Voorbeeldberekeningen met het programmapakket LIMSET

(1)

Voorbeeldberekeningen met het programmapakket LIMSET

Citation for published version (APA):

van Hoogstraten, P. A. A. (1987). Voorbeeldberekeningen met het programmapakket LIMSET. (DCT rapporten; Vol. 1987.037). Technische Universiteit Eindhoven.

Document status and date: Gepubliceerd: 01/01/1987

Document Version:

Uitgevers PDF, ook bekend als Version of Record

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.

• The final author version and the galley proof are versions of the publication after peer review.

• The final published version features the final layout of the paper including the volume, issue and page numbers.

Link to publication

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

• You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:

www.tue.nl/taverne Take down policy

If you believe that this document breaches copyright please contact us at: openaccess@tue.nl

providing details and we will investigate your claim.

(2)

WFW 87.037

V O ~ ~ B E E L D B E R E ~ E N I N G E ~ MET

HET P ~ ~ G ~ A ~ P ~ K K E ~ LI’MSET

P.A.A. van Hoogstraten j u l i 1987

VAKGROEP FUNDAMENTELE WERKTUIGKUNDE FACULTEIT DER WERKTUIGBOUWKUNDE TECHNISCHE UNIVERSITEIT EINDHOVEN

(3)

in deze voorbeeldenverzameling zijn de berekeningen met het programmapakket LINSET opgenomen, waarnaar wordt verwezen in WFW-rapport 87.036: "Het bepalen van periodieke evenwichtsoplossingen van niet-lineaire dynamische (rotor-)systemen"

zoals dat op het beeldscherm verschijnt wanneer met LIMSET wordt gewerkt.

Sporadisch wordt commentaar gegeven met teksten tussen haken: [commentaar].

Regelmatig wordt bij vragen een voorstel voor het: antwoord gegeven. U i t

voorstel wordt door ronde haken omgeven: (voorstel). Wanneer de gebruiker dit voorstel wil accepteren, volstaat het: intoetsen van de returntoets. Dit wordt aangegeven met het symbool <cr> of met het niet afdrukken van een

antwoord. Met het intoetsen van de returntoets kunnen ook de menus, behorend

bij de zogenaamde COIN-structuur van LIMSET, worden opgeroepen.

(4)

Inhoudsowave

INLEIDING INHOUDSOPGAVE

HOOFDSTUK

1

: BEREKENINGEN AAN DE DIFFERENTIAALVERGELIJKING VAN DUFFING

$1.1 : De invoerfile 1.1

$1.2 : De systeemdefinitie 1.2

$1.3.1 : Statische evenwichtsberekening i v 3

$1.4 : Berekeningen uit $2.2.2: p=-O.O4, D=O.I 1.9

$1.4.1 : Statische evenwichtsberekening 1.9

$1.4.2 : Gedwongen responsieberekening 1.10

$1.4.3 : Periodieke evenwichtsberekening 1.11

$1.3 : Berekeningen uit $2.2.2: p=O.O4, D=0.1 1.3

$1.5 : Berekeningen uit $2.2.3: p=O.O4, D=0.01 1.17

$1.5.1 : Statische evenwichtsberekening 1.17

HOOFDSTUK 2 : BEREKE~INGE~ AAI? DE DUFFING-VERGELIJKING VAN BECKER EX SEYDEL

$2.1 : De invoerfile 2.1 $2.2 : De systeemdefinitie 2.2 $2.3 : Statische berekeningen 2.3 $2.3.1 : Statische evenwichtsberekening 2.3 $2.3.2 : Gedwongen responsieberekening 2.4 $2.4 : Periodieke evenwichtsberekeningen 2.5

$2.4.1 : Berekening van de primaire tak 2.5

$2.4.3 : Berekening van de tweede secundaire tak 2.15

$2.4.2 : Berekening van de eerste secundaire tak 2,IO

HOOFDSTUK 3 : BEKEKENUWXN AAN DE DSFFEKENTSAALVERGELIJKING VAN VAM DER POL

$3.1 : De invoerfile 3.1

$3.2 : De systeemdefinitie 3.2

$3.3 : Berekening van een periodieke startoplossing 3.3

$3.4 : BCM-berekening vanuit de gevonden startoplossing 3.5

HOOFDSTUK 4 : BEREKENINGEN AAN HET RUBBING-PROBLEEM

$4.1 : De invoerfile

$4.2 : De systeemdefinitie

$4.3 : Berekeningen aan het ongeëxciteerde systeem

$4.3.1 : Statische evenwichtsberekening

$ 4 ’ 3 . 2 : Stabilitietsbepaling van de gevonden statische

$4.3.3 : Periodieke evenwichtsberekening vanuit de

evenwichten Hop€-bifurcatie

$4.4 : Berekeningen aan het geëxciteerde systeem

$ 4 . 4 . 1 : Statische evenwichtsberekening $4.4.2 : Gedwongen responsieberekening $4.4.3 : Periodieke evenwichtsberekening 4.1 4.2 ~ 4.4 4.4 4.5 4.7 4.12 4.12 4.13 4.14

(5)

Hoofdstuk 1: Berekeninaen aan de differentiaalverqeliikina van Duffing 31.1: De invoerfile C C C C C C C C C C C C

c

. . .

*

INVOER VOOR HET DUFFING-PROBLEEM

*

. . .

*

vergelijking: ji i. 2 D ir -i- x i x3 = cos(uit) = cos(Srrft1

x := QC(1)

D := QR(1) ; DAMPING

:= QR(2) ; KUB.STF

f := QK(3) ; FKEQ. [HZ]

SUBROUTINE FT(QFL,QA,QW,QCfQR,QTrNV,NR,NS) IMPLICIT DOUBLE PRECISION (A-H,O-Z)

DIMENSION QFL( 1)

,

QA(

I}

,QV( 1)

,

QC( 1) QR(3) ,QT( 1

QFL( 1 )=QA( 1 ) +2UO*QR( 1) *QV( 1 )+QC( I )+QR(2) *QC( 11*QC( 'I *QC(

1

RETURN

END

SUBROUTINE F ~ 0 R ( Q R E , Q 1 M , Q R , ~ ~ 0 R , N ~ , N R ~

IMPLICIT DOUBLE PRECISION (A-H,O-Z) DINENSION QRE(I),QIMll),QR(3) QHE( 1 )=I130 QIM(I)=ODO RETURN END S'JBROUTTNE ~ M ~ ~ Q M A , Q A , Q ~ , Q C ~ Q R ~ Q T ~ N V , N R , N S ) DINENSION QMA( I I 1 ) i QA ( 1 1 QV( 1 1 QC ( 1

1 ,

QR ( 3

,

QT ( 1 QMA(l,'I)=lDO RETURN END SUBROUTINE FMV(QMV,QA,QV,QC,QR,QTfNVfNRfNS) IMPLICIT DOüBLE PRECISION (A-H,O-Z)

DINENSION QMV(I,1),QA(1)IQV(1),QC(l),QR(3),QT(1) QMV(I,I)=SUO*QR(l)

RETURN END

SUBROUTINE FMC(QMC,QA,QV,QC,QR,QT,NV,NR,NS) IMPLICIT DOUBLE PRECISION (A-H,O-Z)

DIMENSION QMC( 1

,

1) ,QA(

I

} ,QV( 1) ,QC( 1)

,

QR(3)

,

QTf 1

QMC(1,1)=1U0+3~0*QR(2)*QC(1)*QC(1)

RETURN END

(6)

-1.2- $1.2: De systeemdefinitie [aanroep programma] $ DUFETNG

. . .

*

LL 1111 M~

MMM

SSSSSSSS EEEEEEEE TTTTTTTTTT

*

SSSSSSSSS EEEEEEEE TTTTTTTTTT

*

LL I'l: M ~ M M MM^ I1 PM MM MM MM SSSS EE TT

*

LL I1 MM MM^ MM SSSS EE TT

*

LL I1 MM MM PlM

sssssss

EEEEEEE TT

*

LL

*

LL I1

m

Mp9 SSSS EE TT

*

LL I'd MM MM SSSS EE TT

*

LLLLLLLL I1 IviM PlM SSSSSSSSS EEEEEEEE TT

*

LLLLLLLL IT11 MMMM ~M~ SSSSSSSS EEEEEEEE TTTT

*

. . .

*

LL IT NM MM SSSSSSS EEEEEEE TT

*

PROGRAMMA VOOR HET BEREKENEN VAN STATISCHE EVENWJ'CHTSSTANDEN PERIODIEKE OPLOSSINGEN EN QUASI PERJODIEKE OPIIOSSINGEN

ALSMEDE DE STABILITEIT VAN DEZE OPLOSSINGEN

ZOAXS DEZE KUMNEN VOORKOMEN IN

STELSELS NIET LïNEAIRE GEWONE DIFFERENTlA~LVERGEL~J~INGEN

VAN UE TWEEDE ORDE

VEXDERE INFORMATIE BIJ HARC CKOOIJMANS

Give identification of problem (IDENTIFICATIE)? DUFFING

ENTER COMMAND: ter>

GM

-

GLOBAL-MENU SD

-

SYSTEM-DEFINITION CA

-

CALCULATION EX

-

EXECUTE RS

-

RESULTS R

-

RESTORE-FILE S

-

SAVE-FILE PR

-

PROGRAM-FILES Q

-

QUIT

(7)

ENTER CONMAND: SD

System definition: Number of genesalised coordinates ( O ) ? 1

System definition: Number of design variables ( O ) ? 3

System definition: Number of forced periods ( O ) ?

I

System definition: Minimum number of forced periods ( O ) ? O

System definition: forced period number 1

Give design variable number for period time ( O ) ? 3 System definition: Design variable nr. 1

Give name os description (max.16 char.) O ? DAMPING

Give units (niax.8 char. 1 ( I ?

Give name o r description (max.16 cliar.)

O?

#UB.STF

Give units (max.8 char.) O?

Give name or description (max.16 char.) O ? FREQ.

Give units (max.8 char.) O ?

is stiffness matrix explicitly given(O=yes, l=no) ( O ) ? O

Is dempingmatrix explicitly given(Q=yes,l=no) ( O ) ? 0

is massmatrix explicitly given(O=yes,l=no) ( O ) ? O

Design variable derivatives given(O=yes,l=no) (O)? O

ENTER COMMAND:

System definition: Design variable nr. 2

$1.3: Berekeninsen uit $2.2.2: u=O.O#. D=O.I

$1.3.1: Statische evenwichtsberekeninq ENTER CONMAND: <cr> GM

-

GLOBAL-MENU SD

-

SYSTEM-DEFINITION CA

-

CALCULATION EX

-

EXECUTE RS

-

RESULTS R - RESTORE-FILE S

-

SAVE-FILE PR

-

PROGRAM-FILES Q

-

QUIT ENTER COMMAND: CA CALCULATXON EMTER COMNAND: <cr> GM

-

GLOBALMENU CR

-

CREATE DE

-

DELETE IN - INFORM CALCULATION ENTER COMMAND: CR O : Return 1 : Equilibrium 2 : Stability 3 : Forced response

(8)

-1.4-

Give number fox kind of calculation ( O ) ?

1

Give label of calculation ( 1 2 SA

Startpoint: Regularzl, Singular=2 (I)? 1

Startpoint: Same order=l, Lower order=S (I)? 1

Startpoint: Manual input=i, From data base=2 (I)? 1

Give parameter value ( . O ) ? 0.1 Give parameter value ( . O ) ? 0.04

Give parameter value ( . O ) ? O

Give design variable nmber that varies in calc.proc. (I)? 1

Give dimension of equilibrium ( O ) ? O START POINT OF EQUILIBRIUM

1

DAMPING

2 KUB. STF

3 FREQ

.

Total number o f values to be given is 1

Item number 1

Give item value ( . O ) ? 1

Give direction of des.variable (positiv or negativ) ( . O ) ?

1

Stepsize criteria in BCM algoritm

Fixed stepsize (y)? Y

Give initial stepsize ( . O ) ? 0.01

STOP CRITERIA AFTER EACH CALCULATION STEP Convergence criterium parameter eps (.IE-8)?

Nax. iterations in one step (SO)?

STOP CRITERIA OF ENTIRE CALCULATION

Hax. value for design variables ( . O ) ? 1 Max. number o f steps (IO)?

1

O : Return

1

: Eyuj.librj.um

2 : Stability

3 : Forced response

Give number for kind of calculation ( O ) ? O CALCULATION ENTER COMMAND: / ENTER C O M ~ ~ N D : < c r > GM

-

GLOBAL-HEMU SD

-

SYSTEN-DEFINITION CA - CALCULATION EX - EXECUTE RS

-

RESULTS R

-

HESTOKE-FILE S

-

SAVE-FILE PR

-

PROGRAM-FILES Q

-

QUIT ENTER COMMAND: EX Trace calculation (n)? N

(9)

1 1 . 3 . 2 : Gedwonqen responsieberekeninq ENTER COMBAND: /CA CR

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind o f calculation ( O ) ? 3

SUMMARY OF OBTAINED RESULTS Give label of calculation ( I ? SA

61ve equilibrium point number ( I ) ? 1

Give time number of forced response calculation ( I ) ? 1

Give number of calculation (2O)? 100

Equidistant frequencies in interval (y)? Y

GIVE FREQUENCIES OP FORCED EXCITATION (HERTZ)

Give start value of range ( . O ) ? 0.0 Give last value of range ( . O ) ? 0.5

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind of calculation ( O ) ? CALCULATION

ENTER COMMAND: /EX EJ SA

[ grafische uitvoer

I

ENTER COMMAND: /RS PL

Do you want to store plot in a plotfile (n)? N

SUMNARY OF OBTAINED RESULTS Give label o f calculation O ? SA

SA

DESIGN VARIA8LES VALUES

Nr: 2 KUB.STF =.o4

Nr: 3 EREQ. = . O

DISCRETISATION DATA

Dimension o f equilibrium is O CALCULATION SA

Number of equilibrium calculations made are 1

Design variable with name DAMPING is varied

First value . I Last value . I

O : No more data

1 : Of calculation process

2 :

3 : In one equilibriumpoint

Choose kind of data that you want ( O ) ? 3

1 : Equilibrium data vs. equilibrium data

2 : Equilibrium data vs. time

3 : Eigenvalues and eigenforms

4 : Eigenform data vs. time

5 : Forced response data

Choose betweem alternatives ( I ) ? 5

(10)

-1

-6-

units

SUMMARY of forced response calulation for point nr.

1

Give time number of forced response calculation (I)? I

Amplitude diagram (=I) or phase diagram ( = 2 ) (I)?

1

Give start value of range (I)?

1

Give last value o f range ( I O O ) ? 100 Do you want symbols in points (y)? Y Do you want origin in plot (y)? Y

Design variable nr name

Forced timenr. Number of calc. First freq. Last freq.

I

1

O0 .O .5

1

DAMPING

2 KUB. STF

3 FREQ

.

Give datanr. to be printed (O=coiitinue) ( O ) ?

1

Design variable nr name units

1 DAMPING

2 KUB. STF

3 FREQ

.

Give datanr. to be printed (O=continue) ( O ) ? 2

1

DAMPING

2 KUB. CTF

3 FREQ

.

Give datanr. to be printed (O=coatinue) ( O ) ? O

O : No more data

1 :

Of calculation process

2 :

Choose kind of data that you want ( O ) ? O Continue (n)? N A s a function of equilibriumpoints RESULTS DWFJNG 6'w

F

5.w 4.w

1

3.m 3 zw 1.00 0.53 0.00 1.03 2.w 3.m m. 4.M *IO-' 5.03 SA iATWNG .1 XJñSiF M

(11)

31.3.3: Periodieke evenwichtsberekening

ENTER COMMAND: /CA CR

O : Return

1 : Equilibrium

2 : StabilLty

3 : Forced response

Give number for kind o f calculation ( O ) ? 1 SUMWRY OF OBTAINED RESULTS

Give label o f calculation ( ) ? PA

Startpoint: Regulitr=?, Singular=2 ( I ) ? I

Startpoint: Same order=li Lower 0rder=2

(I)?

2

Startpoint: Manual input=l, From data base=S (I]? 2

SUMMARY OF OBTAINED RESULTS

SA

PA SA

Give identification o f old calculation ( ) ? SA Give stepnumber o f solution (I)?

I

SUMMARY o f forced response calulation f o r point nr.

1

Forced timenr. Number of cafc. First freq. Last freq.

1 1 O0

.o

.5

Give calculation number (I)?

I

DESIGN VARIABLES VALUES

Nr: 1 DAMPING = * 1

Nr: 2 KUB.CTF =.O4

Ni-: 3 FREQ. = . O

Give design variable number that varies in calc.proc. ( O ) ? 3

Discretisation i : l=Single, 2:Double, 3=variable

(I)?

1

f Single := tweede orde differentieschema's

f

f Double := vierde orde differentieschema's

1

Number of discretisation points (I)? 40

Give direction of des.variable (positiv or negativ) ( . O ) ? 1 Stepsize criteria in BCM algoritm

Fixed stepsize ( y ) ? N

Give initial stepsize ( . O ) ? 0.001 Give minimum stepsize ( . O ) ? 0.0001 Give maximum stepaize ( . O ) ? 2.5

Stepsize criterium parameter a l f 1 ( . O 5 ) ? 0.05 Stepsize criterium parameter alf2 ( . 8 ) ? 0.8

STOP CRITERIA AFTER EACH CALCULATION STEP

Convergence criterium parameter eps (.1E-8)? @ax. iterations in one step (5Q)?

STOP CRITERIA OF ENTIRE CALCULATION Max. value for design variables ( . O ) ? 1.0

Max. number of steps (IO)? 100

O : Return

I : Equilibrium

2 : Stability

3 : Forced response

Give number for kind o f calculation ( O ) ? CALCULATION

ENTER COWAND: /EX N

[ Gemiddeld wordt elke evenwichtsoplossing geaccepteerd na 1 predictorstap

en 3 correctorstappen. Elke stap kost ongeveer 0.43 seconden CPU-tijd.

(12)

-1.8-

ENTER COMNANI): /RS pr,

SUMARY OF OBTAINED RESULTS

PA

SA

Give label of calculation O? PA

DESIGN VARIABLES VALUES

Nr: 1 DAMPING =, 1

Nr: 2 KUB.STF =.O4

DISCRETISATION DATA

Dimension of equilibrium is 1

First perind: discsetisation scheme nr I, number of points 40

period time is forced by design variable nr. 3

CALCULATION PA

Number o f equilibrium calculations made are 38

Design variable with name FREQ. is varied

First value .O Last value 1.728

O : No more data

1 : Of calculation process 2 :

Choose kind of data that you want ( O ) ? 2 Give first and last equilibrium point ( I ) ?

1

Give last eyuilibsium point ( 3 8 ) ? 3 5

I : Coordinate information

2 : Varied design variable

3 : First period time

4 : Second period .time

5 : Eigenvalue information

Choose data along axis (I)? 1

Number o f lines you want to get (I)? 1

1 : Problem coordinates

2 : Displacements

3 : Velocities

4 : Accelerations

Choose display form ( 2 ) ? 2

1 : Coordinate

2 : Amplitude

3 : Mean value

4 : Nean square deviation

Give information you want ( I ) ? 2

Do you want stepnumbers along x-axis (n)? N

1 : Coordinate information

4 : Second period time

Choose data along axis ( 1 ) ? 2

Do you want symbols in points ( y ) ? Y

DO you want origin in plot (n)? Y

As a function of equilibriumpohts

TYPE OF DATA ALONG THE Y-AXTS

TYPE OF DATA ALONG THE X-AXIS

1

DAMPING

2 KUB. STF

3 FñEQ ,

(13)

I PA 3.m 4.w +IO' 1.w 203 m. 0.m COOK =I O : No more data 1 : O f calculation process 2 : 3 : in one equilibriumpoint

Choose kind o f data that you want ( O ) ? O Continue

(n)?

N

RESULTS

A s a function of equilibriumpoints

31.4: Berekeninsen uit 12.2.2: u=-O.O4. ü=O.I 31.4.1: Statische evenwichtsberekeninq

ENTER COPIMAND: /CA CR

o

: xieturn

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind o f calculation ( O ) ? 1 SUMMARY OF OBTAINED RESULTS

PA CA

Give label o f calculation O ? CB Startpoint: Xeyular=l, Sinyular=2 (I)?

Startpoint: Same order=l, Lower order=:! (I)? Startpoint: Manual input=l, From data base=2 (I)?

1 DAHPING Give Give Give Give Give parameter value ( . O ) ? 0.1 parameter value ( . O ) ? -0.04 2 KUB. CTF 3 FREQ

.

parameter value ( . O ) ?

design variable number that varies in calc.proc. (I)?

(14)

-1.10-

START POINT OF EQUILIBRIUM

Total number of values to be given is 1 Item number 1

Give item value ( . O ) ?

Give direction of des.variable (positiv or negativ) ( . O ) ? Stepsize criteri.a in RCM algoritm

Fixed stepsize ( y ) ?

Give initial stxpsize ( . O ) ?

STOP CRITERIA AFTER EACH CALCULATION STEP Convergence cri.t:erium parameter eps (.IE-8)?

Max. iterations in one step (5O)?

STQP CRITERIA OF YNTLRE CALCULATION

Max. value for design variables ( . O ) ?

Max. number of steps ( I O ) ? 1

O : Return

I : Equilibrhm

2 : Stability

3 : Forced response

Give number for kind o f cafculatiun ( O ) ? CALCULATION

31.4.2: Gedwcmsen responsieberekening ENTER COMWND: /CA CR

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind of calculation (O)? 3

SB PA

SA

Give label of calculation O? SB

Give equilibrium point number

(I)?

1

Give time number of forced response calculation

(I)?

1

Give number of calculation (2O)? 100

Equidistant frequencies in interval ( y ) ? Y

GIVE FREQUENCIES OF FORCED EXCFTATTON (HERTZ)

Give start value of range ( . O ) ? O

Give last value of range ( . O ) ? 0.5

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

(15)

$1.4.3: Periodieke evenwichtsberekeninq

E

PBL = linker tak van A-f-curve ;

PSR = rechter tak van A-€-curve ]

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind o f calculation ( O ) ?

1

SIHMARY OF OBTAINED RESULTS

SR

PA SA

Give label o f calculation O? PEL

Startpoint: Regular=l, Singular=2 (I)? 1

Startpoint: Same order=li Lower order=2

(I)?

2

Startpoint: Manual input=l, From data base=2 (I)? 2

SUNMARY OF OBTATNED RESULTS

PBL

SE

PA

SA

Give identification of old calculation O? SB

Give stepnumber o f solution

(I)?

1

SUWMARY of forced response calulation for point nr. 1

Forced timenr. Number of calc. First freq. Last freq.

1 1 O0 .O .5

Give calculation number

(I)?

I

Nr: 1 DAMPING =. 1

Nr: 2 KUB.STF =- .O4

Nr: 3 FREQ.

=.o

Discretisation 1: l=Single, S:üouble, 3=variable

(I)?

1

Number o f discretisakion points (If? 40

Give direction of des.variable (positiv or negativ) ( . O ) ? 1

Stepsize criteria in BCM algoritm Fixed stepsize ( y ) ? N

Give initial stepsize ( . O ) ? 0.001 Give minimum stepsize { . O ) ? 0.0001 Give maximum stepsize ( . O ) ? 2.5

Stepsize criterium parameter alf1 (.O5)?

Stepsize criterium parameter alf2

(.BI?

STOP CRITERIA AFTER EACH CALCULATION STEP

Convergence criterium parameter eps (.lE-8)?

Max. iterations in one :step (50)?

STOP CRITERIA OF ENTIRE CALCULATION Max. value for desiyn variables ( . O ) ? O

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

(16)

-1.12-

SUMMARY OF OBTAINED RESULTS PBL

SB

PA

SA

Give label o f calculation O? PBR

Startpoint: Regular-I, Singular=2

(I)?

1

Startpoint: Same order=l, Lower order=2

(I)?

2

Startpoint: Manual input=l, From data base=2

(I)?

2

SUIVIMARY OF OBTAINED RESULTS PBL

PBR SB

PA SA

Give identification of old calculation

O?

SB

Give stepnumber of solution (I)? 1

SUNWARY of forced response calulation for point nr.

1

Forced timenr. Number of calc. First freq. Last frey.

1 1 00

.o

.5

Give calculation number [I)? 100 DESIGN VARIABLES VALUES

Nr:

I

DAMPING =. 1

Nr: 2 KUB.STF =- .O4

Nr: 3 FREQ. =.5

Give design variable number that varies in calc.proc. ( O ) ? 3

Discretisation 1: l=Single, 2:Double, 3=variable (I)? 1

Number of discretisation points ( I ) ? 40

Give direction o f des.variable (positiv or negativ) ( . O ) ? -1.0 Stepsize criteria in BCM algoritm

Fixed stepsize ( y ) ? N

Give initial stepsize ( . O ) ? 0.001 Give minimum stepsize ( . O ) ? 0.0001 Give maximum stepsize ( . O ) ? 2.5

Stepsize criterium pararneter alf1 ( . O s ) ?

Stepsize criterium parameter alf2 (.€!I?

Convergence criterium parameter eps (.1E-8)?

Max. iterations in one step (50)?

STOP CRITERIA OF ENTIRE CALCULATION Nax. value fox design variables ( . O ) ? O

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind o f calculation ( O ) ? O CALCULATION ENTER COMMAND: GM - GLOBAL-MENU CR - CREATE DE

-

DELETE IN

-

INFORM

(17)

CALCULATSON

ENTER COMMAND: fN

******General information about future calculations

number of equilibrium calculations = 2

number of stability calculations

= o

number of forced response calculations = O

CALCULATION

ENTER COMMAND: /EX N ENTER COMMAND: /RS PL

PBL.

PBR

SI3

PA SA

Give label of calculation O? PBL

Nr:

1

DAMPING = . I

Nr: 2 KUB.STX: =- .o4

DISCRETISATION DATA

Dimension of equilibrium is

1

First period: discretisation scheme nr

1,

number of points 40

CALCULATION PBL

Number o f equilibrium calculations made are 28

First value .O Last value

-

.0079S

O : No more data

1 :

2 :

3 : in one equilibriumpoint

Choose kind of data that you want ( O ) ? 2 Give first and last equilibrium point ( I ) ?

1

Give last equilibrium point ( 2 8 ) ? 27

TYPE OF DATA ALONG THE Y-AXIS

1

: Coordinate information

Choose data along axis (I)? I

Number of lines you want to get (I)?

1

2 : Displacements

3 : Velocities

4 : Accelerations

Choose display form (2)? 2

1 : Coordinate

2 : Amplitude

3 : Mean value

4 : Mean square deviation

Give information you want (

1

) ? 2

(18)

- 1 . 1 4 -

TYPE OF DATA ALONG THE X-AXIS

Do you want symbols in points (y)? Y

Do you want origin in plot {n)? N

1

RAMPING

2 KUB. STF

3 FXEQ

.

Give datanr. t o be printed (O=continue) ( O ) ?

1

DAMPING

2 KUB. ClTF

3 FREQ

.

Give datanr. to be printed (O=continuef ( O ) ? 2

1

DAMP ING

2 KUB. STF

3 FREQ

.

Give datanr. to be printed (O=continue) (O)? O

DIJEPING Lm 5.w

4 i

3.00 200 1.w 0.00 0.20 0.40 am 0.80 1.00 t20 m. *li' PEL ~~ DAMPING .1 K ü i Z S I F -.M CUOR. =1

-

O : No m(jLc data

1 :

Of calculation process 2 : 3 : In one equilibriumpoint

Choose kind of data khat you want ( O ) ? O

Continue (n)? Y

(19)

SUMMARY OF OBTAINED RESULTS PBL P8H SB PA SA

Give label of calculation O? PBR

Nr:

1

DANPING =.

1

Nr: 2 KUB.ST’F =- .O4

DISCRETISATION DATA

Dimension of equilibrium is I

First period: discretisation scheme nr

1,

number of points 40

CALCULATION PBR

Design variable with name FKEQ. is varied

First value .5 Last value -.2763E-4

O : No more data

1 : Of calculation process

2 : As a function of equilibriumpoints

3 : In one equilibriumpoint

Choose kind of data t h a t you want ( O ) ? 2

Give first and last equilibrium point ( I ) ?

1

Give last eyuifibrium point ( 2 6 ) ? 25

1

Choose data along axis (I)? I 1 2 2 N 2 Y N 1 2 O

TYPE OF DATA ALONG THE X-AXIS

O : No more data

Choose kind o f data that you want (O)? O

As a function of equilibriumpoints DUFFING 0.w 1.m 2.m 3.m 4m 5.m m. *löl m DAMPIïiG .I m s w -.o4 WOR. =1

-

(20)

-1.16- Continue (n)? N RE SULT S ENTER COMMANI): GM - GLOEAL-MENU IN

-

INFORM PL

-

PLOT PR

-

PKINT DE

-

DELETE RESrrLTS ENTER COMMAND: IN

SUiWíARY OF OBTAINED RESULTS

PBL POR SB PA SA

Give label of calculation

O?

PBL

CALCULATION PBL

First value . O Last value

-

.O0795

DISCRETTSATIOM 13A'PA

Dimension o f equilibrium is 1

First period: discretisation scheme nr 1 , number of points 40

Nr: 1 DAMPING =.

1 Mr:

2 KUB.STF =- .o4

0 : No

1

: On stability data

2 : On bifurcation data

3 : On forced response data

Further information ( O ) ? O RESULTS

ENTER COMPi&ND: IN PBR CALCULATION PBK

First value .5 Last value -.2763E-4

First period: discretisation scheme nr I, number o f points 40

DISCRETISATTON DATA

DESIGN VARIABLES VALUES 4p

Nr: 1 DAMPïNG =.

1

Nr: 2 KUB.STF =- .O4

0 : NO

1 : On stability data

3 : On forced response data Further information ( O ) ?

(21)

$1.5: Berekeninsen uit 12.2.3: u=O.O4, ü=O.Ol 31.5.1: Statische evenwichtsberekening

O : Return

1 : Equilibrium

2 : Stabj.lit:y

3 : Forced response

Give number f o r kind o f calculation ( O ) ? 1 SUMMARY OF OBTAINED RESULTS

PR?:

PBR

SS

PA SA

Give label of calculation ( ) ? CC

Startpoint: Regular=l, Singular=2

(I)?

1

(I)?

1

Startpoint: Manual input=l, From data base=2 (I)? 1 Give parameter value ( . O ) ? 0.01

Give parameter value ( .O)? O.O4

Give parameter value ( . O ) ? O

Give design variable number that varies in calc.proc. (I)? 1

Give dimension of equilibrium ( O ) ? START POINT OF EQUILIBRIUH

1 DAMPING

2 KUB. STF

3 FREQ

.

Total number o f values to be given is 1

Item number

I

Give direction of des.variable (positiv or negativ) ( . O ) ? 1 Stepsize criteria in BCM algoritm

Give initial stepsize ( . O ) ?

Convergence criterium parameter eps (

.

IE-8)?

Max. value for design variables ( . O ) ? Max. number of steps ( l o ) ?

1

O : Return

1 : Eyui.librj.um

2 : Stability

3 : Forced response

ENTER COMMAND: /EX N

(22)

-1 * 1%-

$1.5.2: Gedwoncien responsieberekening

O : Return

1 : Equilibrium

2 : Stabili-ty

3 : Forced response

Give number for kind of calculation ( O ) ? 3 SUMMARY OF OBTAINED RESULTS

PBL PRE SR PA SC SA

Give label of calculation O ? SC

Give equilibrium point number (I)? 1

Give time number of forced response calculation (I)?

Give number of calculation (SO)?

1

Equidistant frequencies in interval (y)?

GIVE FREQUENCIES OF FORCED EXCITATION (HERTZ) Give litark value of range ( . O ) ?

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind o f calculation ( O ) ? CALCULATION

ENTER COWAND: /EX N

$1.5.3: Periodieke evenwichtsherekening ENTER COMMAND: /CA CR

O : Keturn

1 : Equilibrium

3 : Forcect response

Give number for kind of calculation ( O ) ? 1 SUMMARY OF OBTAINED RESULTS

2 : Stability PBr.. PBR Si3 PA SC SA

Give label of calculation O? PC

Startpoint: Regular=l, Singular=S (I)? 1

Ctartpoint: Came order=l, Lower order=S ( i ) ? 2

(23)

SUWMAKY OF OBTAXNED RESULTS PEL PBR SB PC PA SC SA

Give identification of old calculation ( I ? SC

Give stepnumber of solution I 1 I ?

SUMMARY of forced response calulation for point nr. 1

FQ~cPCI ti.menr. Number of calc. First freq. Last frey.

1 I .O .O

Nr:

1

DANPING =.o1

N r : 2 KUB.STF =.O4

Nr: 3 FREQ. =.O

Discretisation 1: I=Single, 2:Double, 3=variable (I)? 1

Give direction of des.variable (positiv or negativ) ( . O ) ? 1.0

Stepsize criteria in BCM algoritm Fixed stepsize ( y ) ? N

Give initial stepsize (.O)? 0.001

Give minimum stepsize (.O)? O.00001

Give maximum stepsize ( . O ) ? 2.5

Stepsize criterium parameter alf1 ( . O 5 ) ? Stepsize criterium parameter alf2

( . a ) ?

Convergence criterium parameter eps (.lE-8)?

Pilax. iterations in one step ( S O ) ?

Max. value for design variables ( . O ) ? 1.0 Max. number of steps ( I O ) ? 150

O : Return

1 : Equilibrium

2 : Stability

3 : FOKCed response

Give number for kind o f calculation {O)? O

CALCULATION

ENTER COMMAND: /EX N

[ Gemiddeld wordt elke evenwichtsoplossing geaccepteerd na 1 predictorstap

en 2 correctorstappen, Elke stap kost ongeveer 0.43 seconden CPU-tijd ]

ENTER COMMAND: /RS PL

Do you want to stone plot in a p l o t f i l e (n)? N

SUMMARY OF OBTAINED RESULTS PBL PBR SB PC PA SC SA

(24)

-1.20-

DESIGN VAKIABLES VALUES

Nr: 1 DAMPING =.o1

Nr: 2 KUB.STF =.O4

DISCRETISATION DATA

First period: discretisation scheme nr I , number of points 40

CALCULATION PC

is varied

üesign variable with name FKEQ.

First value .O Last value 1.893

O : No more data

I : Of calculation process

Choose kind of data that you want ( O ) ? 2 Give first and last equilibrium point ( I ) ? 1

Give last equilibrium point ( 1 4 4 ) ? 142

3 : First gerj.od time

Number of lines you want to get (I)? 1

2 : Displacements

3 : Velocities

4 : Accelerations

Choose display form (2)? 2

1 : Coordinate

2 : Amplitude

3 : Mean value

Give information you want (I)? 2

Do you want atepnumbers along x-axis (n)? N

TYPE OF DATA ALONG THE X-AXIS

Choose data along a x i s ( I ) ? 2

Do YOU want origin in plot (n)? Y

1 DAMP ENG

2 KUB. STF

3 FHEQ

.

Give datanr. to be printed (O=continue) ( O ) ? 1 2 O

(25)

DUFFING

F

3.m 4.m 5.m 6M FRF.Q. *lÖ1 Lm 200 0.00 pc DAMPING .O1 m.sm .c4 O : No more data I : O f calculation process 2 : 3 : In one equilibriumpoint

Choose kind of data that you want ( O ) ? 3

I : Equilibrium data vs. equilibrium data

Choose betweem alternatives (I)? 1

CALCULATION PC

As a function o f equilibriumpoints

Design variable with name FREQ.

Give number of equilibrium points ( I ) ? 1

Give stepnumber of solution ( I ) ? 32

O : Return

1 ; Displacements

2 : Velocities

3 : Accelerations

Choose display form ( I ) ? 2

O : Return

1 : Displacements

2 : Velocities

3 : Accelerations

Choose display form ( 2 ) ? O

0 : Return

1

: Displacements

2 : Velocities

3 : Accelerations

Choose display form ( 'i I ? 1

Do you want origin in plot ( y ) ? Y

is varied

First value . O Last value 1.893

(26)

-1.22-

units

1 DAMPING

2 KUB. STF

3 FREQ.

Give datanr. to be printed (O=continue) ( O ) ? 1 2 3 O DUFFING 1.m r O : No more data 1 : O f calculation process 2 : 3 : In one equilibriumpoint

Choose kind o f data that you want ( O ) ? 3

1 : Equilibrium data vs. equilibrium data

Choose bekweem alternatives ( I ) ? 2

As a function of equilibriumpoints AMPING .O1 uB.sTP .M REQ. .o55383 Q.FUlNT 32 COOR. J

-

CALCULATION PC

Number o f equilibrium calculations made are 144

Give number of equilibrium points ( I ) ? 1

Give stepnuniber of solution ( I ) ? 32

TYPE OF DATA ALONG THE Y-AXIS

O : Return

1 : Displacements

2 : Velocities

3 : Acceleratinns

Choose display form (I)? 1

O : Keturn

1 : Displacements

2 : Velocities

3 : Accelerations

Choose display form (2)? O

Do you want origin in plot ( y ) ? Y

is varied

(27)

Design variable nr name

I

DAMPING

2 KUB. STF

3 FREQ

.

Give datanr. to be printed (O=continue) (O)? 1 2 3 0

1.50 1.W 0.50 P 3 8 O.M -1.W -L% units 3 0 3 t O : No more data 1 : Of calculation process 2 : 3 : In one equilibriumpoint

Choose kind of data that you want (O)? O

Continue (n)? N

RESULTS

(28)

(29)

Hoofdstuk 2: Berekeninsen aan de Duffina-veraeliikins van Becker & Sevdel 42.1: De invoerfile C C C

c

C C

c

C C C C C C

. . .

*

INVOER VOOR DE DUFFING-VERGELIJKING

*

VAN BECKER EN SEYDEL

*

. . .

*

vergelijking:

x

:= QC(1) k := QK(1) f := QR(2) 1 2 15 5 5 1 2

-

5

x

+

8 ,3 =

2

cos(wt) =

-

cos(S+ft) i i + - 25

1

= LIN.STF =

-5

= FREQ, [Hz] SUBROUTINE FT(QFfQA,QW,QC,QR,QTfNV,NRfNS) IMPLICIT DOUBLE PRECISION (A-H,O-Z)

DIHENSION QF( 1

1 ,

QA(

1

,QV( 1 ) I QC( 1

1 ,

QR(2

1 ,

QT ( 1

QF('l)=QA(1)+(4U-2)

*

Q V(l)+QR(l)*QC(l)+(~~O/l5DO)"QC~l~*QC~1)"QC~l~

RETURN END

SUBROUTINE FFOR(QRE,QTM,QR,IFOR,NV,NR) DIMENSION QRE(1) ,QIM(l),QR(2)

QRE(1)=2DO/SDO QIPJI(l)=OnO RETURN END

SUBROUTINE F ~ ( Q M ~ , Q A ~ Q V ~ Q C f Q R f Q T , N V r N R f N S ) DIMENSION QMA( i

,

1)

,

QA( 1)

,

QV(

1 )

,

QC(

1 )

,

QR(2)

,

QT( 1 )

QMA(

1 ,

1) =ID0 RETURN END SUBROUTINE F M V ( Q ~ ~ , Q A r Q V f Q C f Q R f Q T f N V f N R f ~ S ) DI'MENSXON QNV( 1

,

1 )

,

QA ( 1 QMV(Ifl)=4D-2 RETURN END SUBROUTINE FMC(QMC,QA,QW,QC,QR,QT,NV,NR~NS)

IMPLICIT DOUBLE PRECISION (A-H,O-Z)

DINENSXON QMC( 1

,

1

)

,

QB( 1) Q V ( 1)

,

QC( 1

,

QR(2)

,

QT ( 1 QMC (

1 ,

I

1

=QR ( 1

1 +

( 2 4DO/ I5 DO ) *QC ( 1 1 *QC ( 1

RETURN END

IMPLICIT DOUBLE PRECISION (A-H 0 - 2 )

IMPLICIT DOUBLE PRECISION (A-H

,

0-2 )

INPLICIT DOUBLE PRECISION (A-H,O-Z)

(30)

- 2 . 2 - SUBROUTINE ~R(QF,QA,QV,QC,QR,QT,IR,NV,NR,NS) DIMENSION QF( 1

1 ,

QA( 1 ) QV(

1 1,

QC( I

1

E QR( 2

1 ,

QT (

1

GOTO (1,2),1R I QF(I)=QC(l) GOTO 3 2 QF(I)=ODO COT0 3 3 RETURN END

IMPLICIT DOUBLE PRECISION (A-H,O-Z)

$2.2: De svsteemdefinitie [aanroep programma] $ BECSEY

. . .

*

LL

m r

~ N M MM MM ~ SSSSSSSS EEEEEEEE TTTTTTTTTT

*

IX MM MMNMM SSSSSSSSS EEEEEEEE TTTTTTTTTT

*

LL I1 MM MM MM MM SSSS EE TT

*

LL

*

LL IT MM MMNM NM SSSS EE TT EEEEEEE TT

*

LL XI

m

NiM

sssssss

TT

*

LL IT MM MM SSSSSSS EEEEEEE SSSS EE TT

*

LL

I1

NM MM NM SSSCSSSSS EEEEEEEE TT

*

LLLLLLLL

11

MM

*

LLLLLLLL IIII MMMM M ~ NSSSSSSSS ~ EEEEEEEE TTTT

*

. . .

*

LL I1 c4M

m

SSSS EE TT

PROGRAMMA VOOR WET BEREKENEN VAN STATISCHE EVEN~rCW~SST~NDEN

PEHIODTEXE OPLOSSINGEN EN QUASI PERIODIEKE 0PIK)SSINGEN ALSMEDE DE STABILITEIT VAN DEZE OPLOSSINGEN

ZOALS DEZE KUNNEN VOORKOWEN IN

STELSELS NIET LïNEAIRE GEWONE D ï F F E R E N T ~ A ~ L ~ E R G E L I J ~ ~ N G E N

VAN DE TWEEDE ORDE

VERDERE INFORMATIE BIJ MARC CROOIJNANS

Give identification of problem (IDENTIFICATIE)? 'BECKER & SEYDEL'

ENTER CONMAND: /Sû

System definition: Number of generalised coordinates (O)?

1

System definition: Number of design variables ( O ) ? 2

System definition: Number of forced periods (O)? 1

System definition: Minimum number of forced periods ( O ) ? O

System definition: forced period number 1

(31)

Give name or description (max.16 char.) O ? LIN.STF.

Give units (max.8 char.) O ?

Give name or description (nax.16 char.) ( ) ? FREQ. Give units (max.8 char.) O?

Is stiffness matrix explicitly given(O=yes,l=nu) (O)? O

i s dempingmatrix explicitly given(O=yes,l=no) (O)? O

Is massmatrix explicitly given(O=yes,l=no) ( O ) ? O

Design variable derivatives given(O=yes,l=no) (O)? O

ENTER COMNANU:

8 2 . 3 : Statische berekenhaen

$ 2 . 3 . 1 : Statische evenwichtsberekeninq

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number f o r kind of calculation (O)? I

Give label of calculation O? SA

Startpoint: Kegular=l, Singular=2 (I)?

1

Ctartpoint: Came order=l, Lower order=2

(1)?

1

Give parameter value ( . O ) ? -0.2 Give parameter value ( . O ) ? O

Give design variable number that varies in calc.proc. Give dimension of equilibrium ( O ) ? O

START POINT OF EQUILIBRIUM

1 LIN. STF

.

2 FREQ

.

Total number of values to be given i s 1

item number

1

Give direction o f des.variable (positiv or negativ) (

Stepsize criteria in BCM algoritm

STOP CRITERïA AFTER EACH CALCULATION STEP

Convergence criterium parameter eps (.IE-8)?

Max. iterations in one step

(so)?

STOP CRPTER'CA OP ENTIRE CALCULATXON Max. value for design variables ( . O ) ? Wax. number of steps ( I O ) ? 1

O : Return

1 : Equj.librium

2 : Stability

3 : Forced response

ENTER COMMAND: EX

Trace ca1culatj.m (n)? N

(I)?

1

(32)

-2.4-

32.3.2: Gedwonaen responieberekeninq ENTER COMMAND: /CA CR

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind of calculation (O)? 3

Give label of calculation O? SA

Give equilibrium point number ( I ) ?

Give time number of forced response calculation (I)?

Give number of calculation (ZO)? 100

Equidistant frequencies in interval (y)?

GIVE FREQUENCIES OF FORCED EXCXTATION (HERTZ)

Give start value of range ( . O ) ? O

Give last value of range (.O)? 0.35

O : Return

I : Equilibrhm

2 : Stability

3 : Forced response

Give number f o r kind o f calculation ( O ) ? CALCULATION ENTER COWAND: EX Trace calculation (n)? N SA

=.o

ENTER COMMAND: /RS IN

SUMMARY OF OBTAINED RESULTS Give label of calculation f ) ? SA CALCULATION SA

C A

Number of equilibrium calculations made are

1

is varied liesign variable with name LIN.STF.

First. value -.2 Last value -.2

DISCRETISATION DATA

Dimension of equilibrium is O

NI: 2 FREQ.

O : No

1 : On stability data

Further information (O)? 3

SUMMARY of forced response calulation for point nr.

1

Forced timenr. Number of calc. First freq. Last freq.

1

1 00 .O .35

O : Nü

2 : On bifurcatjm data

(33)

32.4: Periodieke evenwichtsberekeninqen 32.4.1: Berekenins van de primaire tak ENTER COMMAND: /CA CR

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind of calculation (O)? 1

Give label o f calculation O? PA

(I)?

1

Startpoint: Same order=lr Lower 0rder=2 (I)? 2

SA

PA SA

Give identification o f old calculation

O?

SA

Give stepnumber o f solution ( I ) ?

1

SUMMARY of forced response calulation for point nr. 1

Forced timenr. Number o f calc. First freq. Last freq.

1 1 O0

.o

. 3 5

Give calculation number (I)? 100

DESIGN VARIABLES VALUES

Nr: I LIN.hiTF. =-.2

Nr: 2 FKEQ. =. 3 5

Give design variable number that varies in calc.proc. (O)? 2

Discretisation

I:

I=Cingle, 2:Double, 3=variable (I)? 2

Give direction of des.variable (positiv or negativ) ( . O ) ? -1

Stepsize criteria in BCM algoritm

Fixed stepsize (y)? N

Give initial stepsize ( . O ) ? 0.05 Give minimum stepsize ( . O ) ? 0.OûOOO1

Give maximum stepsize (.O)? 1.0

Stepsize criterium parameter a ï f l ( . O S ) ?

Stepsize criterium parameter alf2 ( . û ) ?

Convergence criterium parameter eps (.IE-8)? .1E-12

Max. value for design variables (.O)? 0.1

Max. number of steps ( I O ) ? 200

O : Return

1

: Equilibrium

2 : Stability

3 : Forced response

ENTER COMNAND: EX

Trace calculation (n)? N

[ Gemiddeld wordt elke evenwichtsoplossing geaccepteerd na

1

predictorstap

en 3 correctorstappen. Elke stap k o s t ongeveer 0.4.3 seconden CPU-tijd.

Voor het bepalen van een evenwichtsoplossing is dus ongeveer 1.7 s CPU

(34)

-2.6-

ENTER COMMAND: /RS IN

SUMWARY OP OBTAINED RESULTS

PA

SA

Give label o f calculation O? PA

CALCULATION PA

Design variable with name FKEQ. i s varied

First value .35 Last value .O9159

Dimension of equilibrium is

1

Fixst period: discretisation scheme

nr

2 , number o f points 40

DISCRETISATION DATA

DESSGN VARIABLES VALUES

Nr: 1 LIN.CTF. =-.2

O : No

Further information (O)? O

RESULTS

ENTEK COMPIAND: /RS PL

SUM MAR^ OF OBTAINED RESULTS PA

SA

Give label of calculation O? PA

DESIGN VARIABLES VALUES DISCXETSSATIOM DATA

Nr:

1

LïN.STF. = - . 2

Dimension of equilibrium is

1

First period: discretisation scheme

nr

2, number of points 40

period time is forced by design variable nr. 2 CALCULATION PA

Design variable with name FKEQ. is varied

First value .35 Last value .O9159

O : No more data

Choose kind of data that you want ( O ) ? 2

Give first and last equilibrium point (I)?

Give last equilibrium point ( 6 1 ) ?

1 : Coordi.nate information

3 : First perj.od time

Number o f lines you want to get (I)? 1

2 : Displacements

3 : Velocities

4 : Accelerations

As a function of equilibriumpoints

(35)

I : Coordinate

2 : Amplitude

3 : Mean value

Give information you want (I)? 2

TYPE OF DATA ALONG THE X-AXIS

Do you want symbols in points ( y ) ? Y

Do you want origin in plot (n)? Y

1

LIN. STF

.

2 FREQ

.

Give datanr. to be printed (O=continue) ( O ) ? O

5.m 4.00 3'w 2 8 2.w 1JM Oni 0.M) 1.00 zal 3.m 4.w m. d O : No more data 1 : Of calculation process 2 : 3 : In one equilibriumpoint

Choose kind of data that you want; ( O ) ? Continue (n)? RESULTS ENTER COMMAND: As a function of equilibriumpoints PRIMAIRBTAKA

-

E

Vervolgens wordt het aantal discretisatiepunten verhoogd, dit om

(36)

-2.8-

ENTER COMMAND: /CA CK

O : Return

1 : Equilj.bri.um

2 : Stability

3 : Forced response

Give number for kind of calculation ( O ) ?

I

SUMMARY OF OBTATNED RESULTS

PA

SA

Give label of calculation O ? PB

Startpoint: Regular=l, Singular=2 (I)? 1

Startpoint: Saaie 0 ~ d e ~ 1 , Lower order=2

(I)?

1

Startpoint: Manual input=l, From data base=2 ( l ) ? 2

PB PA

SA

Give identification of old calculation O ? PA Give stepnumber o f solution

(I)?

61

Nr:

1

LIN.STF. = - . 2

Nr: 2 EREQ. =.O915899558901

Give design variable number that varies in calc.proc. (013 2

Number of discretisation points (40)? 160

Give direction of des.variable (positiv or negativ) ( . O ) ? -1.0 Stepsize criteria in BCM algoritm

Fixed stepsize (y)? N

Give initial stepsize ( . O ) ? 0.001 Give minimum stepsize ( . O ) ? 0.90001 Give maximum stepsize ( . O ) ? 1.0

Stepsize criterium parameter alf1 ( . O 5 ) ? Stepsize criterium parameter alf2 ( . 8 ) ?

STOP CRITERIA AFTER EACH CALCULATION STEP Convergence criterium parameter eps (.1E-8)? Nax. iterations in one step ( S O ) ?

STOP CRITERIA OF ENTIRE CALCULATION Max. value for design variables ( . O ) ?

Nax. number of steps (IO)? 200

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind o f calculation ( O ) ? ENTER COMMAND: /EX N

CALCULATION

ENTER COMMAND: /RS PL

PB PA SA

(37)

DESFGN VARIABLES VALUES DISCRETFSATïON DATA

Nr:

1

LIN.STF. =-.2

Dimension of equilibrium is I

First period: discretisation scheme nr 2, number of points 160

period time is forced by design variable nr. 2 CALCULATION PR

First value ,09159 Last value

.

o

1

O03

O : No more data

i : @f calculation process 2 :

Choose kind of data that you want (O)? 2

Give first and last equilibrium point (I)?

Give last equilibrium point 120O)?

1

Chouse data along axis (I)?

1

Number o f lines you want to get (I)?

1

: Problem coordinates

2 : Displacements

3 : Velocities

4 : Acceleration::

1

: Coordinate

2 : Amplitude

3 : Mean value

4 : iviean square deviation

Give information you want ( I I ? 2

Do you want stepnumbers along x-axis (n)? N

1

2 : Varied design vasiable

Choose data along axis ( I ) ? 2

Do you want origin in plot (n)? N

Give datanr. to be printed (O=continue) ( O ) ? O

O : No more data

I : of calculation process 2 :

3 : In one equilibriumpoint

Choose kind of data that you want ( O ) ? Continue (n)?

RESULTS

As a function o f equilibriumpoints

TYPE OF DATA ALONG THE X-AXIS

I L I N . STF.

2 FREQ

.

(38)

32.4.2: Berekenins van de eerste secundaire tak

[ berekening van startpunt 3

ENTER COWAND: /CA CR

O : Return

I

: Equilibrium

2 : Stability

3 : Forced response

Give number for kind of calculation ( O ) ? 1 Give label o f calculation

O?

PC

Startpoint: Regular=l, Singular=2 (I)?

1

Startpoint: Same order=l, Lower 0rder=2 (I)?

1

Startpoint: Manual input=l, From data base=2 ( I ) ?

1

Give parameter value ( . O ) ? -0.2

Give parameter value ( . O ) ? 0.48

Give design variable number that varies in calc.proc. ( I ) ? 2

Give dimension of equilibrium ( O ) ? 1

Discretisation 1: l=Single, 2:Double, 3=variable (I)? 2

Humber of discretisation points (I)? 8

Free period (=O) or forced time number (2)? I

1

ISIN. STF.

2

E'REQ

.

START POINT OF EQUILIBRTUM

Total number of values to be given is 8

Item number

1

Item number 2 Item number 3 Item number 4 Item number 5

Give item value ( . O ) ? 0.66 Give item value ( . O ) ? 0.65 Give item value ( . O ) ? 0.60 Give item value ( . O ) ? 0.57 Give item value ( . O ) ? 0.56

(39)

Item number 6 Item number 7 Item number 8

Give item value ( . O ) ? 0.57 Give item value ( . O ) ? 0.60 Give item value ( . O ) ? 0.65

tiive direction o f des.variable (positiv or negativ) ( . O ) ? - ? . O Stepsize criteria in BCM algoritm

Fixed stepsize (y)?

STOP CRITERIA AFTER EACH CALCULATION STEP

Convergence criterium parameter eps (.lE-8)?

Max. iterations in one step (5017

Max. value for design variables ( . O ) ?

Nax. number of steps ( I O ) ? 1

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number f o r kind of calculation ( O ) ? CALCULATION

ENTER COMMAND: /EX N

ENTER CONMAND: /RS PL

Do you want t o store plot in a plotfile (nf? N

SUNNARY OF OBTAINED RESULTS

PB

PC

PA

SA

Give label of calculation ( ) ? PC DESIGN VmrABLEs VALUES

Nr: 1 I,IN.STF. = - . 2

DISCRETISATION DATA

Dimension o f equilibrium is

1

First period: discretisation scheme nr 2, number of points 8

period time is forced by design variable nr. 2

CALCULATION PC

Number cif equilibrium calculations made are 1

is varied

First value .48 Last value . 4 8

O : No more data

1 :

Choose kind of data that you want: (O)? 3

1

: Equilibrium data vs. equilibrium data

(40)

- 2 . 1 2 -

CALCULATION PC

is varied Design variable with name FREQ.

First value .48 Last value .40

TYRE OF DATA ALONG THE Y-AXIS

O : Return

I : Displacements

2 : Velocities

3 : Accelerations

Choose display form ( I ) ? 2

O : Return

1 : Displacements

2 : Velocities

3 : Accelerations

Choose display form 1 2 ) ? O

O : Return

1 : Displacements

2 : Velocities

3 : Accelerations

Choose display form ( 1 13 1

Do you want symbols in points ( y ) ? Y

Do you want: origin in plot ( y ) ? Y

TYPE OF DATA ALONG THE X-AXIS

1

LIN. STF

.

2 FREQ

.

Give datanr. to be printed (O=continue) (O)? 2 O

O : No more daka

1 :

O f calculation process

2 :

Choose bind o f data that you want ( O ) ? Continue (n)? As a function of equilibriumpoints units RESULTS BR-BSEYDEL I A 0 10' 0.81 O 2 2

1

4.36 49s -1.54 -TAKA =Q. .a

(41)

[ BCM-berekening

1

ENTER COMNAND: /CA CR

O : Return

1 : Equilibrium

2 : Stability

3 : Forced response

Give number for kind of calculation ( O ) ? 1 SUNMARY OF OBTAINED RESULTS

PB

PC

PA

SA

Give label of calculation O? PD

(I)?

1

(I)?

1

Startpointi Manual input=l, From data base=2 ( A ) ? 2

I?B

PD PC PA

SA

Give identification of old calculation

O?

PC

Give stepnumber of :solution

( 1

) ?

Nr: 1 LïN.STF. = - . 2

Nr: 2 FREQ. =.48

Number of discretisation points ( 8 ) ? 40

Give direction of des.variable (positiv o r negativ) ( . O ) ? -1 Stepsize criteria in BCM algorikm

Fixed stepsize ( y ) ? N

Give initial stepsize ( . O ) ? 0.05 Give minimum stepsize ( . O ) ? 0.OOOl Give maximum stepsize ( . O ) ? 0.1

Stepsize criterium parameter alf1 (.OS)? Stepsize criterium parameter alf2 ( . E l ) ?

Convergence criterium parameter eps ( .1E-8)?

Max. iterations in one s t e p ( S O ) ?

Max. value for design variables ( . O ) ? 0.12

O : Keturn

1 : Equilibrium

2 : Stability

3 : Forced response