and decide which couple fits your data best. Then in the columns for dY we find the corresponding deflection. Make a note of the value of 6 found. Inspect the frequency, and compare this, if possible, with measurements.

Then return to the main menu, select the presentation mode "variation in time", and continue to its submenu. Input the above found 6, choose suitable values for screen boundaries, and inspect the time histories of dT and dY. Does dT resemble to your measurements, and is dY of the type you expected (asymmetric or otherwise) ? If the theoretical results are not consistent with the experiments, reconsider your data. If the ice accretion is not uniform along the cable, select another m/mo; if you suspect asymmetries between spans, try another configuration.

6. Computer program

6.1. Functional description

- preparation, initialisation of variables - logo

- help screen - main menu, input

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- calculation of stationary solution without ice, with ice, and basic elements of the instationary solution - results screen

- time-mode:

- submenu, input

- time plots dY and dT, using the instationary solution as subroutines - amplitude-mode:

- submenu, input

- table of minima and maxima of dT and dY as a function of 6, using a subroutine that calculates the extreme values of dY and dT

- plot of minima and maxima of dT and dY; not limited by max 6 but by max dT and max dY

6.2 List of program variables

AREA AT,BT,CT,KT AY,BY,CY,KY COl,C02,C03 D

DL

DLMX

DLSTP

DT

DY

DO

Dll, ... FRQ G H

IIO

INFO$ K L M MAXT

MAXY

MINT MINY

cross sectional area A

coefficients of dT to determine extreme values coefficients of dY to determine extreme values cos( ~k ), cos( k), cos( Jk)

sag with ice D 6

max6 step size 6

dT

dY

sag without ice Do

fu, ...

frequency

gravitational acceleration g

horizontal tension with ice H horizontal tension without ice Ho

switch for additional information dimensionless wave number k length of unstretched cable L mass per length with ice m

maximum dT maximumdY minimum dT minimum dY

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MD$

MG

MMO

MU

MO

MOG

NL

NMA NMT NMl NSCRN NTOT NUM$ OMQ OMO OM2 PI

s

Sll,SI2,SI3 T TA1,TA2,TA3 TB1,TB2,TB3 TD TEXT$ TMX TN TND TNMXD TNMXT TNO TYPE$ Tll, ..

v

vo

X XTRT

switch for presentation mode (time="t", amplitude="a")

mg

ratio m/mo

J.t

=

mgL4/8EAD3

mass per lengthwithout ice mo

mog

half length of TEXT$

cursor position submenu a-mode cursor position submenu t-mode cursor position main menu

screen number (high resolution=2) number of steps in time plot index of configuration

w~

w0,0

1r

span sizeS

sin( tk ), sin(k ), sin( ~k) timet

tan(tk), tan(k), tan(ik)

wt,2wt,3wt

scaling factor time text array

max time

tension with ice T scaling factor tension max dT in a-mode max dY in t-mode tension without ice To description configuration

ru, ...

vertical component tension with ice V

vertical component tension without ice V0

coordinate s

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XTRY

extreme values of dY

YD

scaling factor dY

YMXD

max dY in a-mode

YMXT

max dY in t-mode

Yll, ...

_{Yu,· · ·}

z

s-

t

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10 ' - berekening spanningaplitude variaties lijndansen IPLEM>

-20'

30 ' analyse en progra..a 1 S. W. Rienstra CW. D., K. U.N.), 26 juni 1988 40'

50 VERSimt=•aa. 06. 2£.• 60'

70 KEY lff:DEFDBL A-M,D-Z:PI==41*ATMUihNTDT=SOO:NSCRN=2:' NSCRN=2 of 3 ! 80 DIM TVPE$Cl0l₁TEXTSI10l,NUMt110)

90 DIM TMXC10l,TMMXTClO>,TMMXD(10)₁YMXTt10l,YMXDI10)₁Dl(10l,DLMXI10),Nl(10),NMTI10l,NMAI10),XTRTC4),XlRYI4) 100 SOlD 180

110 '

120

SCREEN NSCRN:RETURN

130 IF NSCRN=2 Tl£N VSCI= 9aYSC2= 99:GOTD 160 ELSE VSCI= 20:YSC2=199:60TO 160 140 IF NSCRN=2 TI£N YSC1=100:YSC2-190:GOTO 160 ELSE YSC1=200:YSC2=380:GOTO 160 150 YSC1•1:1F NSCRN=2 TI£N YSC2=190 ELSE YSC2=380

160

VIEWI20,YSC1l-C6J5,YSC2l

11

l:RETURN

170'

180 S=3251:M0=.98911:MM0=1.1f:AREA=28011H0=126501:I~1:MDt=•a•s' voorbeeld 190 E=nOOOIIG--9.806651:ItEOS=•no •

200 TMX(l} =20t1TMMXTm =60001 1TtiiXDm =70001 tYMXTIU =81 :YMXDIU =91 sllUU :e,51 1DLMXm =.61 210 TMXt2) =201:TtiiXTC2) =12001 :TNMXDI2) =15001 :YMXH2) =81 :YMXDC2l =91 :Dl(2) =.51 :DLMXt2) =.61

220 TMU3) =20t:TNMXH3) =60001 :TNMXDI3) •70001 :YMXTI3) =5I :YMXDIJ) =61 :DLC3) =.51 :DLMUJ) =.61 230 TMXI4) =201:TNMXTI4) •15001 1TtfiXDC4) •15001 :YMXTC4> =5I :YMXDC4> =61 :DLC4> =.51 :DLMXC4) •.61 240 TMXCS) =lOI:TtiiXTC5) =90001 :TtiiXDIS) =120001:YMXTC5) =2.2ttYMXDC5) =31 :Dl(5) •.11 dli.JIX(5) =.151 250 TMXC6> •101:TtiiXH6) =70001 aTNMXDC6) •1ooootaYMXTC6) ::21 :YMXD!6) =2.51JDL!6) =,151:DLMXl6) •.21 260 TMXC7l =201:TtiiXTC7l •30001 :TNMXD(7) ~ :YMXTm =61 :YMXDC7> =71 :DLC7l =.51 :DLMX17) •.61 270 TMXI8) =20t:TMMXH8l ::9001 :TMMXDI8) =8001 :YMXH8) =61 :YMXDI8) =71 :Dl(8) •.51 :DLMXI8l •.61 280 TMXf9) =20t:TtiiXT19) •30001 tltfiXDI9l =30001 :YMXTI9> =3.5t:YMXDI9) =41 1Dl19) =.51 :DUIXI9l =.61 290 TMXUOl=201:TtllXTUOJ::9001 :TtllXDUOl=700f :YMXH10)•3.51:YMXDUOl•41 sDLU0)•.51 :DLMXU0)=.61

JOO I

310 TYPESI1)••1ultispan (cable)• 320 1YPE$(2)=•1ultispan !chain)• 330 TYPESC3)=••ultispan end (cable)• 340 TYPEfl4)=•1ultispan end (chain)•

350 TVPESCSJ=•t span, 1-loop•

360 TYPEft6)=•t span, 2-loop• 370 TYPESC7J••J span Iiddle !cable)•

380 TYPESCB>=•J span Iiddle (chain)•

390 TYPESI9)=•J span end (cable)•

400 TYPESClOJ=•J span end (chain)•

410 NUMtCt>=•ctal•:NUMSC2J••ctb)•:NUMSC3>=•c2aJ•:NUMtC4l=•c2b>•:NUMSC5)=•c3> • 420 NUMtl6)=•14l •:NUM$C7J=•tSal1_:NUMSC8l•1_{(5b)•:NUMSC9J=•t6a)•aNUMfl10)=•(6bl}1

430 TEXTSI1>=•1ultispan Cdl in cable)• 440 TEXTSI2J=••ultispan CdT

in

chain)•

450 TEXT$(3J=••ultispan, end section ldT in cable)• 460 TEXTSC4J=•Iultispan, end section (dl in 1st chain)• _.70 TEXTSC5J=•t span, 1-loop•

480 TEXUI6)=•t span, 2-loop (at x=\)•

490 TEXTSI7)=•J span, Iiddle section CdT in cable)• 500 TEXTSC8J=•J span, Iiddle section ldl in

chain)•

510 TEXTSC9>=•J span, end section CdT in cable)• 520 TEXT$UOJ=•J span, end section Cdl in chain)•

530 DYTt=•dY-dt•:VARITt=•variation in U~e•

540 FOR N=l TO 10:NLINl=lENCTEXT$CNll/2:NMTCNl•lcNMACNl=l:NEXT N 550 tfll=h' tfll, fill en tftT zijn cursor posities in llenU's 560 t

570 GOSUB 5070:' logo

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600 OOSUB 5210:' uitleg 610 AS=INKEVt:IF Af=•• THEN 610 620 IF ASC(Al)=27 THEN 640 ELSE 680 630'

640 ClS:lOCATE 8, 30, O:PRINT"DO Vlll WANT TO ST(J) ? (V /. ) •

650 AS=INKEV$: IF At= .. THEN 650 ELSE IF Af=•y• OR Af=•y• THEN END ELSE GOTO 600 660'

670 '

680 ' invoer problen parueters; ~enu

690 SCREEN O:CLS:GOSUB 5000

700 LOCATE 4, 12:PRINT

•u

configuration •;NIJitCJ~) ;• = •;TVPEtem; 710 LOCATE 6,12:PRINT '2) presentation lOde = •;

720 IF MDt=•t• n£N PRINT VARITf; ELSE PRINT DVTS;

730 LOCATE B, 12:PRINT •3) span S (I) =• ;S;

740 LOCATE 10, 12:PRINT •41 lliiSS {no ice) .0 Ckg/a) =";MO;

750

LOCATE 12,12:PRINT

•51

ratio aass with/without ice

=•;MMO;

760 LOCATE 14, 12:PRINT •6) area cross section A (aiJ =•;AREA;

no

LOCATE 16, 12:PRINT

•n

horiz. tension (no ice) HO CNI =• ;HO; 780 LOCATE 18, 12:PRINT •8) Young's IOdulus E lN/IF) =• ;E; 790 LOCATE 20,12tPRINT '9) gravit. acceleration g (1/sl) =•;CSNG!Gl; BOO LOCATE 22, 12:PRINT •tO) additional infor~~ation = •; INFO$; 810 N:tfll-1

82(1 '

830 N=(N+10lMDD 10

+I

840 LOCATE 21H+2,11,1

850 AS=III<EV$:1:W LENlAll+l GOTO 850,860,930 860 IF ASCCAll=9 THEN 1260:' tab: klaar ~~et

invoer

870 IF ASC(A$1=27 THEN 600:' esc: terug

880 IF ASClAll=lJ THEN 980:' ret: invoer of selecteer 890 IF ASC!All=8 Tf£N 900 ELSE 920:' backsp: selecteer terug

900 IF N=l THEN 11-=U~+8lMOD lO:GOTO 980 910 IF N=2 DR N=IO THEN 980

920 GOTO 850

930 IF RIGHTS tAl, l):•p• TI£N 830:' Dn: cursor down

940 IF RIGHTS lAS, U=•H• THEN N=CN+8UIJD 10 +I:' Up: cursor up

950 IF RIGHTS tAl, U:•g• TI£N N=IO:' PgDn1 cursor bott011

960 IF RIGHTtCAl, U=•J• THEN N=h' PgUp: cursor top 970 GOTO 840

980

ON N

GOTO 990,1010,1040,1060,1080,1100,1120,1140,1160,1180 990 I1-=<I~

MOD

10l+1:LOCATE 4,29:PRINT NUM$(1~l;

1000 LOCATE 4, 48:PRINT SPC(25) ;:LOCATE It, 48:PRINT TYPES II~) ;:NMl=N:GOTO 840 1010 IF

MDS=•t• THEN

MDf=•a•

ELSE

MDS=•t•

1020 LOCATE 6,48:IF MDt=•t• THEN PRINT VARITf; ELSE PRINT DYTf;SPClt2); 1030 tMl=N:GOTO 840

1040 LOCATE 8,60:ItRJT;Al:A=VAl.CA$hiF A()O Tf£N S=A:NMl=N 1050 LOCATE 8,1t7:PRINT SPCC34);:LOCATE 8,1t7:PRINT S;:GOTO 1200 1060 LOCATE 10,60:ltfJUT;Al:A=VAl.(A$hiF AOO

THEN

MO=AdiU=N 1070 LOCATE 10, 47:PRINT SPCCJU; :LOCATE 10,47:PRINT MO; :GOTO 1200 1080 LOCATE 12,60: ItfJUT;Al:A=VAL (A$): IF AOO THEN fiMO=A:NMl=N

1090 LOCATE 12, ~7:PRINT SPC!Jit) J :LOCATE 12,1t7:PRINT MMO; :GOTO 1200 1100 LOCATE 14,60:ltflliT;Al:A=VAUAlhJF AOO THEN AREA=A:NM1=N 1110 LOCATE 11t,lt7:PRJNT SPCCJiti;:LOCATE 11t,47:PRINT ARBipGOTO 1200 1120 LOCATE 16160:ItRJT;Al:A=VAL.tAlhiF AOO THEN HO=A:NMI=N

1130 LOCATE 16,47:PRINT SPC(Jit);:LOCATE Ui₁47:PRJNT HO;:GOTO 1200 1140 LOCATE 18,60:ItfJUT;Al:A=VAUAlhiF AUO TI£N E=Adt41=N 1150 LOCATE 18, lt7:PRINT SPCIJit) ;:LOCATE 18,47:PRINT E; :GOTO 1200 1160 LOCATE 20160:ItRJT;Af:A=VALIAlhiF AOO TI£N G=A:tMl=N

1170 LOCATE 20,47:PRINT SPC(Jit);:LOCATE 20,47rPRINT CSNGU:i)pGOTO 1200 1180 IF INF£J$=•yes• THEN INFO$="no • ELSE INF£J$=•yes•

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1210 '

1220 F=LOBCXtSQRCltXtXII+XfHO/EA-MOGtS/2/HO:RETURN

1230 F=LOBCX+SQRC 1 +XtXI HVIEA-XtS/L:RETURN

1240 '

1250'

1260 ' berekening andere para~~~eters

1270 M=ltiOfJIIO:EA:EIMEA:MOG=MOIG: MG=MIG

1280 Xl=O:F1=-MOGIS/2/HO:X2--MOGtSI£A/HO/H0/1024:DIF=1

1290

X=X2:GOSUB 1220:F2=F:IF F2l0

n£N 1300

ELSE X2=2tX2:GOTO

1290

1300 WHILE

IDIFI1E-10l

AND

CABSCF2li1E-10l

1310 XJ=CX1ff2-X2ff11/CF2-F1l:X=X3:GOSUB 1220:F3=F

1320 IF F1ff3(0

THEN

F1=Fl/2 ELSE Xt=X2:F1=F2

1330 X2=XJ:F2=F3:DIF=ABSC1-X1/X2l:WEND

1J40 I

1350 VO=X3fHO:L=2tVO/MOG:TNO=SQRUt0tHO+VOtVOl :DO= C. 5/EA+1/

CTNO+HOI

)fVOfVO/MOG:V=MGfl/2 1360 '

1370 Xl=O:Fl=V/EA:X2=(((SQR(1.061f1.06+4fS/LfV/EAl+1.06l/(2fS/Ll)A2)/8:DIF=1

1380 X=X2:GOSUB 1230:F2=F:IF FcHO

n£N

1390 ELSE X2--21X2:60TO 1380

1390

WHILE

CDIF>1E-10l

AND

CABSCF2111E-101

1400 X3=CX11F2-X21F11/(F2-F11:X=X3:GOSUD 1230:F3=F

1410 IF FlfFJ<O

THEN

FI=Fl/2 ELSE X1=X2:F1=F2

1%20

X2=X3:F2=F3:DIF=ABSC1-X1/X2l:WEND

1430

I

1440 H=V/X:TN=SQR(HfH+VfVI:D=C.5/EA+l/CTN+Hll1VfV/MG

1450 EPS=D/L: MI.J=III3IL fL fL fl!( 81£Afl)fDfD) :' d i IIIE!ftSi

e loze

paraeters

1460

TD=ltSQR(M/EAI/EPS:TND=EAIEPSfEPS:YD=lfEPS:ENRD=MGtlfltEPS:'

schaalfactoren

1470

I

1480 6DSUB

3180 :' configuratie

afhankelijke

para~eters

1490 ' 1500 '

1510

CLS:GOSUB

5000:LOCATE 5,36,0:PRINT •Results

:•t

1520 LOCATE 81 18:PRINT •Mithout ice• TABt5U •"ith ice•;

1530 LOCATE 10, 12:PRINT USitl'1 •sag

=

IHII. HH •• ;00 1540 LOCATE 11,12:PRINT USING •tention

=

IIHII.Ift N•;TNO 1550 LOCATE

12,

12:PRINT USING •hor. tens.

=

ltltH.Itt N•

;HO

1560

LOCATE 1J112:PRINT USING •ver.tens.

=

ttltll.lll N•;vo

1570 LOCATE 14112:PRINT USING •tength

=

ttllt.llll ••;L

1580 LOCATE 10145:PRINT USING •sag • 11111.1111 ••;D

1590 LOCATE 11145:PR1NT USING •tention

=

Hlttl.lll N•;TN

1600 LOCATE 12, 45:PR1NT USING •hor. tens. = 111111. IH N• ;H 1610 LOCATE 13,45:PRINT USING •ver. tens.

=

HHH.IH N•;V 1620 LOCATE 14,45:PRINT

USING

•length •

tltti.HH a•;L

1630

LOCATE 16,45:PRINT USING •frequency: IH.IIIIII Hz•;DMO/TD/2/PI

1640 IF CABSUJI0-4)).2

OR I~-5) ll£N

1670

1650 LOCATE 1818:PRINT USING •ATTENTION : frequency is near H.HII, where 1st and 2nd har.onic•;2/TD/PI

1660 LOCATE 19, 20:PR1NT •are in resonance, so 1st har1110nic may not be doMinant •;

1670 IF

Uti <100 AND Ill>. 01) THEN 1720

1680 LOCATE 2018:PRINT "ATTENTION : relative elasticity

=•;

1690 IF IIJ)IOO THEN PRINT USING •tlllllll.l .ay be too large•;I'RJ 1700 IF IIJ<.Ol THEN PRINT USING •t.IHIIIH uy be too .a11•111J 1710 LOCATE 21,20:PRINT

•tor

the instationary theory•;

1720 IF ltt=O$=•no • THEN

1770

1730

LOCATE 23115:PRINT USING •e =IIIH. ltltlt" ;EPS;

1740

LOCATE 241 15:PRINT USING •p =tltll.llltii";IIJ;

1750 LOCATE 23148:PRINT USING •k =lllti.IIHH•;K;

1760 LOCATE

24

148:PRINT USING •g =IIIH.IIftH•;IJIIO;

1770 At-INKEYS:IF Af=•• THEN 1770

1780

IF ASCU~$)=9 OR ASCCA$>=13 n£N 1820:' doorgaan

1790

IF

ASCCA$)=27 THEN 680:1 _terug

1800 GOTO

1770

1810 I

1820

IF

MDt=•a• THEN 2500 1830 t

(15)

1850

1 _~~~mu_{voor lOde}

_t

1860 ClS :SCREEN 0 :BOSUB 5000: 60SUB 5040

1870 LOCATE 2

1

33-Nllli):PRINT "dVCtl,dT(t) : •;TEXTSCiil;

1880 LOCATE

91

26:PRINT "11

Max

ti.e lsi =";TMXCiil;

1890 LOCATE 11

1

26:PR1NT "21

.ax

dY t1l

=•;VMXTCiil;

1900 LOCATE 13,26:PRINT "31

.ax

dT INI

=";TNMXTIIil;

1910 LOCATE 15,26:PRINT "41

&

=•;DLHil;

1920 N=NMTIIil-1

1930 N=IN+41MOD 4 +1

1940 LOCATE 2tN+7

12511

1950 A$=ltt<EYS:IJ4 LEtHA$1+1 OOTO 1950,1960

1

1970

1960 IF ASCCA$1=9

nEN

2140 ELSE IF ASCIA$1=13

nEN 2020

ELSE IF ASCCA$1=27 THEN 1510 ELSE OOTO

1950

1970 IF RIGHTS!A$

1

1l="P• THEN 1930

1980 IF RIGHTS(A$

1

1l="H"

THEN

N=!N+21MOD 4 +1

1990 IF RIGHTS!A$

1

1)=•Q• THEN N=4

2000

IF

RIGHT$

CA$

1 U

=• I"

TI-EN

N=1

2010 SOlO

1940

2020 ON N

OOTO 2030,

20501

2070

1 2090

2030 LOCATE

91

57: It,ror;AS:A=VAI..lA$1: IF

AOO TI£N

TMX 111-I=A:NMHiil=N

2040

LOCATE

91

44:PRINT SPCC36l; :LOCATE

91

44:PRINT TMX Uil ;:SOTO

2110

2050

LOCATE

111

57:lt,roi;A$:A=VALtA$hJF

AOO TlEN

VMXTUii=A:NKTUii=N

2060

LOCATE 11

1

44:PRINT SPCl36l;:lOCATE 11

1

44:PRINT YMXTllil;:SOTO 2110

2070 LOCATE

13₁

57:INPUT;AS:A=VALCA$hiF AOO

TlEN

TNMXTCiii=A:NMTUii=N

2080 LOCATE 13,44:PRINT SPCC361 ;:LOCATE 13

1

44:PRINT TNMXHiil; :SOTO 2110

2090

LOCATE 15,57: INPI.IT;ASdi':VALCA$1 :IF AOO

TI£N

DI..Uii=A:NKTCiii=N

2100 LOCATE 15

1

44:PRINT SPCC361;:LOCATE 15,44:PRINT DLCiil;:GOTO 2110

2110 PRINT TABC731 "I";:GOTO 1930

2120'

2130 '

2140

1 _klaar

_Met

_{invoer; config • .et kabelsp. relat. aan kettingsp.}

2150

ON

Ii GOTO 2160

1

2170

1

2180,2190,2250

12250122001

2210,2220

1

2230

2160 TMXC21=TMX!1l:YMXTC2l=YMXTC11:DLC2l=DLC11:GOTO 2250

2170 TMXC11=TMXC2l:VMXTI1l=VMXTI2l:Dllli=Dl121:GOTO

2250

2180

TMXC41=TMXC31:VMXTI~I=VMXTI31:Dli41=DLI31:GOTO 2250

2190

TMXIJI=TMXI41:VMXT!3l=VMXTC~I:IlLIJI=DI..t41:GOTO 2250

2200 TMX CBI=TMXm :VMXH81=VMXTC71:1lll81=DU71:GOTO 2250

2210 TMXC71=TMXI8):VMXTI71=VMXTC81:DLC71=DLI81:GOTO 2250

2220 TMXI101=TMXI91:YMXTI101=YMXTC91:DLC101=DLI91:GOTO 2250

2230 TMXI91=TMXI101:YMXTI91=YMXTC101:DLC91=DLI101:60TO 2250

2240'

2250 '

plotten voor lOde t

2260 CLS:BOSUB

120:Dl=DLII~I

:T=O

2270 LOCATE

25,

38:PRINT

•ume•

;:LOCATE

25,

80-lENCSTRSCTMX

Ulll))

:PRINT TMX Uil ;:LOCATE

25,

2:PRINT 0;

2280

60SUB

4880:FRQ=COMO+DlfDl.IOM21/TD/2/PI:'

energie en frequentie

2290

Af=•t6=•+STRSIDI..)+•, En=•+STRSCCSNGCFIX!ENflOII/10111+•, frq="+STRSCCSNGIFIXIFRQflOOOOII/10000111+"1•

2300

LOCATE

11

42-LENIA$1/2-NUI1.1 :PRINT TEXT$111.1 ;:LOCATE

11

80-LENIA$1 :PRINT AS;

2310 '

2320 LOCATE

6, 1

:PRINT "dY"; :LOCATE 2

1

1 :PRINT STRSIYMXT Uil I; :LOCATE

12, 1

:PRINT STRS 1-YMXT (11.)

I;

2330 GOSUB 130:NINDOWIO,-YNXTCI"II-ITMXII"I,VMXTII")):LINEIO,OI-ITNXCI"I,OI

2340

GOSUB

3210:PSEHT,DYI

2350

FOR N=l TO NTOT

2360 T=NITMXII"I/NTDT:GDSUB 3210:LINE-IT,DYI

2370 A$=IN<EY$:IF A$0 ..

THEN

IF ASCIA$1=27 THEN 1850 ELSE IF ASCIA$1=9 THEN 2400

2380 NEXT N

2390'

2400 LOCATE 18,1:PRINT •dt•;:LOCATE 14,1:PRINT STRSITtfiXTUillpLOCATE 24,1:PRINT STRSC-TtiiXTCI1.H;

2410 GOSUB 140:WINDOWC0

1

-TNMXTCI")I-CTMXIl"I,TNMXTII"Il:LINECO,OI-ITMXClii,OI

2420 T=O:GOSUB 3210:PSETCT,DTI

2430 FOR N=l TO NTDT

2440 T=NITMXCiii/NTOT:SOSUB 3210:LINE-IT,DTI

2~50

AS=Itt<EYS:IF A$() .. THEN IF ASCCA$1=27 OR ASCIA$1=9 THEN 1850

2460 NEXT N

(16)

2490

I

2500 '

EnU

voor IIOde a

2510 CLS:SCREEN O:GOSUB 5000:GOSUB 5040

2520

LOCATE

2,36-Nlll~l:PRlNT

DYTt;• :

";TEXTS!I~l;

2530 LOCATE

91

C6:PRINT

"11 aax 6 =";DLMXII~l;

2540 LOCATE 11,26:PRINT "2)

max

dY l1l

=•;YMXDII~l;

2550 LOCATE 13, 26:PRINT •;3)

lllix

dT !Nl

="; TNMXD

CI~l

;

2560

N=NMAII~)-1

2510 N=IN+3lMOD 3

+1

2580

LOCATE 21N+7

₁

25

1

2590 AS=Iti<EY$:~

LENIA$1+1 6DTD 2590

1C6001

2610

C600

IF ASCIA$)::9

TI£N

2750 aSE IF ASC!A$)=13

11£N

2660 ELSE IF ASCIASJ=27

THEN

1510 aSE 6DTD

2590

2610 IF RlGHT$1AS,1l="P"

THEN

2570

2620

IF RIGHTSIAS,li="H"

THEN

N=IN+lJMDD

3

+1

C630

IF RIGHTSIA$

1

U="Q"

THEN

N=J

2640 IF RlGHTf(A$

₁

1)="1•

THEN

N=1

2650 SOTO 2580

8&60

ON

N GOTO 2670,2690,2710

2670 LOCATE 9,57:INPUT;AS:A=VAUASI:IF AOO

TI£N DLMXU~J=A:NMIHI~l=N

2680

LOCATE 9,44:PRINT SPC!36J;:LOCATE 9

1

44:PRINT

DLMXII~l;:GOTO

2730

2690 LOCATE 11,57:INPUT;AS:A=VALIA$l:IF A(lO THEN

VMXDII~l=A:NMA<I~l=N

2700 LOCATE

11₁

44:PRINT SPCC36l ;:LOCATE 11,44:PRINT

YMXDU~l

;:GOTD 2730

2710 LOCATE 13

1

57:INPUT;AS:A=VAI...IAS>:IF AUO

TI£N TNMXDII~l=A:NMAU~l=N

2720 LOCATE 13

1

44:PRINT SPCI36J; :LOCATE 13

1

44:PRINT

TltiXDU~J ;:GOTD

2730

2730 PRINT TABI73J "I";:SDTO 2570

2740'

2750 'klaar

~et

invoer; config •

.et kabelsp. relat. aan kettingsp.

2760

~ I~

GOTD 2770,2780

1

2790,2800,2850,2850

1

2810

1

2820

1

2830

1

2840

2770 DLMXI21=DLMXI1l:YMXDC2J=YMXDI1J:GOTO 2850

2780 DLMXIll=DLMXI21:YMXD!1J=YMXD!2l:SOTO 2850

2790 DLMXI4l=DLMX13l:YMXDI4l=YMXDIJl:GOTO 2850

2800 DLMXI3l=DLMX<4l:VMXD13)=YMXD14),GOTO 2850

2810 DLHXI8l=DLMXI7l:YMXDI8l=VMXD17l:GOTO 2850

2820 DLMXC7l=DLMXI8l:YMXD!7l=YMXDI8l:GOTO 2850

2830 DLMX!10J=DLMXC9l:YMXDI10l=YMXDI9):60TO 2850

2840 DLMXC9)=DLMXI10l:YMXD!9J=YMXDI10):60TO 2850

2850'

2860 '

tabl!l voor lOde a

2870 CLS:LDCATE

,0

2880 PRINT" ";STRINB$178

1

196);• •;

2890 PRINT "f";:LOCATE

2,~o-NL!Ill:PRINT TEXTSII~l

TAB!801

•1•;

2900

PRINT"

";STRINBtl9,196l;"r";STRINBSI25,196l;"r";STRINGtl21,196l;"I";STRING$120,196l;"~";

2910 PRINT • • TABI6l

"&"

lABil )

"I"

TABI25l "dT" lABI37l

"j"

TABI~9)

dY" TABI59l

"I"

TAB\63)

"frq"

TABI74l "En"

TABI80)

"1

11

'

2920

PRINT

·~·;STRING$19,196l;"t";STRINBSI25,196J;"t";STRINB$C21,196l;"f"iSTRlNG$120,196);"i";

2930 FOR N=2

TO

20

2940 DL=N*DLMXCI~)/20:FRQ=IOMO+DLtDLfOM2l/TD/2/PI:GOSUB 3250:GOSUB

4880:LOCATE

N+~₁1:

2950

PRINT USING

"I

t.lttl ' lttllll.lll 111111.111

I""·""

10.1111 , ... lttl IIIIII.H

I";DL,MINT,MAXT,

MINY,MRXY,FRG,EN;

2960 At=JNKEYS:IF A$0 .. TI£N IF ASC(A$)=27 THEN 2500 aSE IF ASCCA$)::9 THEN 3010

2970 t£XT N

2980 LOCATE 25

1

1:PRINT

"L";STRINB$191196);•~·;STR1NG$1251196J;•~•;STRINGSI211196l;"L";STRINBSC201196);•J•;

2990 At=IN<EYS:IF A$= .. THEN 2990 aSE IF ASCIA$)=27 THEN 2500

(17)

3010 ' plotten voor MOde a

3020

CLS:GOSUB 120:li.STP=DLMX

(I

,C)

/40

3030 LOCATE

251

40:PRINT "dT•;:LODATE 25

1

80-LEN<STRSITNMXDII,Clll:PRINT TNMXDlJj);tLODATE 25

1

2:PRINT -TNMXDIIJl;

3040 LOCATE t,l:PRINT STRStYMXDti,Cll;:LOCATE 24

1

1:PRJNT STR$l-VMXD(J,C)l;

3050

LOCATE

12, I:

PRINT "dY"; :LOCATE 2

1

37-NLU;):PRINT DYTS; • : • ;TEXTSCI,Cl;

3060 GOSUB

150:WINDOWC-TNMXDCIJl,-VMXDCI,Cll-tTNMXD(l,Cl

1

YMXDCI;))

3070 LINEC0

1

-VMXDCI,Cll-(0

1

.8tYMXDCI;l):LINEC0

1

.981YMXD!J,C))-(0

1

YMXDCJjJ):liNE<-TNMXDCI,Cl

1

0l-tTNMXDCI,Cl,Ol

3080 DL=O:MRXT=O:MINT=O:MRXY=O:MINY=O

3090

WHILE ((MRXHTNMXDUJI

AND

MRXYCYMXDUJll

OR

OIINTl-TNMXDU;l

AND

MINYl-VMXDCIJlll

3100 Dl=Dl+DLSTP:OMAXT=MAXT:OMINT=MINT:OMAXY=MAXY:OMINY=MINY:GOSUB 3250

3110 IF COMAXT<TNMXDCI,Cl

AND

OMAXYCYMXD(Jj))

THEN

LINE lOMAXT,OMAXYl-tMAXT,MAXYl

3120 IF tOMINTl-TNMXDUll

AND

OMINY>-YMXDUJll

nEN LINE

<OMINT

₁

0MINYl-tMINT,MINY)

3130 AS=INKEYS:IF Aso•• TI£N IF ASC<ASI=9 OR ASCIASl=27

THEN 2500

3140 WEND

3150 IF lti<EY$=" •

TI£N

3150 ELSE GOTO

2500

3160 '

3170'

3180 'berekening configuratie afhankelijke

para~~eters

3190

~

JJ GOTO 3530

1

3530,3530

135301

3910

1

4300

1

4470,4470

1

4470

1

4470

J200 I

3210 'dY en dT voor gegeven t en

6

en x=.5 (11=.25

bij

1-span/2-loopl

3220

TB1=TitllMO+Dl1DliOM2l/TD:TB2--2HDl:TB3=31TBl:lF IJ=6

THEN

X=.25 ELSE X=.S

3230

ON

IJ GOTO

3580

1

3580

1

3720

1

3720

1

4120

1

4350

1

4520

1

4520

1

4700,4700

3240'

3250 ' berekening van het

uxiiUII en het MiniiUII

van dT en dY

3260 FOR NX=1 TO 4:XTRTtNXl=O:XTRYtNXl=O:NEXT NX

3270 T=O:GOSUB 3210:

1 01

de coefficienten Y11

1

T11

1

etc. te bepalen

3200 ~ 1;

GOSUB

366013660,3820, 3820142501 ~420,

4620,4620,4000,4000:' dan de AT,

BT,

etc,

3290

XTRT<1J=AT-BT-cT+KT:XTRT<2J=-AT-BT+CT+KT

3300 XTRYill=AY-BV-cY+KY:XTRYI2l=-AV-BY+CY+KY

3310 DETM=BTIBT+31ATICT+91CTICT:IF DETMCO THEN GOTO

3360 3320

IF CTCJO

THEN

ST=I-BT+SQRCDETMl)/6/CT ELSE ST=AT/4/BT

3330 IF ABSCST)(l

THEN XTRTI3)=ATIST+BTt(l-2tSTIST)+CTtSTf(3-4*STIST>+KT

3340

IF CTOO

THEN

ST=<-BT-SQRfDETMJl/6/CT ELSE GOTO

3360

3350 IF ABSCST)

(1 THEN

XTRTC4)=ATIST+BTti1-21STIST)+CTtSTt(3-4*STISTJ+KT

3360 DETM=BY*BY+31AYICY+91CYICY:IF

DEl~<O

THEN GOTO 3410

3370 IF CYOO

THEN

ST=C-BY+SQRIDETMH/6/CY ELSE ST=AY/4/BY

3380 IF ABSIST)(1

THEN

XTRYI3l=AYIST+BYf(1-2*STIST)+CYtSTfl3-4fSTtST>+KY

3390 IF CY<>O THEN ST=I-BY-SDRIDETMIJ/6/CY ELSE GDTO 3410

3400 IF ABSIST) 11

THEN

XTRYt4)=AYIST+BYI(1-2STtST>+CYISTtl3-4fSTSTl+KY

3410 MAXT=O:MINT=O:MAXY=O:MINY=O

3420 FOR NX=1 TO 4

3430 IF MAXT<XTRTINXl THEN MAXT=XTRTfNX)

3440

IF MINT>XTRTCNXJ THEN MINT=XTRTCNXJ

3450 IF MAXVCXTRYINXl

THEN MAXY=XTRYCNX)

3460 IF MINY>XTRVtNX)

THEN

MINY=XTRYINX>

3470 NEXT NX

3480 RETURN

3490

I

3500'

3510

1

_{de basis for.ules}

3520 '1,2) Multispan, even span

3530

K=PI :IJIO=KtSQRUIH

~~ 3540 T20=31/8*DM0/116+31MU)

3550 T22=KIK*OMQ/8/116-DMQ)

3560 DM2=0MOII21T20-T22l/4/MU

3510

RETURN

3500 Y11=SINCK1Xl

3590 Y20=41T201X-XX)/MU

3600 Y22--2tT221(COSI2fKIX)-1)/0MQ

3610 Y33=T22/161SlNIK1X)/MU

3620 DY=YJ}IDl1CV11tSINITB1l+DltiY20+Y22COSCTB2>+DlY331SlNITB3l))

3630 IF IJ=l THEN DT=TND•DL•ll.tCT20+T22*COSCTB2>h' kabel

(18)

3660 AV=YDtDlfY11:9Y=VDtDltDltY22:CY=YDtDltDL•DL*Yll:KY=VD•DL•DL•Y20

3670 IF

1~1 THEN

AT=O:BT=TND•DL•DL*T22:CT=O:KT=TND•DltDLIT2Q

3680 IF 1~=2

THEN AT=O:BT=TNDtEPStDLtDLt8fT22:CT=O:KT=O

3690 RETURN

3700'

3710 '3

1

4

l 1ult ispan, end section

3720 Y11=.5tSINCK•Xl

3730 Y20=4fT20fCX-XtXl/MU

3740 V22=2tT22t(COSI2tKtXl-ll/OMO

3750 Y33=T22/32tSINCKtXl/MU

3760 DV=VDIDlt(Y11tSINCT91l+Dlt(Y20+V22fCOS(TB2l+DltY33tSlNCTBJlll

3nO

IF

I~J THEN

DT=TNDtDLtDLt<T20+T22ICOS<TB2l l :'

kabel

3780 IF

1~=4 THEN

3790

ELSE

3810:

1 _{in eerste ketting}

3790

DT=8tT22tCOSCTB2l-.5fDLfKt(CT20-T22/2ltSINITB1l+91/16tT22tSlNCTB3ll

3800

DT=TNDIEPSfDlf(-.5fMUIKtS1NITB1l+DltOTl

3810

REniRN

3820

AY=VDfDltV11:BV=VDIDltDLtV22:CY=VDIDltDlfDltV33:KY=YDtDltDltV20

3830 IF

1~3 THEN

AT=O:BT=TND1DltDUT22:CT=O:KT=TNDtDl1DltT2Q:'

kabel

3840 IF

I~

THEN 3850

ELSE

3870:

1 _ketting

3850

AT=-.51TNDIEPStDLfKt(MU+DltDltiT20-T22/2ll:BT=TNDtEPStDltDLt8tT22

3860

CT=-9t/J2tTNDfEPStDl1DltDltKtT22:KT=O

3870 RETURN

3880 F=SINCXl/X-C1-MUIXtX/16ltCOSCXl:RETURN

3890

I 3900

'51

1-span, 1-loop

3910 Xl=Pl/2:X2=4.51

3920

X=Xl:SOSUB 3880:F1=F

3930 X=X2:GOSUB 3880:F2=F

3940 WHILE IABSCX2-X1ll1E-10l

AND

CABSIF2ll1E-10l

3950

XJ=CX11F2-X21Ftl/CF2-Ftl:X=XJ:GOSUB 3880:FJ=F

3960

IF F1tF3(0 THEN F1=F1/2

ELSE

X1=X2:F1=F2

3970

X2=X3:F2=F3

3980

lEND

3990 K=2tX2:0MO=KtSOROilll

:OMO=IJIOIOMO

4000 TA1=TANIK/2l:TA2=TANIKl:TAJ=TRN13tK/2l

4010 CDl=COSIK/2l:C02=COS!Kl:COJ--cOSl3*K/2l

4020 SI1=SIN<K/2l:SI2=SINCKI:SI3=SINIJ*K/2l

4030 D11=KfK/8fCOl:T11=D11tMU

4040 D20=31/8*KfKt(JtS12/K-2tCD2-1)/(16+3tMUl:T20=D2QtMU

4050

D22=KtKtK/24t(5tSI2-2tTA2-3*Kl/(DMQ-16+16tTA2/Kl:T22=D22tMU

4060

D3l=O:T31=DJllMU:' mag

alles zijn

4070 D33=6•D221(1JtTAJ+8tTA2-55fTR1J+D11tD11tC27tTA3+32tTA2-85fTA1-30tK/COl/CD1l

4080 D33=31/160fD11tD33/CTRJ-31/2tKtC1-91/64tOMQ)I:T33=DJJtMU

4090

~(5tD22+18tD20+191/3tD11tD11Jt(2tTA1-Kl-KtCJtD22-GtD20+5fD11tD11)tTA1tTA1+4tCD22+21/3tD11tD111tCTA1+K/2-TA2l

4100 OM2=21/3/K/K/KIOMOIC01tD11tOM2/(CD2+2-3tSl2/KI

4110 RETURN

4120 Z=X-.5

4130 V1l=COSlKtZl-CD1

4140 V20=-D11/2tV11-D20f(41ZtZ-1l

415() V22--2tCD22+21/3tD11tD11lt(C0S(24KtZI-CD21/K/K/CD2-D11/6tV11

4160 V31=K/2tC51/12tD11tD11-D2<l+D22/2+210M2/0MOlt(.51SilfCDSCKtZJ-ZtSINCKtZIICD1)/C01

4170 Y31=V31+CD31/Dll-D20-D22/6-D11tD11/9-210M2/0MOJtV11

4180 V31=Y31+41/3tD11tCD22+21/3tD11tD11ltCCOSt2tKtZI-CD21/K/K/CD2

4190 Yll=D11/2t(D22-D11tD11/61tY11/K/K/C01

4200 YJJ=V33+41/5tD11tCD22+21/3tD111D11Jt(C0S(2tKtZI-CD21/K/K/CD2

4210 V33=VJ3+(81/9tDJJ-131/101D11tD22-91/20fD11tD11*Dlll1CCOSC3tKtZI-C031/K/K/CDJ

4220 DV= YiltDltCV11tSINtTBli+Dlt(V20+Y22tCOSITB21+DlttV3ltSINCTBli+Y33tSINCTB3llll

4230 DT=TNDtDLtCT11tSINITBll+Dli(T20+T22tCOSITB21+DLtCT31tSINCTS1l+TlltSINCTBJllll

4240 RETURN

4250 AY=YDIDlt!Y11+DLIDltV311:BY=VD•DL•DL•Y22:CV=YDDlDlDlYll:KY=VDfDltDltY20

4260 AT=TNIIIDltCTll+DltDLtT31l:BT=TNDtDLtDLtT22:CT=TNDIDLtDltDltTJJ:KT=TNDtDltDLIT2Cl

4270

RETURN

(19)

~90 1

_{6) 1-span 2-loop}

4300 K=21PI :IJIO:::KISOR

!MIJ)

:()111Q..-QIIIOIOMO

4310 T20=31/8tOMQ/116+3tMUJ

4320 T22=KtK*DM0/8/(16-0MQJ

4330 OM2=0M0/4112tT2o-T22l/MU

4340 RETURN

4350 Yll=SIN!KtX)

4360 Y20--4tT20tiX-XIX)/MIJ

4370 Y22--2tT22tiCOSI21KtX)-1)/0MQ

4380 Yl3=T22/16tSIN(KIXJ/MU

439() DY=VDfDLtiY111SlNlTD1l+Dlt(Y20+Y22fDDS(TB2l+DltY33tSINITB3J))

4400

DT~TNDfDLIDlt!T20+T22tCOSITD2ll

4410 RETURN

4420

AY=YDtDLtYll:BV=YDtDLIDLtY22:CY~YDtDLIDLtDltY33:KY=YDtDLtDLtY20

4430 RT=O:BT=TNDfDLtDLtT22:CT=O:KT=TNDtDLtDLtT20

4440 RETURN

4450'

4460 '7,81 3-span middle section

4470

K=PI:DMO=KtSORIMUJ:OMD~OMOIOMO

4480 T20=31/1610MQ/(16+3tMUl

4490 T22=K*KIOMQ/16/116-0MDl

4500 OM2=0M0/4t(2tT2o-T22J/MU

4510 RETURN

4520 Yll=SINIKtX)

4530

V20=41T20t(X-XtXl/MU

4540 Y22=2tT22t!COSI2tKIX)-1)/0MQ

4550 V33=T22/161SINIKtXl/MU

4560 DY=YDtDlt!Yll1SlNITB1l+Dli(Y20+V22tClHrtTD2l+DLIV331SINlTB3llJ

4570

IF Jj:7 THEN

DT=TND1Dl1DlftT20+T22ICOSHB2J

J :'

kabel

4580

IF 1~=8

THEN 4590 ELSE 4610 :' ketting

4590

DT=8tT22tCOSITB2J-.51DltK1IIT20-T22/2)tSINITB1l+91/16tT22*SINlTB3l)

4600

DT=TNDtEPStDLti-.51MUtKtSlNITB1J+DLtDTl

4610 RETURN

4620 AY=YDtDLtY11:DY=YDtDLIDLtY22:CY=YD•DLtDLIDltY33:KY=YD1DltDltY20

lt630

IF Jj:7 THEN

AT=O:BT=TND•DL•DLIT22:CT=O:KT=TNDfDL1Dl1T20

46lt0

IF 1~=8

THEN 4650 ELSE 4670

lt650

AT=-.5tTNDtEPS1DlfKtiMU+DltDLIIT2o-T22/2Jl:BT=TND•EPStDltDLI81T22

4660

CT=-91/321TNDIEPStDl1DltDltKtT22:KT=O

4670

RETURN

4680'

4690

1

_{9, 10) 3-span}

_end

_section

4700 Y11=.51SINIK1Xl

lt710 Y20=4tT20tiX-X•XJ/MU

4720 Y22=2tT22f(C0S(21KtX)-1)/0MQ

lt730 Y33=T22/32tSIN!KtXl/MU

4740

DY~YDtDLtlYll1SINITB1l+Dlt(V20+V22tCOSITB2l+DLIY33tSINITB3llJ

4750

IF I~-9 THEN

DT=TNDtDLIDlt<T20+T22tCOS<TB2l

J :'

kabel

4760 IF

1~=10 1lEN 4nO

ELSE 4790:' ketting

4770

DT=81T22tCOSCTB2l-.51Dl1Kt((l20-T22/2JISINCTBil+91/16tT22tSINCTB3ll

4780

DT~TNDIEPS1Dl1(-.5fMUIKtSINITB1l+DLtDTl

4790 RETURN

4800 AY=YDtDltY11:BY=VDtDl1DlfY22:CY=YDtDltDltDltY33:KY=VDtDL1DltY20

4810

IF 1~=9

THEN AT=O:BT=TNDtDltDLtT22:CT=O:KT=TNDIDltOLIT20

4820 IF

Ilt=lO THEN 4830 ELSE 4850

4830

AT~-.5tTNDIEPS1DltKtCMU+DltDLtCT20-T22/21l:BT=TNDIEPStDLIDLt8tT22

4840

CT=-91/32tTNDIEPStOltDLtDLtKtT22:KT=O

4850

RETURN

(20)

4880

1

_{energieinhoud per sectie, tijdgniddeld}

48'30

Elt-oENRDIDLIDLIK*K/32

4900 ON

I~

GOTO 4910,4910

1

4920

1

4920

1

4930

1

4940

1

4950

1

4950

1

4960

1

4960

4910

RETURN:'

multispan

4920 EN=ENf51/8:RETURN:'

multispan end section

4930 EN=EN•tSl1lSI1+3t/64lOMQfC01tCDl):RETURN:

1₁

_{span 1-loop}

4940 RETURN:'

1

span 2-loop

4950 EN=ENt31/4:RETURN:'

J

span middle section

4960 EN=ENt3f/8:RETURN:'

3

span

end

section

4970

I

4980

I

4990

1

_{kader tekenen}

5000 LOCATE

~,7:PRINT

•L•;STRIN6SI65

₁

19b);•J•;

5010 LOCATE 1

1

7:PRINT "r•;STRIN6t(65

1

19b);•1•;

502{)

FOR N=2 TO 24:LOCATE N

₁

7:PRINT•I•;:LDCATE N

₁

73:PRINT"I•;:NEXT N

5030 RETURN

5040 LOCATE

3,

7:PRINT • t";STRING$(65, 196) ;"r:RETURN

5050' 5060'

5070 ' logo

5080 CLS:LOCATE 3,17,0:PRINT •r•;STRINB$(40,196);•

_1•;

5090 FOR N=4 TO 24:LOCATE N,t7:PRINT •t•;:LOCATE N

1

5B:PRINT •1•;:NEXT N

5100 LOCATE 24,17:PRINT •L•;STRIN6$(40

1

196>;•J•;

5110 LOCATE 6

1

35:PRINT •CABLE•;

5120 LOCATE 7,35:PRINT

"illi'Jiiffiffii";

5130 LOCATE 8

1

35:PRINT

·~~·;

5140 LOCATE 12

1

30:PRINT ;;version ";VERSION$;

5150 LOCATE 18

1

29:PRINT "by S.W. Rienstra•;

5160 LOCATE 20

1

25:PRINT "Wiskundige Dienstverlening•;

5170 LOCATE 21

1

22:PRINT •Katholieke Universiteit Nijmegen•;

5180 RETURN

5190

t

5200

I

5210 ' uitleg, korte beschrijving en handleiding

5220 CLS:LOCATE

~,t,O:PRINT

•L•;STRING$(78

1

196);•J•;

5230 LOCATE 1

1

1:PRINT •r•;STRING$(78

1

196);•1•;

5240 FOR N=2 TO 24:LOCATE N,l:PRINT•r;:LOCATE N,80:PRINT•

₁

•;:NEXT N

5250 LOCATE 3

1

2:PRINT • CABLE

an 1nteractive program for IBM Personal Coaputers and

eo~patibles•;

5260 PRINT

•!

to analyse the dyna•ics of free vibrations of suspended elastic";

5270 PRINT •

cables in a number of elementary configurations

c•

5280 LOCATE , I

•1

1. aultispan, 2-periodic : sections, coupled via suspension chains, in•

52'30

PRINT • •TABIJ2)•symmetric up-down-up etc. MOtion !lowest lOde)•

5300 PRINT • - even number of spans

: up-down periodic; effectively described by 1. •

5310 PRINT • 2. 1ultispan

1

end section: end section of semi-infinite version of

t.•

5320 PRINT • 3. I span, 1 loop

: single section in lowest sym.etric lOde"

5330 PRINT • 4. 1 span, 2 loop

: single section in lowest asymmetric MOde"

5340 PRINT • 5. 3 span, Middle section : the middle of

3

coupled sections lends fixed)•

5350 PRINT • •rABt32) •in sywEtric up-down-up 10tion Uowest lode) •

53GO PRINT • 6. 3 span, end section

: end section of 5. •

5370 LOCATE 7,1:PRINT

"I

Output : stationary solution ••• aaximu. and 1inimua of tension and•

5380 PRINT •tTABI14)•vertical displacement as function of the

a~plitude

of the first•

5390 PRINT • •TABI14)•harmonic ••• variation in

ti~e

for given aMplitude ••• tension•

5400 PRINT • •rABI14) •variation in cable or suspension chain ••• frequency ••• energy•

5410 LOCATE

,1:PRINT •r•;STRINS$178,196);"1•;

5420 LOCATE 23

1

1:PRINT • KEYS: ITab)=for..ard

<Ret>

=select

<Crsr Up/Dn)=choose"

5430 LOCATE 24, !:PRINT • • TABUU • CEsd=back..ard

IBcksp}=select backNard <PgUp/Dn}

=top/bott01•;

(21)

table

submenu a-mode

logo

help screen,

.,_...,..10--i

description end of session ? main menu plot dV-dT results submenu t-mode plot time va rlation

(22)

CABLE

version 88.06.26

by S.W. Rienstra

Wiskundige Dienstverlening Katholieke Universiteit Nijmegen

figure 2. Logo

an interactive program f'or IBM Personal Comp1.1ters and compatibles to analyse the dynamics of free vibrations of suspended elastic

cables in a number of' elementary configurations 1

1. multispan, 2-periodic 1 sections, coupled via suspension chains, in

even number of spans section

symmetric up-down-up etc. motion (lowest mode)

1 up-down periodic' effectively described by 1.

end section of semi-infinite version of 1. single section in lowest symmetric mode 2. multispan, end

3. 1 span, 1 loop 4. 1 span, 2 loop 5. 3 span, middle

1 single section in lowest asymmetric mode

section 1 the middle of 3 coupled sections (ends fixed)

in symmetric up-down-up motion <lowest mode)

6. 3 span, end section 1 end section of 5.

Output 1 stationary solution ••• maximum and minimum of tension and

vertical displacemeYrt as function of the amplitude of the first harmonic ••• variation in time for given amplitude ••• tension variation in cable or suspension chain ••• frequency ••• energy

KEYS I <Tab>=forward <Esc)•backward <Ret> •select <Bcksp>•select backward <Crsr Up/Dn>•choose <PgUp/Dn> •top/bottom

(23)

1> configuration <1a)

=

multispan <cable>

2) presentation mode • dV-dT

3> span S <m> .. 325

4) mass <no ice> mO <kg/m) . . . 9891

5> ratio mass with/without ice .. 1. 1

6> area cross section A <mm2) - 280

7) horiz. tension <no ice) HO (N) • 12650

8) Young's modulus E (N/mm2) • 77000

9) gravit. acceleration g (m/s2) • 9.80665

10> additional information • yes

figure 4. Main menu

Res\.tlts I

without ice with

tuag

...

10.1310 m sag

..

tension

-

12748.211 N tension

..

hor. tens.

..

12650.000 N hor. tens •

..

ver. tens.

-

1579.358 N ver. tens.

-length

-

325.6491 m length

...

frequency 111 E .,. }1 ... 0.031425 0.649154 k .. g

-figure 5. Stationary results, some basic parameters

ice 10.2335 13884.478 13775.360 1737.294 325.6491 0.173051 3.141593 2.531185 m N N N m Hz

(24)

dV-dT 1 multispan <dT in cable>

1> max

o

.... &

2) max dV <m>

=

9 3) max dT <N>

=

7000

figure 6. Submenu amplitude-mode (for dY- dT)

dV<t>,dT(t) 1 multispan <dT in cable)

1) max time <s> = 20

2) max dV (m) • 8

3) max dT <N> • &000

4) 0 . . . 5

(25)

multi span (dT in cable) 6 dT dY frq En 0.0600 -32.892 73.414 -0.3873 0.6404 0.1729 39.48 0.0900 -119.008 163.181 -0.8607 0.9802 0.1728 88.83 0.1200 -211.570 293.654 -1.1204 1. 3328 0.1723 157.92 0.1500 -330.578 458.835 -1.3664 1.6982 0.1722 246.73 0.1800 -476.032 660.722 -1.5984 2.0762 0.1719 355.32 0.2100 -647.932 899.316 -1.8163 2.4667 0.1714 483.63 0.2400 -846.279 1174.617 -2.0200 2.8696 0.1709 631.68 0.2700 -1071.072 1486.625 -2.2094 3.2847

o.

17(13 799.47 0.3000 -1322.311 1835.339 -2.3844 3.7118 0.1697 987.00 0.3300 -1399.996 2220.761 -2.5448 4.1310 0.1690 1194.27 0.3600 -1904.127 2642.889 -2.6904 4.6019 0.1682 1421.28 0.3900 -2234.705 3101.723 -2.8212 5.0646 0.1674 1668.03 0.4200 -2591.729 3597.265 -2.9370 5.5388 0.1665 1934.52 0.4500 -2973.199 4129.513 -3.0463 6.0244 0.1655 2220.73 0.4800 -3385.113 4698.469 -3.1635 6.5214 0.1645 2526.72 0.5100 -3821.478 5304.130 -3.2882 7.0293 0.1634 2852.43 0.3400 -4284.286 5946.499 -3.4207 7.5486 0.1622 3197.88 0.5700 -4773.541 6623.575 -3.5609 8.0787 0.1610 3563.08 0.6000 -3289.242 7341.357 -3.7090 8.6196 0.1597 3948.01