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NAS102 November 2001, Page 11-1

Residual Vector Methods

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NAS102 November 2001, Page 11-2

Section 11

Residual Vector Methods

CONCEPT OF MODAL APPROACH.. 11 - 3

HOW DO I COMPENSATE FOR THE MISSING MODAL CONTENTS.. 11 - 5

RESIDUAL VECTOR 11 - 6

USER INTERFACE FOR RESIDUAL VECTOR.. 11 - 8

EXAMPLE...11 - 10

INPUT FILE FOR USING MODAL METHOD WITH

RESIDUAL VECTOR 11 - 11

RESULTS COMPARISON11 - 12

GENERAL RECOMMENDATION11 - 14

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NAS102 November 2001, Page 11-3

q Assume response can be represented as a linearcombination of calculated modes

{ U } = [ ] { }

q Number of possible modes = number of degrees of

freedom with mass on them

q Same results as direct if all modes are retainedNot practical

Defeats purpose of modal approach

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NAS102 November 2001, Page 11-4

q { U } = [ ] { } = [ ]r { }r + [ ]n { }n

where [ ]r = modes that are retained

[ ]n = modes not retained

q [ ]r is usually a small subset of [ ]

q Quality of modal solution depends on how well a linearcombination of [ ]r can represent the actual solution dueto the applied loads.

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NAS102 November 2001, Page 11-5

q Two methods are available to compensate for the missing

modal contents

Residual Vector (Recommended method)

Mode Acceleration (See Appendix F)

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NAS102 November 2001, Page 11-6

q Augment modes with static vectors obtained from staticloading

q The response of the neglected modes tends to be static ifthese frequencies are high as compared to the excitationfrequency

As (/n)

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NAS102 November 2001, Page 11-7

q Supports superelement analysis

q Two eigenvalue tables printed

Original eigenvalue table

Second eigenvalue table with the additional eigenvalues appended

at the endone for each additional residual vector.

q Re-orthogonalization is performed to ensure that linearlydependent vectors are removed

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NAS102 November 2001, Page 11-8

q Three available options:

Static shape obtained from spatial distribution of load (e.g.,DAREA, FORCE, PLOAD4, LOADSET/LSEQ etc.)

Static shape obtained from inertia loads (PARAM, RESVINER, YES

or PARAM, INRLM, -1 )

Define USET,U6,GID,C or USET1,U6,C,GID1,GID2,

Each degree of freedom defined on the USETi, U6 entry generates a

static shape with a unit load applied in that direction

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NAS102 November 2001, Page 11-9

q Activated with PARAM,RESVEC,YES

q PARAM, RESVINER, YES or PARAM, INRLM, -1 augmentsadditional static shapes due to inertia loads.

q SUPORT entry required for free-free structure

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NAS102 November 2001, Page 11-10

q Using the same plate model, apply a single-cycle sine loadin the y-direction at grid point 11 at 250 hz. Monitor theresponse at grid point 11 using the following methods andcompare the results.

1. Modal method, retaining 4 modes and using a modal damping of3%

2. Repeat step 2 and include residual vector

3. Direct method with G=.06

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NAS102 November 2001, Page 11-11

$

BEGIN BULK

PARAM, COUPMASS, 1

PARAM, WTMASS, 0.00259

param,post,0

param,resvec,yes

$$ PLATE MODEL DESCRIBED IN NORMAL MODES EXAMPLE PROBLEM

$

INCLUDE 'plate.bdf'

$

$ EIGENVALUE EXTRACTION PARAMETERS

$

EIGRL, 100, , ,4

$

$ SPECIFY MODAL DAMPING

$

TABDMP1, 100, CRIT,

+, 0., .03, 10., .03, ENDT

$

$ APPLY POINT LOAD (250 HZ)

$

TLOAD2, 500, 600,, 0, 0.0, 4.E-3, 250., -90.

$

DAREA, 600, 11, 2, 1.

$

TSTEP, 100, 100, 4.0E-4, 1

$

ENDDATA

$

$ resvec2.dat

$

SOL 112

CEND

TITLE = TRANSIENT RESPONSE WITH POINT LOAD IN THE Y-DIRECTION

SUBTITLE = MODAL APPROACH - REQUESTING 4 MODES - plus RESIDUAL VECTORECHO = UNSORTED

SPC = 1

SET 111 = 11, 33, 55

DISPLACEMENT(SORT2) = 111

SDAMPING = 100

SUBCASE 1

METHOD = 100

DLOAD = 500

TSTEP = 100

$

OUTPUT (XYPLOT)

XGRID=YES

YGRID=YES

XTITLE= TIME (SEC)

YTITLE= DISPLACEMENT RESPONSE AT LOADED CORNER

XYPLOT DISP RESPONSE / 11 (T2)

YTITLE= DISPLACEMENT RESPONSE AT TIP CENTER

XYPLOT DISP RESPONSE / 33 (T2)

YTITLE= DISPLACEMENT RESPONSE AT OPPOSITE CORNER

XYPLOT DISP RESPONSE / 55 (T2)

$

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NAS102 November 2001, Page 11-12

Direct Method

Modal Method with ResidualVector

Modal Method withoutResidual Vector

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NAS102 November 2001, Page 11-13

q The first 4 modes are out-of-plane bending and torsiontype modes

q Linear combination of these 4 modes will not be able tocapture motion due to an in-plane type loading

q Modal method with first 4 modes without residual vectorgives unacceptable solution

q Modal method with first 4 modes with residual vectorcompares favorably to direct solution.

q Note that modal damping is used in the modal solutionand structural damping is used in the direct solutionwhich accounts for some of the slight differences in theresults

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q Always include residual vector in a modal response

analysis (param,resvec,yes)

q Include the residual vector due to inertia load(param,resviner,yes) for non free-free structure

q Use residual vector as an augmentation tool--not as areplacement tool, as used in the example problemto the

modal contents