76-fmn 13? NAVE PROPAGATION AMD DYNAMICS OF LATTICE STRUCTURESCU) Il/lft NE CRIUIDS NA J N NILLIANS I1 OCT 6?

WOSR-TR-U-SU2 F49626-65-C-6146LWIJISFED F/G 22/5 ML

Lak

111114 111

-1111.25 *- 111'

.A / -- I.i

AMC FILE COPY.4k UNCLASSIFIEDSECURITY CLASSIFICATION OP: THIS PAGE

*AD-A190 03732b OELAS~IICATIN/OOW

R.. FUEB D2tib to Unli ited4. PIERFORMING ORGANIZATION REP %F MUERIS) MONITORING ORGANIZATION REPORT NUMUBERISI

Lj_ AFOMiR-fth 88-00(;2GA. NAME Of PERFORMING ORGANIZATION Gb. 0 eE SYMBOL 74. NAME OF MONITORING ORGANIZATION

WEA

6c. ADDRESS (City. State and ZIP Code) 7b AORESS (City, &tsar and ZIP Code,

P.O. Box 260, MIT Branch AF Sr'~ 20/5,58((0 Cambridge, MA 02139 Bolling AFB3, DC203 lic

Go. NAME OF FUNDING/SPONSORING 8b. OFF ICE SYMBOL 9. PROCUREMENT INSTRUMENT IOENTIFICATjbN NUMBERORGANIZATION Air Force office (it applicablu)

of Scientific Research AFOSR/NA F49620-85-C-0148

at, ADDRESS iClly State and ZIP Code) 10 SOURCE OP FUNDING NOS

PROGRAM PROJECT TASK WORK UNIT1:0 Boiling AFB, D.C. 20332 aELEMENT NO. NO. NO.NO

11. TITLE 'naa euaClafaaanavPoaainnd 61102F 2302 B1

Tlvnamfcsq of Lattice Structures (Unclassified)_____________12. PERSONAL AUTMORISI

James H. Williams, Jr.13la TvPE OF REPORT 13b. TIME COVERED 41. DATE OF REPORT iYr. M1a.. Do, 15 PAGE COUNT

Final FRO,,IQ et 85 TO3OSept 7 7 ctbr 4016. SUPPLEMENTARY NOTATION

17 COSATI COOES_ I~ SUBJECT TERMS 1COatIA" Oft 'erie iff negigiery and 8dmncify by bdoei #lumber)

w FIELD GROUP sue GR Wave Propagationi Lattice Structures).~

I Dynamic Failure,~ Large Space Structures,''

19. ASSTR*CT iConsl han on vuerse if neceaaary and jden tj'y by block numberp,

One of the most attractive structural configurations for large space structures(LSS) for outer space applications is the repetitive lattice concept. Achieving theoperational requirements of such structures will necessitate considerable knowledgeof the dynamics, control, materials and nondestructive evaluation (NDE) of thesestructural systems. Wave propagation analyses provide potentially valuable perspectivesfrom which to consider this broad range of analysis, design and synthesis issues.

The theoretical and experimental results of a two-year research program on the(X wave propagation and dynamics of LSS are briefly reviewed. Potential benefits of wave

propagation analyses in the vibration, parameter identification, dynamic failure, controland NDE of lattice structures have been identified and are summarized in this report.,

it. 20. OISTRIBUTION/AVAILABILITY OP ABSTRACT 21 .ABSTRACT SECURITY CLASSIF ICATION

UNCLASSIPIEO/UNLIMITEO 3 SAME AS RPT C OTIC USERS C Unclass if ied

22& NAME OF RESPONSIBLE INDIVIDUAL 22to TELEPHONE NUMBER 22c. OFFICE SYMBOL

(w LDO FORM 1473. 83 APR EDITION OP I JAN 73 IS O@SOt.ETE. UNCLASSIFIED

-1- SECURITY CLASSIPICATION OF THIS PAGE

ACKNOWLEDGMENTS

The Air Force Office of Scientific Research (Project Monitor,

Dr. Anthony K. Amos) is gratefully acknowledged for its support of

this research.

NOTICE

This document was prepared under the sponsorship of the Air Force.

Neither the US Government nor any person acting on behalf of the US

Government assumes any liability resulting from the use of the information

contained in this document. This notice is intended to cover WEA as well.

Acoesslen For Y

NTIS GRA&I 0

DTIC TAB 0oi*Unannou.nc ed 0]

Justitftition''By-

_DistrI but ion/

Ava ilabli ty C odes

Avi

-2- S8 2 P

AFOb R- I A. 6 -U0 62

INTRODUCTION

Many papers and reports may be found in the literature on the

concepts, design, analysis and potential uses of lattice structures

in outer space. Such structures include large antennae, solar power

systems and habitable stations for support of space colonies.

Currently, both deployable and erectable concepts are being inves-

tigated for the implementation of lattice structures. Also, investigations

of size considerations indicate that small antennae ranging from tens

of meters in span to solar power collectors ranging up to several thousand

meters have been proposed. Such structural sizes along with stringent

operational requirements will require considerable information of dynamics,

control, materials, nondestructive evaluation (NDE), environmental effects

and wave propagation relating to their design and analysis.

Much has been written on the theoretical aspects of the control of

such structures. Also, a large number of vibration analyses have been

undertaken. However, despite a distinct recognitiofi of the importance 0

of wave propagation in many of the control, vibration and NDE investiga-

tions, very little can be found on wave propagation in large space

structures (LSS). The major goal of this program was to pursue the .0

development of several aspects of wave propagation analyses in LSS.

-3-

S

ACCOMPLISHMENTS

A number of theoretical and experimental analyses have been undertaken.

Some of these efforts have been documented in reports and some as yet remain

undocumented in formal reports. The formally documented accomplishments

will be described briefly.

As indicated above, the focus of our investigations has been the wave

propagation of broadband and narrow-band signals in lattice structures for

outer space applications. Theoretical and experimental analyses which have

resulted in formal reports are listed here.

1. Theoretical formulations of the input-output relations for arbitrary

pairs of locations on periodic structures have been initiated. In this

formulation, we have used (and are continuing to use) a transfer matrix

technique for analyzing periodic structures which can be modeled as one-

dimensional continua, two-dimensional rectangular trusses and three-

dimensional tetrahedral trusses. The elements in these structures are

capable of transmitting longitudinal, shear and flexural waves. Our

efforts on this topic have resulted in reports* as follows:

- J.H. Williams, Jr., H.K. Yeung and R.J. Nagem, "Joint Coupling Matrices

for Wave Propagation in Large Space Structures", AFOSR/WEA Technical

Report, April 1986

- J.H. Williams, Jr., R.J. Nagem and H.K. Yeung, "Wave-Mode Coordinates

and Scattering Matrices for Wave Propagation in Large Space Structures",

AFOSR/WEA Technical Report, October 1986.

* Reports written on this topic and other topics that were published on an

earlier contract are relevant but are not listed here. For the listing ofthose reports, refer to J.H. Williams, Jr., "Wave Propagation and Dynamicsof Lattice Structures", AFOSR/WEA Final Report, October 1985.

-4-

0

2. The dynamic properties of two two-dimensional lattice structures have

been investigated both analytically, using the NASTRAN finite element

code and transfer matrices, and experimentally, using an HP Fourier

analyzer. The natural frequencies obtained via the three approaches

were compared and shown to agree within seven percent of each other.

These results are reported in a document as follows:

- J.H. Williams, Jr. and R.J. Nagem, "Computation of Natural Frequencies

of Planar Lattice Structures", AFOSR/WEA Technical Report, March 1987.

More recently, this work has been extended to consider the nondestructive

detection of damage and is reported as follows:

- J.H. Williams, Jr. and R.J. Nagem "Natural Frequencies and Structural

Integrity Assessment of Damaged Lattice Structure", AFOSR/WEA Technical

Report, April 1987.

Further, in these efforts we have collaborated with colleagues

at Stanford University and Virginia Polytechnic Institute and State

University. In fact, both 5-bay and 22-bay lattice structures which

we have fabricated and tested have been sent to colleagues at Stanford

for testing.

3. In lattice structures where the signal propagation is dominated by 0

longitudinal waves, we hope to develop general closed-form expressions

for the input-output relations of arbitrary pairs of locations of the

structure. This type of analysis requires the reckoning of each wave

front which leaves joint i and arrives at joint j, having undergone

a series of reflections and transmissions at each intervening joint

encountered along the way. Such an approach may be called a "wave

summation analysis". We have been able to duplicate these results

-5-

using wave-mode coordinates. Our efforts thus far on this topic have

resulted in a report as follows:

- J.H. Williams, Jr., R.J. Nagem and H.K. Yeung, "Comparison of Wave-

Mode Coordinate and Pulse Summation Methods", AFOSR/WEA Technical

Report, December 1986.

4. The wave propagation characteristics of a 5-bay aluminum planar lattice

were studied experimentally. Wave propagation speeds and frequency

spectra were obtained, and wave propagation reciprocity was observed.

Wave propagation attenuation was quantitatively measured and an atten-

uation parameter expressed on a per-bay basis was defined. Similar

results for a 22-bay structure are reported as follows:

- J.H. Williams, Jr. and J.J. Zhang, "Wave Propagation Measurements

on 22-Bay Lattice", AFOSR/WEA Technical Report, June 1987.

5. One of the most distinctive uses of wave propagation versus modal

analysis lies in the description of nonlinear behavior. Our work on

dynamic failure and techniques for arresting such failure has provided

a fascinating application of wave propagation analyses in LSS. This

work is reported as follows:

- J.H. Williams, Jr. and R.J. Nagem, "Dynamic Failure of a Periodic

Lattice Structure", AFOSR/WEA Technical Report, October 1985.

- J.H. Williams, Jr. and S.S. Lee, "Failure Propagation in Continuum

Models of LSS, Part I", AFOSR/WEA Technical Report, November 1986.

- J.H. Williams, Jr. and R.J. Nagem, "Dynamic Failure Arrest in

Lattice Structures Via Wave Deflectors", AFOSR/WEA Technical Report,

December 1985.

- J.H. Williams, Jr. and S.S. Lee, "Failure Propagation in Continuum

-6-

6S

Models of LSS, Part II", AFOSR/WEA Technical Report, February 1986.

- J.H. Williams, Jr. and R.J. Nagem, "Dynamic Failure Arrest in LSS

Via Active Control", AFOSR/WEA Technical Report, July 1986.

6. When the wavelength is long compared with the length of lattice elements,

continuum models may be used to provide computationally efficient

analyses. Wave propagation in a tetrahedral lattice, which was modeled

as a transversely isotropic continuum, was conducted to provide some

insight into the nonintuitive behavior of long wavelength dynamics of

LSS. This work is reported as follows:

- J.H. Williams, Jr., R.J. Nagem and K.G. Salam6, "Wave Propagation in

Transversely Isotropic Continuum Models of LSS", AFOSR/WEA Technical

Report, January 1987.

-7-

SUMMARY

While there continue to be misconceptions and misrepresentations

of the wave propagation perspective of dynamics of LSS, the value of

wave propagation analyses of dynamic phenomena in LSS is no longer an

anomalous curiosity. In an attempt to assist in the enlightenment of

the technical community regarding wave propagation in LSS, a presentation

entitled "Wave Propagation in Large Space Structures" was presented at S

the Fifth AFOSR Forum on Space Structures in Monterey in August 1987.

The abstract and the transparencies for that presentation are given as

the appendix of this report.

-

S

-8- '

~'QI~'* R

APPENDIX

Wave Propagation in Large Space Structures

James H. Williams, Jr.

Raymond J. Nagem

Department of Mechanical EngineeringMassachusetts Institute of Technology

Cambridge, MA 02139

ABSTRACT

Waves and modes are discussed in the context of dynamics of large space structures.It is observed that wave propagation analysis is much more general than modal analysis,and that wave analysis can be applied to a much broader class of dynamic phenomena.Thus, some phenomena which can be conveniently described by wave propagation have noequivalent modal representation. In linear analysis, when wave propagation analysis andmodal analysis are theoretically equivalent, the preference between a wave analysis anda modal analysis is assessed in accordance with the ratio of the wavelength of a typicaldisturbance function to the characteristic structural length. A definition of a large spacestructure is given in terms of the characteristic structural length and the typical disturbancewavelength. Recent research results in continuum modeling, scattering theory, controlsystem design and dynamic failure are given to illustrate applications of wave propagationanalysis in the dynamics of large space structures.

Sponsor: AFOSRProgram Manager: Anthony K. Amos

-9-

WAVE PROPAGATION INLARGE SPACE STRUCTURES *

James H. Williams, Jr.and

Raymond J. Nagem

M.I.T. -

(AFOSR: Anthony K. Amos)

S

* Because the original transparencies were multicolored, the quality

of these copies is relatively poor.

-10-

IRecent Titles on

WAVE PROPAGATION IN LSS

* Wave Propagation and Dynamics of Lattice Structures.

0 0 Dynamic Analyses of Two-Dimensional Lattices.

0 Wave Propagation Through T and L Joints.

e Nondispersive Wave Propagation in Periodic Structures.

* o Feedforward Control of Waves in Lattice Elements.

o Wave Propagation Measurements on Two-Dimensional Lattice.

o Wave Measurements on Truss Model.

e Wave Propagation and Dynamics of Lattice Structures. t

e Dynamic Failure of a Periodic Lattice Structure.

e Failure Propagation in Continuum Models of LSS, Part I.

o Dynamic Failure Arrest in Lattice Structures Via Wave Deflectors.

o Failure Propagation in Continuum Models of LSS.

o Joint Coupling Matrices for Wave Propagation in Large Space Struc-tures.

9 Dynamic Failure Arrest in LSS Via Active Control.

o Wave-Mode Coordinates and Scattering Matrices for Wave Propaga-tion in Large Space Structures.

e Comparison of Wave-Mode Coordinate and Pulse Summation Meth-

ods.

e Wave Propagation in Transversely Isotropic Continuum Models of LSS.

e Pattern Recognition of LSS States Via Wave Propagation.o Wave Propagation Measurements on 22-Bay Lattice.e Computation of Natural Frequencies of Planar Lattice Structures.

o Natural Frequencies and Structural Integrity Assessment of DamagedLattice Structure.

-11-

Topics of CurrentLSS Research Activities

* Scattering of Waves at Joints in LSS

* Nondestructive Evaluation of LSS

* Numerical Efficiency of Transfer Matrix Method for LSSApplications

* Wave Propagation in Anisotropic Continuum Models ofLSS

e Control of Wave Propagation in LSS

4p, -12-

vs E&& ..- - - S Ms

IiO~~~f44w Wv~L.M

V~-'~ E~~-*~ vs ~ o.~ E~dc OQOO c

CPP 4~A SU

ts0

vloooe

-1i1

"u4:40

u.~.

.. dr.'

II

06"

PA Ll

jurn

00

0' 0

A a13.

Qk k % Adw0

Vim, %.

0 L0

%DW P~l~ift

rul

0; ?t.

LSS.

Lo Ti S~tr4r iL4.JL bec., ftsjokoPL

e"yrs

*oI &vot 6L acrZII~ 0

ir lr%0

w0

16w' 10

__________ 0

107f 10trl W

00

CIO62~ S10A

3 L WL L04

1,

YHI

r

Ir

00

4 jet

-20

x0

A YI ki YA/'

Typical Repeating Element

L dL ABxO 6 2LIA - 0 L 2 d 7.5mr

s A50xI10 6 m 2 E z71.7Ex:0 9 N/rn2

t IO2 P z 768 kg,/m 3

IC rsss

Secnional1 Lengtn ae I SYMoci

Surface AL PLBarsL

Bot tornSurface A LBars PL

Bracing Ir -

Bars - d d jd

Tetrahedral lattice structure.

-21-1

-04

co

0)U-)

C\J t

-22-

'18 SH\SH SS

I /

I /n

l9/ " /

2nh V / \

Rn/ Rn

I/ / 0 . _

I /

On/ "

Path of SH-SH-... wave which arrives at receivingtransducer after n reflections from bottom boundary.

-23-

(L

90

*nOta~

J a p

0 ,a-a

ou i- 1.

-24-

* Joint

I b2

Mo~del of joint connectinp two'c elastic longitudinal roes.

-25-

0

4 .

Cj

-26-

.~9JK ~ M~LK~ ~AMJ~ ~.A A F K K F -

S

-I0

'0

*f -

I-2-o 0

-7o ~N

- ,~ ~PaIda.

C, Ii ~ *pFp.

cJ -~ -~

o '.. -p.. ~.-* *1

0

-~ =11

C,.-

I---- SC

-* C,

I- -C,~0

U U -.-

- .- ~- Io'$.

5

C:-

0

00 - . p.'..

_____________________________________ ao

o o 0 0 0'- - a - -

.A/(X).1 3 '~)JO3 P~Z)~U~! T~UOISU~WTPUON "p..-'. "p.

0

-27-

S

' %~aa'p. % 'k '~~%?V'~/ * '~ ". ' ~' IP~ ~ a~ PI''p

10

U1%

$It

0~

tAA

-28-Z

Cp 0

-300

1 oil

-9(

-Bob0

F5..frf4

F(TA

WIOx0

--- __0_____au_ X

SO

.RcALoo*vAat.t~

0.) %-

4 3

-too-.SSW

-too 0 16 S

to ooo.

-32-

OPSS

IL-

% Fe

0

Q ~ a~pp~. 9~3Ov(3~'o It u

bt

4loo.9

O~SI.

L .0.6( "O O

00

w04) to O..a s 3

1%

'P"O.00 ".-4 '-

. ~ ~34 . '.e.

0.5.O.".".Z

.5... ,. *° 1" ."

0,0- *,,,1,. - ,',, ,, , o .

.FAILURE PROPA ATION IN LSS4en,74 ice Gxielwmuca SiGcAdMr

2--D 1'Ioeaor Lpt,'ce NAo~A tc

10 a-

aWdA

RFaz bire ?mco7~ '~a~

t4R FaU JLre, Arres4

?N V,. Fa-/.~

-35-

Cr;terie. :fir Falu4re, mac;ic. mlF~~e

Arre4

N',

U7J. ak

No F~ALLNo

'00

No. Ldt-un

I,, IA'L~r Iror~io1-36-}

Loco.+i on Of Failure~ Arres-

1,000

~~=100

L-o

0.1

-37

0

7(r.0

Ltt)

-38-

400

s4-,

t* lkr ct iro

ic-39-

L &c~o~ \~r C~A~~& ~O&~t- AIT~k ~t 0

~k~2 -k~J A~ &J~'Q_~or~ ~ ___ 'V'0

B -~

p'~.

0

4 \)~09.0.~k~ A0

Q01A.A s~a~ ~

~ ~Jo J~ /U

V S.. ,

U

9.-

I-.

A'.i0

.~- ~p.

it- ~"-~- - - - - - - - - - - S

-9.

.9 1..,.

(~~L&

* -~

AIfw4k ~AA

- ~ 0

Iwo .. p

-40- I1*.,d

- 'WI'

-"

-J

-U '

u Im nn | df~

n

r

lb

i

-