Fahy 1968 JSV Some Experiments With Stiffened Plates Under Acoustic Excitation

8/3/2019 Fahy 1968 JSV Some Experiments With Stiffened Plates Under Acoustic Excitation

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J. Sound Vib. (1968) 7 (3), 431436

SOM E EXPERIMENTS WITH STIFFENED PLATES UND ERACOUSTIC EXCITATION

F. J. F A H YInstitute of Sound and Vibration Research, University of Southampton, Highfield, Southam pton,SO9 5NH, England

ANDR. B. S. W E E

Departmen t of Mecha nical Engineering, University of Southampton, Highjield, Southamp ton,SO9 5NH England?(Received 4 October 1967)

Plates w hich will be subjected to intense acoustic excitation are often stiffened w ithbeam s. These are added either for reasons of static stability or to reduce the vibration .Measurem ents have been mad e of the average ac oustically induced strains in a series of_ik n. mild steel plates to which identical beam stiffeners have been attache d in differentway s. It has been found that point attachmen ts such as rivets can be preferable to lineattachm ents such as welds. The m agnitude of the benefit gained from attach ing the stiffenerat discrete points is not explained by existing theoretical vibration analysis.

1. INTRODUCTIONAcoustic fatigue has been a major consideration in the design of aircraft structures for morethan a decade. It has recently reared its ugly head in the field of design of the heavier steelstructures used in the gas circuits of large nuclear reactors. The spatially distributed, highfrequency nature of acoustic pressu re excitation ma kes the problem of design, or latermodification, of structures to minim ize severe vibration rather different from the morefamiliar problems associated with mechan ically induced harmonic vibration. Conseque ntlymeasures which have been found to be beneficial in the latter case may not be so with acousticexcitation. A case in point is that of the stiffening of plate or shell-like structures either toincrease their static stiffness or to reduce their vibration stresses.

Some simple experiments have been ma de to obtain a broad idea of the effect of differentmetho ds of plate-stiffener connection on acoustically induced plate stress [l]. No attempthas yet been made to investigate the effects of variations in stiffener co nfiguration, or in itsstiffness relative to that of the plate. However, it is felt that sufficiently large differenceshave been observed between the stresses in plates stiffened by continuously attached stiffenersand those in which the stiffener w as attached at discrete po ints to justify early publicationof these results, w ithout, as yet, their explanation, to bring to the notice of designers thepossible beneficial effects of correctly applied stiffeners.

2. APPARATUS AND MEASUREMENTSStiffened and unstiffened rectangular 36 in. x 30 in. mild steel flat plates of & in. thickness

were clam ped to a frame of 2 in. x 2 in. x + in. steel angle section which reinforced thei Present address: 2 Depot Road, Block 1 93, Singapore 5, Malaysia.

29 431


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432 F. J . FAHY AND R. B. S . WEEupper edges of a 32 in. x 26 in. x 24 in. steel water tank of O-104 in. thickness. The cisternwa s surrounded by a 4 in. thick layer of sand contained in an outer w ooden box. An intense(148 dB), broadband noise was produced in the box by allowing high pressure air to enter

-a A r a l d i t e

Wet ted G l ued - and bo l t ed

P o i n t bo l t ed U na t t ac hed

Figure 1. Stiffener configurations.

Figure 2. Strain gauge positions.

$in.x l in x4 in2.C l om p l ng

it at the base of one side through a 3 in. gate valve. The air left the tank through a 6 in.diameter pipe, also at the base of a side. Aerodynam ic buffeting of the panels wa s negligible.Microphone traverses of the volume of the box showed that the +-octave sound pressurelevels varied by no more than fl dB from the averag e over the frequency range from 380 to


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SO M E EXP ERI M ENTS W I TH STI FFENED P LATES 43 312,500 Hz, except in the lower region where aerodynam ic effects interfered with the soundmeasurements.

Stiffeners of a standard configuration were attached to the plates in different ways. Thestiffeners consisted of a grillage of 1 in. x 1 in. x Q in. channel sections welded in the formof 6 in. squares. The stiffener attachm ent configurations are shown in Figure 1. The platewa s held agains t the unattached stiffener by a sm all static pressure differential. The ends ofthe grid were clampe d at the boundary together with the plate. Strain gauge s were placedin the positions shown in Figure 2 for all panels. One-third-octave strain levels were mea suredduring excitation. Average m ean square values were obtained by taking the arithmetic mea nof the individual mea n square values. Accelerometer mea surem ents were also mad e tocheck that the ratio between average strain and average acceleration approxima ted to thetheoretical single mode, or diffuse field, value given by (c2) = (n2)wf CL, where w, is thecentre frequency of the filter band and CL is the speed of longitudinal wave s in the platema terial. Me asurem ents were mad e in +-octave band s of the total loss factors of each panelin situ by recording the decay of strain following impulsive excitation. Averages were takenover loading and transducer positions.

3. RESULTSThe results are presented in Figure 3 in the form of radiation loss factor curves. These

have been calculated from a relationship between average mean square acceleration and-3 0

d -6 0Pc- -7 00H2 -80

-9 0- -+-- Glued and bolted sti f fener-a-- Point bolted sti f fener- - - R ive t ted s t i f fener

f oc tave band cen tre f requency (Hz)Figure 3. Radiation loss factors for the set of stiffened plates.

average mea n squ are pressu re derived in reference 2, and discussed in section 4 below,together with the theoretical relationship between average mean square strain and averageme an squ are acceleration of section 2 above. They are presented in this way so that directcom parison can be mad e between the present results and those of previously publishedliterature concerning the response of structures to high frequency, diffuse field acousticexcitation [2,5], in which q radhas been derived from experim ental results in a similar man ner,albeit directly from measured accelerations.

Because the factor of proportionality between T,,~ and the average mean square strainper unit average m ean sq uare pressu re is the sam e for all plate configurations, apart from


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43 4 F. J . FAHY AND R. B . S . WEEthe individual mec hanical loss factors, as show n in section 4, the curves of l;jrad serveas better indicators of relative merit for the various configurations than the measuredstrain/pressure curves because they normalize the results to conditions of equal mechan icaldam ping for all configurations. Of course the relationship presented in section 4 can beused to derive strain/pressure values if it is so desired.Figure 4 show s the total los s factors, qt, me asured by impulsive excitation and decay.It is interesting to note that the high.frequency dam ping m echanism proposed by Ung ar

h I I I I I I I I I I I0,026Poin t bo l ted

.Glued and bo l ted

/ Unattached

--L-,002


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SOME EXPERIMENTS WITH STIFFENED PLATES 43 5where r(w ) =: [27r2n,(w)/M P](c/p) an d P(W ) = qrad/(rlrad+ 71mech) %&I r. Mt, is the ma ss ofthe panel, c i.c, he speed of acoustic waves, p is the density of the air, 7],,d is the loss factor ofthe panel due to acoustic radiation and q,,,h is the loss factor due to mechanical dissipationand radiation into surrounding structures. In the present cases 7 ) m e c ~ ~ % a d a n d p ( w ) i s g i v e napproximately by ~rad/~m ech.The moda l density of a uniform panel, n,(w), is given by-n,(w) = 2/3A/2nhC, where A is the area of the panel and h is the thickness.

This relationship had previously been derived for homogen eous panel vibration [2]. Itmay be used unchang ed for the stiffened panels under the assumption s that the mod aldensity of a stiffened p anel is equal to the sum of the moda l densities of the stiffener, nb(o),and of the panel, n,(w), and also that the ratio of average mean square stiffener vibrationvelocity to plate velocity is given by

< G>K v;> = MP %(U)lMb n,(w).The latter relationship has been derived by Heck1 [6] under the assum ption that the

typical length, L, of the subpane ls formed by the stiffener is related to the flexural w avelengthsin the plate and stiffener beams by A,,> L > X,. This relationship holds in the presentcase for the frequency range 500 Hz cf -c8300 Hz. Lyon and Eichler [3] also obtainthis relationship provided that the damping of the stiffener itself is low. The ratio~,n,(w)/~,,n,(w) is approximately @ 035 for the tested structures. n*(u) is given by

rib(u))= L/2rr(w2 EI/p, A)-/4where L is the length, I is the second mom ent of area, ps is the density and A is the cross-sectional area of the beam .

M aidanik [5] found that the attachment of beam s to a plate increased its radiationresistance, R,,, (=Q~,,uJ,MJ, so that the response of the heavier stiffened panel to a diffusefield exceeded th at of the unstiffened panel. The explanation of this increase lay in thedecoupling of the sub-pan els by the stiffeners which destroyed acoustic canc ellation byadjacent internode regions of opposite phase at frequencies below the panel critical frequencyf c . he critical frequency for a uniform panel is given by f c = c2/1+8 hC,. In the present ca se,f c N 8000 Hz for air at 15 C. The ratio of stiffened to unstiffened radiation resistance is givenby 1 + PJP, where P, is twice the total length of the stiffeners and P, is the parame ter of thepanel. In the present case this ratio h as the value 5.5. The max imum ratio of stiffened tounstiffened qrad, which w as observed with the glued and we lded structure at 1000 Hz, agreeswell with this figure. Below and above this frequency the ratio falls off, indeed to less thanunity, below 630 HZ and above 1600 HZ. The low frequency reduction in radiation resistanceexhibited by this type of structure wa s also observed by Ma idanik. He attributed it to thefact that a t low frequencies (in the present case below 5 00 Hz) the panel waveleng th exceedsthe subpanel dimension L and the stiffener then adds fairly uniform mass and stiffness butdoes not greatly decouple adjacent sub-pan els. The radiation loss factor of the glued andwelded pa nel does indeed fall off rapidly below abo ut 500 Hz.

The stiffener configurations other than the glued and bolted structure cannot be consideredto act in the same man ner because flexural waves would pa ss, largely unscattered, across thepoint bolted conn ections and also it could be observed that panel rotation in a plane norm alto the beam s was not greatly constrained by the connections of the rivetted structure. Henceit would be expected th at these, and the unattached panels wo uld not exhibit the increasedradiation resistance discussed above. On this basis it would be expected th at the radiationloss factor of these configurations would be similar to that of the plain pa nel. Figure 3 show sthat this is not at all the case and tha t the average r.m.s. stresses in the attached panels areapproximately an order less than those of the glued structure over a wide frequency range.It should be noted here that the difference between the max imum stresses may not be so


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43 6 F. J . FAHY AN D R. B. S . WEEgreat because the dynamic stress concentrations at a point attachm ent could well exceedthose at a line attachm ent [8]. However, it is not likely that this factor would cancel outthe great benefit apparent from average strain results.

It mu st again be stressed that the present results have been obtained from me asurem entson one basic beam -plate system and that no more general conclusion can be drawn thanthat it is worth c onsidering alternatives to continuously welded stiffeners when dealing withhigh frequency acoustic excitation. In the absence of theoretical explanations for the presentresults it would be necessary to investigate the behaviour of any different basic configurationexperimentally, especially since mec hanical loss factors c an vary so much from structure tostructure.

Of the possible c auses of the large discrepancy between theory and experiment it isconsidered that a deviation from the theoretical ratios of stiffener to plate energy is themost likely. However, modification of the plate wave field, with consequent acousticdecoupling, or severe effects on energy distribution of mech anical dissipation in the plate-stiffener coupling cannot be ruled out.

5. CONCLUSIONSMe asurem ents of the response to acoustic excitation of a sm all numb er of steel plates

stiffened in different ways have indicated that wherea s continuous (e.g. fillet-welded)attachm ent of stiffeners may aggravate plate vibration stresses, local point attach me ntssuch as rivets or bolts can greatly reduce these stresses. Different basic plate beam systemswill require specific investigation but the present results may offer guidance in this respect.

REFERENCES1. R. B. S. WEE 1967 Report submittedfor the degree of B.Sc. with honours in engineering. Departmentof Mechanical Engineering, University of Southampton. Acoustically induce d vibration of stiffenedpanels.

2. R. H. LYONand G. MAIDANIK 962 J. acoust. Sot. Am. 34, 623. Power flow between coupledoscillators.3. E. EICHLER 965 J. acoust. Sot. Am. 37,995. Thermal circuit approach to vibrations in coupledsystems and the noise reduction of a rectangular bo x.4. R. H. LYONand E. EICHLER 964 J. acoust. Sot. Am. 36, 1344. Rand om vibration of connected

structures.5. G. M~UDANIK 96 2 J. acoust. Sot. Am. 34,809. Response of ribbed panels to reverberant acousticfields.6. M. HECKL 961 J. acoust. Sot. Am. 33,640. Wave propagation on beam-plate systems.7. E. E. UNGARand J. R. CARBONELL96 6 AZAA J. 4, 1385. On panel vibration damping due tostructural joints.8. E. E. UNGA R 1961 J. acoust. Sot. Am. 33, 633. Transmission of plate flexural waves throughreinforcing beams : Dynamic strain concentrations.

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Fahy 1968 JSV Some Experiments With Stiffened Plates Under Acoustic Excitation