D-A1l6 146 WAVE PROPAGTION EXPERIMENTS ON 22-BY LATTICE(U) WEA 1

CAMBRIDGE MA J H WILLIAMS ET AL. 61 JUN 07

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11. TITLE Include secuity Cljticat(oni WAVE PROPAGATION 61102F 2302 BiEXPERIMENTS ON 22-BAY LATTICE (UNCLASSIFIED)

12. PERSONAL AUTHORIS)

. . .o James H. Williams, Jr. and Jia J. Zhang13a TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT IYr. .o.. Dayj 15. PAGE COUNT

. TECHNICAL FROML Sept 85 TOLJune8, 1987, June, 1 37-10. SUPPLEMENTARY NOTATION

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FIELD "GROUP SUB. GR LARGE SPACE STRUCTURES WAVE EXPERIMENTS

I WAVE PROPAGATION PERIODIC LATTICE

19. ABSTRA ConT inue on mverie ifnecesar and identify by block numberi

Wave propagation characteristics of large space structures (LSS) affect theirperformance, integrity and the ability to nondestructively assess their integrity.

In this study, wave propagation characteristics of an aluminum 22-bay planar latticestructure are determined experimentally. Two ultrasonic piezoceramic longitudinaltransducers are mounted at various locations on the structure. Wave measurementsare obtained by injecting an impulsive load via the transmitting transducer andrecording the response via the receiving transducer. The waves injected into thestructure are longitudinal waves, transverse to the surface, although a complexstress distribution which may be described by directivity functions is actuallyrealized. The impulsive loading signal has a broad frequency spectrum containing

" ' frequencies greater than 0.5 MHz. gat 4

In the lattice considered, waves propagate throu ,h "T" and "L" joints intovarious members of the structure. The speeds of arrival of the initial waves are

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19. ABSTRACT (cont'd)

measured. The resulting speeds of wave propagation along members of the lattice aremeasured to range from 4.53 km/s (14,800 ft/s) to 5.18 km/s (17,000 ft/s). It isindicated that the measured wave speed is between the longitudinal wave speed and

the flexural wave speed.The frequency spectra of the output signals are also obtained. It is observed

that the frequency at the maximum amplitude of the output spectrum generally occursbetween 353 kHz and 450 kHz. It is also observed that, beyond the first five bays,the maximum amplitude of the output spectrum decreases logarithmically with thenumber of bays that the output is located away from the input, regardless of theinDut location on the structure. Thus, an attenuation of the maximum amplitudeof the output spectrum can be defined for LSS based on the number of lattice bays.This attenuation parameter may be convenient for the design of LSS because it is

based on a natural unit of the LSS, namely, the lattice bay. For the planar latticeconsidered, this attenuation is found to be 0.085 neper per bay.

Furthermore, reciprocity between input and output is observed experimentally,- in both the time domain and the frequency domain. The development of quantitativemeasures of reciprocity is recommended.

This experimental study also demonstrates that wave propagation characteristicsof a lattice structure can be obtained. In particular, the wave speed, the frequencyat the maximum amplitude of the output spectrum, and the attenuation of the maximum

amplitude of the output spectrum per lattice bay traversed appear to be usefulparameters in the characterization of wave propagation properties of LSS. Furtherstudy should investigate the effects of boundaries, lattice member connectivities,

and structural defects on these parameters. Perhaps, statistical energy analysisor pattern recognition techniques would also be of benefit in such efforts.

'I

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TALLi CF COLTEifS

.AiLSI FACT . . . . . . . . . . . . . . . . . . . . . . . . . .

,%C.I:COi. LI .GF1.Ei T' . . . . . . . .

I0 Ia CL . . . . . . . . . . . . . . . . . . . . . . . .

IA.Lt. jF CGIILNS . . . . . . 5

LIS'T OF 'TABLES . . .

LIST C.-F FIGL LS . . . . . . . . . . . 7

LATTICL GLOLEIhY, EXPEFI-.EI;TAL ELUIPELT Al:D EXPE-11EITAL

PkI-CEL hE6 . . . . . . . ............. . . .. . .

Latt&ce Geometry . . . . . . . . . . ...

ExIcrirnental Equipment ..................

Lxjtrircrtal Frccedurez. o........ ................ iC

Cnaracterization cf Inut Pulse ............... 11

L2 k'. LISCLSLI.S ....................... 12

Lave 5jeec ......... ...................... .7

Cutput Frequency Spectrurc ..... ............... .

CLstrvaticn of Eeciprocity ..... ............. . 15

CC.CLL.uICI.08 A., LLCOLEL.LATIONS ...... .............. 16

P LLC. ......... ......................... 2C

T ALLLS ................................. .2

0I U L .% . . . .. . . . . . . . . . . . . . . . . . . . .

5

Li', OF TAiLLS

"i= bl e FaE-

1 Sumn.ary of Yeasured I;ave Speeds for Initial 1,avesArriving at Varicus Output Locations for VariousInput Locations . . . . ........... . . . . 22

2 Calculated Flexural I$ Speed in Aluminum Ears ofCrosz Section Cori ing to That of Lattic. atVarious Fr.quencies . . . . ........... 25

6umzrary cf Le-zsured Frequencie& at flax , .urmAnplituae cf Output Frequercy Spectra for I:evesArrivin at Various Output Lccations for VariousInput Lccationa ................... 2

4 2ut;mary cf lYeasured Laximur Ar.Tlitu ces of OutputFrequenc Spectra fcr Uaves Arrivint at VariousOutput Locations fcr Various Input Locations .....

Cor..pariscn of Lave Prcr& ation Craricteristicsbetween tr.a 5-lay and 22-ray Planar Lattice .7.2..

,,I

",

9

~6

LISI CF FIGURES

Figur Page

1 Geometry o! 22-hay lattice structure (dimcnsionsin cm) . ........ . . . .......... 33

2 Schematic of experimental system for measuringuave speed and frequency spectrum of 22-baylattice, showing typical locations of transmittinarna receivr. transcucers .. . . . .. 4

Scher:atic illustrating locations A through V onlattice structure .. ........ . . . . . . . . 35

4 (a) Time trace and (b) frequency spectrum ofoutput from receivinE transaucer when trns:.ittfngand receiving transducers are coupled tocethe-erdirectly (face-to-face) withcut any structural

specimen . . ... . . . . . .. . . . . . . . . . 36

5 Logarithm (base 10) of maximum amplitude (mV) cfoutput spectru. vrsus number of tay widthE thatoutput is located from input for various inputlocations . . . . . . . . . . . . . . . .... . . 37

S%

0%

(%

(?

7!

I V~ TO I; CU C T 101 .

LargE space structures (LSS) are pericdic lattice structures

beinL considered ior use in orbit-n space stations, E59&cESW

coi:nunication antennas ant space jlatforms [1]. The froposed

application of LLS in ieocentric orbit requires structures of

outstar.dir.,. performance anc integrity under extrere or hcstile

environmental conditions. !.ave prcpaEation characteristics of

LLS afiect their performance, integrity and the ability to

noccestructivelj assess their integrity in service.

Lave propa~aion characteristics of an aluminum 22-bay

planar Lattice ztructure[2-4] are measured experimentally in

this study. aiuo ultrasonic piezocerar.ic lonitudinal transducers

are mountac at various locations on the structure. Wave

..,easuremcnts are obtainec by injecting an impulsive load via the

:ransmittin transducer and recorsing the respcnse via th.e

receiving transcucer. The waves injected into the structure are

Eenerated aL lon~itudinal waves, transverse to the surface.

In the lattice considered, waves propagate through "T" and

"L" jointa into various memters of the structure. The resultinE

pteeds o f wEve propagation along meibers of the lattice are

measurec. The irequency spectra of output s~inals at various

locetions due to ir.put excitations at varicus locations on th%

lettice are measured elso. The wave speed and tht frequency

spEctrur. should Le useful in the characterization of wavt

jrcp&&ation properties of LSS.

Li-TTI CE C 101,ETRY, EXPF11'iV. fTAL E LI F.i- 1. 7 AT:1 FXEI PIPBV1-AL

P F GGC £ ] U t. i S

La-tt-icf Ge. netrs

F1.1 Sf:ovs t r.e Eeo:;etry of the 22-bay I larnar latticc

structure ;or.Ziderec in t his study arnd in other studies [2- 4J

ahe structure I.~s twerty-two repeating substructures (bays).

The 22- bx , la ,,a r lattice is rnehirned 1frorr. a sir.L le PiCC- c f

C.S3 cmr (0..375 ir.) thick 6061-T6 aIu rri ru i: platE. Thu, the

~truc-.ure ccrntains rno weluE' or fasteners in its ccrstructio 4 .

1xper.merntal Lquil i~ent

jschemat ic c: the wave ;:easu:ement syster is Eho.r, ir. .c.

2. r e E.,v-tem consists of a brcadbarA ultra~coric puls-er-rec~iVEr

(FLar -trics r~oel -1O052E) to e-nerate and receive elE ctrIca1

Uls1 SESU- tC 370 I.IZ; 2.5 m( in) dip-meter (1.91 cm (0.75 in)

ciamcter fiezcceramzic element) broadtand (0.1 to 310 Klz)

trLsIitti. an~d rtsceivint: lor.Litucirnal transducers (Fanm:-ri-cE

m~odel 'V10~) havir4 an approximnate-ly flat sersitivity of -F5 'i

(relative tc 1 V/ Ear) and weighing C.C82 kef (0.1E lbf) eacrh; a

transducer s ie ci.e n inrterlace couplant (Acoustic E,-issior.

1%Ofcr.OiOLy ..oael SC-C); 26.7 1. (6 ltf) :ocnstant-fcrct- T~:r ir. ts

(1Acourctic r.zs -Lon 'Alechnolo~y m~odel CFC- .C) to secure tLE

.r,:.sducers onto tr.e Zpecimen; and a 1C-Lit di~ie.al cscillc-,ccpe

(bi"c - 1e t rOce 4G0,4 vwith dual-channel P-bit Flus-in ncdel 41-5, 4

CU..l diLk reccrder i:,odel ).F-441/2 anc ;.aveform An~alysis Packe~e)

riv.r, a i£ aximur;514>i~ I requec-ny of 50 ILz (5co N Vz for

r e t ti Zi v E s I ,r-riaxiriu;,- storrage capalilit3 of 15,11"72 d~ta

A .J

PO I n t E pe trace, arnC e Fourier transf orrm softw~.re pac,,.age

capaL.4 .,E Of ha~~~Up toC 2,C4,6 poirnts per trace.

Ixperir.,eertii Pt ocecures

'.ne latti.ce az -,iowtn ir. Yi6. 1 is suspended freely in a r

via twc tni n strings. Two transuucers arc- attached to thf

latt-ce &at various 1ocaticrz us-ing tihe constant-fcrce sprirgs &rnd

are coupled tc the structure via the transducer E;ecirsr.

_.ntr.ace cot-plarnt. !he resultin6 clampinj- pressure cf C.11 '.!.a

( pEi orn 7ne transducer is approx ir ate 1y equal t c t r

saturation kressure Whic. -s defined in [57 as the rinirur

transducer-j..ecir.-., interiace pressure which results in the

L' .-X -r. U f amplitude cf the output -ignal, all ether pDararn-ters

beinL rneld constant. lurtheri-ore, the orientatiocn of each

transcu er relativ- tc -:he ctructural mezmbers of the lattice is

rairntazned thrcu,,hout to avciL any variations that cculc be

introduced by tne directional effects cf the transducer

I.ezccerarnic element.

An i;.pulse is inkut into the trarnsmittinE transduce-r via the

ultrascnic puIser-receiver. '.he sz.;nal arrivinCg at the rEceivinL-

transducer is recorced on a 13.3 cm (5.25- in) c-arneter aislhette

Us.!r.~ a sa;plii%- frequEncy cf 5+2 &~ nd 15Jf72 data& points per

tracE

Tr.e arrival tirie of the initial output wavce signal is noted

fr om tthe tim~re trace. Fromr this arri4v..l tin.-e and the Sh.ortest

hk; Ve fratr. I enE t I tweEn tr.(- tranE:s.it tirCg a nc thne receiving7

trans-ducera- tnrougn the rzlezcnts of the lattice, a wave speec iF

calCuLatec for tr.e --niti~l wave to prcparec fror. the'

1c b

4 7'WMWUW_ ww -.-

trarnsttirng transaucer to thne receiving transducer. Alc7o, tr-

frequercy zpectrur.. of the output signal is obtained v.i: the Fthe

* Fou:ir Transform (FFT) , einployin6~ the iFanrnirn window. proviri.- t

the Jicclet, 1.aveforr.x Analysis Package LSirnE 2,048 ToirtF=

(initiat _d at tne beginrir. ci the output wave packet).

*FiL. 3 snows lcc~itions A through V Used to locate pCSiticn-s

or. tne laz tice. The in;ut is a;.pliea at locations A, L, Vr and

VPant trne output is recordec a-t all the reraininC lozatior5- cr.

* tre 18T-4C .

CnaracterizLation cf Ir~lut Pulse

Ine in~put impulse (irncludinE the transducers rind the

eiectronic equirrnent) Is characterized tit ccuplih-. tihe

trans;~ittirn; ana receivinE -:ransducers directly (face-to-facE.)

w itr-.Cut t n E; r e ser. ce o f an specimen. !-hen the rece iv ing

transducer is coupled directly to the transm~ittin~g transducer

wit~cut the structure, the output of the receiving transducer is

&Z .rco;.n ir i'ig. 4a. The corresponain: frequency Epectrum is

snovwn .1r. Fit. 4b.

Cn tine time scaie tCeint usocd in these experimerts, there is

no c LS rvaLle tim~e neiayr between tr.e input ar~c the output w h --r.

tine traxrsducers re coulled facE-to-face a-v shown in Fie. 4B. In

trtc frequency L-zn.a in, as sh own in F iE. 4t, the input sicnal

cornzains a broad frequency spectrum IrciL. zero :'requency to

frcqLuencicc Fzk_.ater trnen C.5 Lz

-A. *.P '.F

hLJIASAILL LISCUSL.IOLS

Trne REaSurec wave -;,eecs for in-tial vamve fronts 6rriving- at

various 0output locaticns for varicus -Jnjut locatiorns are

* suii:&iazzed in Table 1. Trie measuremert cerror of the wave pe

16 te-tii..atea to Le leszt than 2 jerc~nt.

As shcwr. ir. Table 1, ihe wave speed range.s from L:5 E-/

*(14,80G i't/s) Tc. lt ki-/z (17,00C ft/!z). The lcr.Citudirnai v

.4eed i . an aluminur: roci is 5.23 kr/s (17,200 ft/s) [6. Th.e

shear wave ae in. an alurrinur7 rod is 3.1,3 Im/s (10, _00o f t/)

t73. 'Ihe flexural wave speed in alumnirum bars cf t ne cros

secticr: correspondi:L to that cf The lattice depends sn the

fr~quenc arnc is tabulated irn Table 2 [6j. lhuL: l. e 7.easEu resd

wave spee.a appears to be beti.een the longitudinal wave speed arr'

thto :!eXLrai wave spE"- if a frequency of Creater than 35 C Ikhz 4-1

ccrnaiaerEc for the fiexural wave. (The longitudinal ena flexural.

avt.,len~trs at 350 k~z are 1. 4 c cm (C.5EF in) and 1.31 Cv. (C-51

j~ aiEcussec. in [E], the cutput sifnal con-ains many %--ve

reilecticns from ruitijpic wave paths arriving a-- the receivinE

GutpuLt irequency Spectru.

As GiscussesC in [,trnE ire ,uercy spectrur:. contbiir..s anY'

rE--o.ncCS of the structure. 'T-e measured frequencies at tfhe

[,a X I . U r- Fr li tu C. o the output free uenc-.; spectra for v es

arr .vir., at varicxua ;ut ,.ut loc:Iticns for variou.: inTut IOC[.tiC!-S

are suL;rmarized in Table 3. The corresponding measured maxirum

amplitudes of the output frequency spectra for waves arrivin at

various output locations for various input locations are

sunr.arizea in lable 4-

Yrom Table 3, at is observed that the frequency at the

maximum amplitude of the output spectrum, generally occurs betwEO:.

353 k2-z anc 450 k.z. The exceptions are for inputs at location A

kitL correspcnang outputs at locations S,T,U,V and in;uts at

*ocation V witn corresycndin outputs at locations t,B,C,D.

Apparently, for the most distant locations, the hi. frequcncy

coLpinents arn attenuated and trne frequency at the maximum

arpliug of the output spectrum is lowered to approxirately 115

khn.

from. Table 4, it is observed that the maximum amplitude of

the output spectrum generally cecreases with increasinf

transzit.er-receiver cistance, except for the first five bays.

Ei&.5 snows trne loGarithm (base i) of the r.aximum aerlitude of

the output spectrum plotted versus the nurber of bay widths away

from1 the input for inputs at locatioLs A, L, V0 and V . Fore

precisell, tre nuLber cf bay widtns away is cefined as th-

distarce separatin6 the vertical cross sections cortainin the

input anu output locations, rcrmalizea with respect to the Lay

wicon. ior exat.ple, ii the inut is at location A, lccaticns D

an 1 are cefined as three bays away.

A straight line is drawn "nrcugr: the 110 date points in iL.5

uLinL linear regression, reLardlesE of input location, except for

trie iirst five LaY3. 'he resultin correlatior coefficient i'

C01SL. ,-us, it appeerE that the maxirur amplitudc C! the

13

% - ' . '. . " e _ -

outkut s;ectrum decreases lcgarithrically with the number of tays

away from the input, rebarclcss cf input location. Specificall),

the ccvi elation equat-cn foi the .aximur amplituae of the output

for a zpecific& nurber of LZYS away f:-o the input iE

Lo 1C (Ai.plitLae in .,V) = 1.10334 - C.03tgx(L.o. of iays) (1)

Eqn. ki) can De manipulateo and rewritten as

Am.litude in. mV = 12.E9 e-C .0C - x(I , of F ays) (2)

ThuL, an attenuLtion of the maxiru.m amplitude of the outlut

spectrzu i, can Le cefined ior LSL based on the number of lattice

tayL anc ecn. (2). for the planar lattice structure considered,

tnis attenuation is found fror. eqn. (2) to be 0.085 neper per

bay. The attenuation described by nepers per bay may Le

convenient in the dEzign of LSS consisting of pericdic lattice

bays because it is based on a natural unit of the LSS, namely,

the iattice bay. It relresents an insertion loss in the maximum

a.plitLude of the output spectru, for wave proparation due to the

adaiticn ("ir-s=rticn") of a periodic latticc bay.

Lecaust the icth oi a bay is 6.25 cr. (2.46 ir.) as shc ;n ir.

Fig. 1, the attenuation cf 0.065 neper per bay can also be

exjreEsed as C.014 neper/ci. (C'.035 neper/in). This compares with

the ioniLtuain~al attenuation cf 0.015 neper/ca. (0.036 neper/in)

for Lulik alumiaui:, at uitrasonic frequencies of the order of 1 Vl-z

[10]. } owever, when vibr~ticrnal dampin data obtained for a 22-

bay aluminum planar littice at frequencies -elow 1 kHz [4] are

usec to ezxtrapolate tre attenuaticn [11] at frequencies of the

14

S % % % -i

orodE: of several hunarecds of kb~z, 'the predicted Etteruation

ranges frct 10- neper/cm (2.5x10'7 neper/in) to 10O neper/crt

(2.5x10- neper/in). Thus, it appears that the etternuatfon

ir.creasca si4nificantly with frequency.

OUCervati'on of Reciprocity

As diEszussed in [8], froc Tables 1, 3 anc 4, it ic clserve-d

t~ t r the ir.;;ut arnc cut .,ut locaticrsz zre irterchar.ec, ti>K

resuitE are very sim~lar.

Table 5 shoha various compariscns of7 wave propagation

charac'teristics between tne 5-bay an~d 22-bay planar lattices.

1 r.

%* *I*%*;VV\ '

COL1CLUSIO S AI._D JIaCCI, ILI. A"IOIS

i.ave propagation characteristics of an aluminum 22-bay

planar lattice structure have becn considered. Two ultrascnic

piezoceramic longitucinr-l transducers were mounted at various

locaticns on the structure. Vave measurerents were obtained by

injectin; an impulsive loao via th. trarsmittirn.- transducer and

recordi; the respone via the receiving transducer. lhe waves

ino-cted into tne structure wer, loiLitudinal waves traIsversE to

the surface although a complex stress distribution, described by

airectivity functions, was actually realized [10]. The impulsive

loa0inL sijnal had a broaa frequency sFectrur containing

frequerncies greater than 0.3 Ihz.

Easea on the results of this study, the follc:ir -

ccniclusions can be made:

(1) The rieasurea wave speed for initial wave arrivals ranges

from 4.53 km/s (14,ECC it/s) to 5-le km/s (17,000 ft/s),

which is between the longitudinal wave speed and tho

flexural wave speed for flexural waves of frequencies

grEater than 350 kiz.

(2) The cutjut zignal ccr.tairs ns any .ave reflections from,

multiple wave paths arrivinE at the receiving transducer.

(3) 1he measured frequencj at the m.axium aamplitude of the

cutput frequency spectrum generally occurs between 353 l:Fz

ano ., 5 O kz.

(4) Txhe meazured maximum amplitude of the output frequerc::

ipectru.. decreases logarithmically with increasing number of

lattice LayS away fro:. the input location, regardlf-ss ."

'1

urIR -V"ww uw w -, wv.rU .~ rX. IX ?W% 7WX - 1011.

input location on tne structure, except for the first five

Lay s .

(5) In accordance with the preceding conclusion, an attenuatfor

of tr.e maximum &i.plitude of the output spectrum can be

defined for LSS basec or. the number cf lattice bays ai.ay

from the input. This attenuation may be convenient for the

design o LSS because it is based on a natural u.it of the

L6-, namely, the lattice bay. For the planar lattice

considerd, this attenuation is found to Lc C.0e5 neper

per bay.

(C) Aa discussed in [8], reciprocity betl eEn input and output

is observec experimentally.

Easea on the results of this study, the followinE

reccmencaam'_ons can be m-ae:

(1) Tris experimental study should be extended to 3-dirensioal

lattice structures such as tetrahedral trusses.

(2) Scaling laun for other structural sizes, geometries,

frcquences and materials snould be develo;ed; and thE

effects of jcints on suct. scaling lawrs snould Le delineated.

(;.) 'ne vali.Lity of the attenuat:ic., , of the maximum, amplitude of

tne cutput Epectrum defined Lased on tht number cf bays aiay

Iron the inpuz regardless o tne input location in the L~S

should be verified by ccnsiaering other lattice structure-.

(4) Ine effects of boundarie-z, lattice member connectivities,

and structural ccfects on tne wave speed, the frequency at

tne maximu%. amplitude of the output frequency spectrum, end

tre attenuatiorn of The raximurr amplituds cf the output

spectruLr per bay scould be considered.

17

-- - C - ** - C . . * S . .

(5) The r.easurea initial wave sileed appears tc be between the

longitudinal wave sjpeed and the flexural wave speed. The

exact nature of the wave mode transnissicn should be

investigatcd. Tne pcssibility of wave rode conversion for

waves jropagatinE through a "T" or "L" joint should not be

excluded.

(t) The ;Cssibility of a decrease in the frequency at trhe

r.aximun amplituce cf the cutpuz spectrum as the signal

prcpagates 6hould te invesrt-ated. It's effect on the

attenuation cf tne maximur. amplitude of tk.e output spectrum

per lattice bay should also be conaider-d.

(7) ior the 22-bay iattice, at the frequencies considered, the

measurec dttenuation of the mLaximum amplitude of the output

spectruum per bay happers to correspond clcsely to the

lorLituainal attenuation in bulk aluminur. The exact nature

of this attenuation should be investigated.

(.) Reciprocity bet .een the input and the output has been

observed qualitatively. However, quantitative measures cf

reciprocity should be devcloped.

(9) Analjtical efforts for predicting the output signal measured

fror, tne planar ±attice should be uncertaken [12-15].

P?haps the analytical skill so ceveloped could be extended

to Letter uncerstanc wave propa~ation i. three-dimensional

L$ . Perhaps, statistical ener65 analysis (SEA) or patter

recoLnition tecnniques snould also be consicered in tniE

rebal c. jIn ccnciusion, tris experinientLl study demonstretes tlh

18

(- ,%%',.%" %%%%- .- ,,- . .%% ' ,. .%%j . , % ,%%%%, %%% ,

Wave 1 roja;ation characteristics of a lattice Etruczure can bE

cvtainec. In particular, tne wave speca, the frec.uency at the

maximum irmplitude of the output sjectru., anc tkae attenuation of

the vaximur, amplitude of the output spectrum per lattice Lay

appear to be useful parameters for the characterization of 6ave

propa~aticn properties of LSb.

C..

ILI

1%%Y,

Z! t.° N Z2

LKL Fah; LZ~ A

L] IL -i. Carc and t. . J Boyer, "L&r&e 5-pace Structurts-- -* Fantasiez: and Facts", Proceedines of AIAA, AS.E/ASCE/AYS 21Ft

Etructures, Structural Lyna-ic.Z and Naterials Conference,he: ir. Seattle , v.A, L*ay 12-14, 1980, Part 1, A F:r ic i. nIns-titute of Aeronautics End Astronautics, IV. Y, liy, I FC,~lPP- 101-114.

L [2 J.I1-. -L*I Ii a .1, Jr., FR.H. Leiler, Jr. arnd S.E. Lee, '1atPropfa,.etic. 'rnrcu~h 'T' and ILI Lattice Jcints", Air EcrceContrtctzcr ieport, October 19F,4.

1. i 1. Li.L a ;%s, Jr., L.A. Schrccer and S.S . Lee , "iy..aicAnal~sis of 'wo-L;iren..or.&l Lattices", Air lorce Contractor

* Feport, Aueust 1S64.

L]D.L. Edberg, "i.aterial rampirng of Simple Structures irn aSimulated Space Envi4ronierEnt", Lepartment of Aeronautics arneAztror.ut.ics, Sctarnfcro University, Stanford, CA, JanuaryJ

196~5

[5 J.-L. - illiarrnz, Jr., Hi. Nayeb-Hasheni and S.S. Lee,"Ultrasonic Atten~uation and Velocity in AS/3501-6 GraphiteFiber Com~posite", Journal of Nondestructive Evaluation, Vcl.1, Lo. 2, June 1'9'0, PP. 137-148.

[ 6j K.F. craff, l~ave :oticn. in Elastic Solids, Onic teUniver--ity PreE.., Columbus, Oil, 1975.

I 7J J. Krautkranier and r-.Krautlhrarrer, Ultrascnic Testing, ofaterialLa, 3rd ed., Srprineer-Verlag, N.Y., N1, 1983.

*[&j J.H. 1-1im Jr., J.J. Zrtang and S.S. Lee, "Lave

Propatat2.on INeasurer.ents on :wo-Iirnensioral Lattice",Air Fcorce Co.tractor Rezort, Septenler 1S85.

19] J. H. 1.i. lliams, Jr., L.E. ~:ahn and S2.S. Lee, "Effects ofSpecir:en Resonances on Accustic-Ultrasonic Testing",L&ttriLls Evaluation, Vol. 14, 110. 13, Lecer.er 198.3, .

15C2-15 10.

010 J.?r, V'illiams, Jr., E. Karskulle and S.L.. Lee, I"UltrasonicIrnput-Cutput for TransmittinC and Receiving Lonfitudinal'Iransducers Coupled to Sar..e Face of Isotrspic EliasticPlate", 1Eaterials L.valuation, Voil. 40, Lo. Ei, r~ay 19F2, pT.655-662.

[ii] j.h. I.,ilffizas, Jr. , S;.S. Lee and H. Fayeh-Eas .emi,"Ui.trascr. ic L.ave Prcpagatior. LosL Factor in Ccrmposite in'jerms of Constituen. Properties", Journal cf 1,ondestructive

IL Lvaiuataon, Vol. 1, !.o. 3, Selternber 196C, pp. 191-199.

[1!7Ji. ilins, J. F.C. Erg and 5.S. LEE, "I FVe

20

Propagation and Dynamics of Lattice Structures", Air ForceContractor Report, May 1984.

[131] J.H. Williams, Jr. and H.K. Yeung, "Nondispersive WavePropagation in Periodic Structures", Air Force ContractorReport, January 1985.

L14J J*H. Williams, Jr., H.K. Yeung and R.J. Nagem, "JointCoupling Matrices for Wave Propagation Analysis of LargeSpace Structures", Air Force Contractor Report, April1986.

[15i J.H. Williams, Jr., R.J. Nagem and H.K. Yeung, "Wave-ModeCoordinates and Scattering Matrices for Wave Propagation inLarge Space Structures", Air Force Contractor Report,October 1986.

ILI

21

-2 " .'; " _..'.' ' .. .'. '. -"- - " v' < " ' " " "-."-." " - -" ' .'_." -.' *" " .

em,J.

TAELL 1 Summary of L easur c ,ave Speeds for Initial [,.aveArrivin6 a- Various Output Locaticns lor Various InputLocations.

Leasured Ehave Speed (kin/E)

Output for Input LocationLocation -

A L V v

A * 5.04 4.(7 4.70

U b.01 5.C2 4.66 4.70

C 5.12 5.04 4.67 4.66

4.68,

5.14 5.06 4.61 4.6(

L 5.12 5.O( 4.72 4.65

P 5.12 5.12 4.72 4.62

C 5.08 5.12 4.7l 4.5

55 1 I 4.78

-5.04 5.12 4.76 4.53

I 5.C2 5.90 4.74 4.70

L 5.05 5 4.73 4.63

S4 -E 1 5 CO 4.71 4.- '6

4 K 4.C 5.12 4.6 4.74

C 4.81 5.1 4.72 4.0"

5.03C' 4.61 5.14 4.72 .•0I I,

-- -----------------------------------------------------

(Continued on next Fage)

22

" " " " . . . . ~% % " " % % % N '- ' "% '% * ' '-% % "% " '*" % '

'" ' "

ALLi 1 (Ccntinuec) Surmary of Ieesured I.ave Speeas fcr lnriti*lLaves .rriving at Various Cutput Locationsfc- Various Inut Locations.

Ieasiured .ave S;eed (kr./s)Ou tut for Input Location

Location --------------------------------------------A L V V 1

I----------------------------- ----------------------------------------------

C. 4 C5 5.11 4 - 4 5

E 4.65 5. C. 5.06 4.72

S 4.69 5.05 4.9e 4.61

T 4.71 5.05 4.93 4.96

U 4 . 73 4 99 5 1 c 4 .4•I,, ••I

V 4.71 5.00 * 44I 4 -

"1 4•64 4.74 4 • . -1 4.71Oi ,

1 4.64 4- 71 4.(15 4 , 73

C 4.Sf6 4.70 4.65 4.711 ".-

I 4.79 4.65 4 6 4 70

h 4.73 /,.61 4.68 4.t7

- 4.65 4.57 4.7C 4.F3

1I 4.7 4.51 4.79 4.73

1 4.5k .,,69 4.60 4 .Pl

1 4.2 4.61 4.77 4.7 -

I 4.E i 4.96 4.77 4.61

(Continued or. next pace)2.3

23'

'IALLL 1 C~ntinuec) Sur:i~ary Of lieESurec lave &peoEas for Init ialILaves- Arriving. at VarioLS Output Locaticrsior Various Input Lccatior.

Measureu li.ave Speed (kr,/s)Output for Input Lccation

* ~Locaticn ------------------------------------------------------- I

A L V0 v------------------------------------ ----------- -------------------------------------

L 4-69 4.64 4.7 5 ~. C

4~~ ~ ~ ---6 -750

1 4.5 4-8 4- L5 I

P 4.6 4. 4.74.0 5.0 9

1-C .5 I 5-0 5I

4.53 4.65 4 c 4.73*1.C

I .5 49 4.67 '.0

1 j I I-- -- - - - - - - - -- - - - - - - - - - - - - - - - -

Ic appicbl

2 4

TABLE 2 Calculated Flexural Wave Speed in Aluminum Bars ofCross Section Corresponding to That of Lattice atVarious Frequencies [6, page 1433.

------------------------------------------------------------------------

ISCalculated Flexural Wave Speed

Frequency I -----------------------------------(kHz) (k/a

(km/s) (ft/u)( 4.-

----------------------------------------------------------------------------------------

100 1.89 6,200

150 2.32 7,600

200 2.67 8,800

250 2.99 9,800 A

300 3.28 10,700

350 3.54 11,600 1|400 3.78 12,400

450 4.01 13,200I II -

500 4.23 13,00I II "

25

-,-..-

uLL 3 u -. ry of irEcasurec i requenc :.c- et 1,a xirur- A. rit C-

C utiu t Fre~juency Spect~ra o oee Arrivin.5c-CLu,;ut Lccatlons for VarioLZ Ir ut Locaticn.

Ieasurod Frequency (z)at Vaxi.umr Arplitude* lof Cutj-ut frequency S-ctrum fcr Ir~ut Locaticn:

Loat.~.------------------------------------------------------ I

A L v V------------------------------------------------------------ -----------

7 0

L c 370 'Z

L7 37-3,

L373 1 4C 1770 3 c

1-73790 3 7 _ 9

S3~ C, II 43

L4 373 C

3 I 37r 36C

0 3SC 435uC07

L 443 41 7

% %

TALLL (Lornir.uea) Sur.rary of Neasured Frequencies at 1.cxrur.A-,pli tuae c: Output Irequency Spectra fc -!.ave3 ArrivinL ct Var cuE Output Lccati nsfor Various Ir.ut Locaticn.

----------------------------------------------------------------------------------------

i.,easured Frequency (kHz) at .axirum Arplitudeof Outjut Frequency Spectrum fo: Input Locaticr.

Luczticn ....A L vC V 1,

-,C 355 3 37C

38b 390 357 355

123 375 443 358

123 393 450

U 115 393 440 360

V 115 393 * 360443 393 3(6. 115

1 443 393 370 115

44E, 393 3-8 115

L 358 390 368 123

L 370 390 413 370I

F 368 358 366 373 11I i "I

C353 445 3c> 3(6

h 39C 440 558 I

1 .390I I

J1 390 44E 3(3 397

(Continued on i.ext pa t)

th.

271

3(Contir~ueu) Sur.mar) cf Measured FrequercieEr at I. Ex r- u1 '-it u d of ..utput Freciuenc.- S cc tr& f or

l.aves Arr'VinL at Variour (Gutput Lcczticr.-* for VariCu3 Ir.iut Locaticr..

*LeaSureC FrrequEncy (ikHz) at 1.CXir.Lm ArT1I 'tur&lcf Cutiut Frequenc Sjectr-r for InPLu: Lccaticn!

cutA..tLocaticn--------------------------------------------------------I

A L v 0 I

------------------------------------------------------------------------------- --------------

E 3 9C i 395 3 E5 393

L I

11393 11 ],95 11 3F I 395

4 e 3)6 E c .

G3ttL 36C 443 0

388 4/.3 I 35L

s39C 3511 -7

TS1 3 11 39C 35C 373 1

T 23393453C

U 115 4/. 3S31-- - - - -- - - - - - -- - - - - - -- - - - - - -- - - - - -

* .cot app.Licablc

28

%1

7ALLL 4 SUIFuMry of L.easureed Elaxi:u Az, plituces of Cut; utFrequency SpectrE for iaves Arriving at Varicus OutputLccations for Vatious Input Locatior.s.

05

Leasured P.aximu. A.pl-tuce (r:V) of OutputFrequency Spectrum for Input Locaticn

GutputLocation -

I I '1 a IL V0

A 3 9 .c. 1 3 - C .

E 11.63 9.65 -.23 4.29

C 11.33 9.95 3.55 4.91 "i g

w

D , 11.69 10.30 3.61 5 ..

£ 11.24 51031 5.30

F 11.70 1C.85 4.61 5.64

U 12.53 11.03 5.04 .05.

. 12.90 11.23 5.69 8.41

I 12.56 11.91 6.1< 1.L8

J 12.43 10.95 6.49 10.21

K 10 .89 1C .94 6.54 10.29

L 9.89 * 6.63 1 C.8C

1 9.78 10.94 -7.7s 11.4(:

7.61 11.59 8.CO 11.33

0 7.51 11 .3 8.85 11.79

5-C4 11.54 9.38 11.13I

---------------------------------------------------------------------------------------------------------

(Continued or. next page)

29

-e-- -d, %...

!ALL (Contir.uE ) SL..r.ary c: i easured r'ixrur. Ar,.f11tldes ofCLtqut irt iuency S;tctr for lav. s Arrivinat '.zriouc CutL-u- Loc.tiorz for .ricuE InutLocaticnE.

i eaaured Laxirmun. r;:lituce (rV) of Out-utFrequency- Spectru:. for Irnut Locatio

* Cu:jiut i

Lccator. ----A L v V

9------------------------------------------------------------------------------ ---------------

5.26 11.41 9.96 11 .2/

4.L 10.60 10.51 1.5

S4.1l 10.25 11.24 10.25

3.69 1C .04 11.33 10 -9 I

3.L5 10.(19 11 .57 10.14

V 2.99 9.44 1C.14

A 10.> 6.98 .08 _.46

.39 9.24 3.1. 4.15

C1 1C.4E E . O 3.30 / .2S

I: 1C.53 1C.2C 3-t 4.,94 -

L 11.2C, 10.39 3.,7 4,11 .4.26 4.1C 4.E5

C1 11 .F4 1l; s 4 ., 6 5 .,C

I 1 .c 10.(5 4 6 6. 3

11C 11.S4 10.2 4.N

Ji 11.89 1C.20 5.31 .03

(Continued on. next pa e)

31

%---.

TI,!,LL 4. (Ccntirnuea) Summary ~f iLeesured ieaxiimur P~plituc'-s C.Output Fre(,uency Slectra fcr iaves Arrivini-at Various Cutput Lccaticnz for Various Il'utLocatiox..t.

0- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

1 F.easured Plaximuim Amplitude (mV') of Output* i requency- Spectrur fOr Input Locatiorn

Lccet..cn-- - - - - - - - - - - - - - - - - - - - - - -A L V o

--------------------------------------------------------------------- ---------------

11.1c, 10.-5 1 1 5.46 11 10.CC*

L 9.63 10.14 6.5F 12.2EL 1

9.7,, 10.3 6.9 12.Z6

( I 9.1 10. -48 7.95l24

0j b.05 10.29 E.39 1.8

1~ rF 7.6 -5311.45

u-41 10C-3 4 10. -43 11.0 C4

1 6 I

C5.05 10C).3 1. 3/1 11.-24

T 1 1 45 9 .6E0 11.-63 11 .41 1

U 11 3.55 9 .7-1 11 .71 11 .(4

1

* 1ct applicable

TAELL 5 Loiari.ons of lave PropaEatic Character.stics Eetheenthe 5-iay and 22-Eay Planar Lattices.

-----------------------------------------------------------------

5-Lay LLttice 22-Lay Lattice

I I------------------------------------- -------------------4 Frci I To I rom To

-------------------------------------------------- --------- -------- --------- -------

lav= br. eed (hrr./s) 4.13 5.10 4.53 5.1

------------------------------------------------- ------------------ --------- ---------

frequency (kfiz) 283 355 353 450

I------------------------------------------------------------- ----------------------------- A

Arplitude ,ers.s Nurber01 Lay L

Ccrrelaticn Coefficient9 0.929C 0.9156

Attex.uaticn (Leper/Eay) 0.35. C.C£5C

Attenuation L.eper/cm) 0.013 0.C14

I(

'

F..~-

LUCODS

0c

*Z *

0 9 *

-33-

Osc illIoscopeInput Pulser -Receiver

SignalChannel I

Channel1 2

SYNC Signal

E xternal I

TransmittingTransducerReivn

Transducer R %

i sc~emiticof xpeimenal vstm fo mesurng wve.pee

and requncyspecrUMof lttie, sowig tyica

locaionsot tansittig an recivig trnsduers

cD a)

u

c) z.*f

U)U

CY 4Ji

00

-35-i

Vertical Scale:

1.00 V/Division

Horizontal TimeSweep Rate:

(a) 0 9.90 ws/Division

Vertical Scale:15.63 mV/Division

Horizontal Scale:

f 64.00 kHz/Division(b)

Fig. 4 (a) Time trace and (b) frequency spectrum of output fromreceiving transducer when transmitting and receiving transducersare coupled together directly (face-to-face) without anystructural specimen.

m-

-36-

%.%

4p~

0N

00000 o o 0

CD( <m

00 ~O0. 0 000 -

-0 o o IL

0 0-

C)C

0 M40

CDC

0l E 2z

4-1

04UE)

N OD f- (D v

(AwuiwjnipedS Indino loapnlildwV WnWIXDN J 0 160-1

-37-

- - ~- - a. ~A - -. - - .- V.

(A

~i.

r.

L.

a a

N.

I

S.-

.5.

.5

S.

5-

A5 .*: a~