Some Recent Information on Aircraft Vibration Due to Aerodynamic Sources

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SOME RECENT IWORMATION ON AIRCRAFT VIBRATION DUE TO AERODYNAMIC SOURCES By Harry L. Runyan N A S A Langley Research Center Langley Station, Hampton, V a .

Presented a t t h e Acoustical Society of America Meeting / I (ACCESSION NUMBER) O t t a w a , Canada May 21-24, 1968 Some Recent Information on Aircraft Vibration Due to Aerodynamic Sources By Harry L . Runyan N A S A Langley Research Center Langley Station, Hampton, Virginia May 21-24, 1968 The purpose of t h i s paper is t o point out some of the aerodynamically induced yibration problems of aircraft. Specifically, the problems t o be discussed are l i s t e d on f i g u r e 1. The problem area is shown on the l e f t , and the bar graph alongside each i l l u s t r a t e s the time during the f l i g h t that the vibration i s most significant. Going down the list, it i s shown that, i n general, (1) boundary-layer noise i s of significance during the cruise or

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major portion of the f l i g h t ; (2) buffet f o r subsonic a i r c r a f t i s similarly hr of importance during the high-speed f l i g h t , whereas f o r supersonic a i r c r a f t the buffet region i s normally during the ascent-descent phases when the a i r c r a f t is i n the v i c i n i t y of Mach No. 1; ( 3 ) f o r gust response, f l i g h t i n the lower portion of the atmosphere represents the more important portion of f l i g h t t i m e , whether f o r supersonic or subsonic a i r c r a f t ; (4) engine noise of course, during ground operation and and sonic fatigue a r e important, take-off; ( 5 ) with regard t o helicopters, t h e picture is black throughout the whole f l i g h t range.

Boundary-Layer Noise Noise from the boundary l a y e r which, of course, i s i n a turbulent condition, is important from two aspects: (1) The noise generated is trans- mitted through the vehicle skin i n t o the interior, which could damage L-6074 - 2 - equipment o r cause discomfiture of passengers. (2) The noise generated could damage t h e exterior skin structure through long-term exposure and resulting fatigue failure.

A tremendous amount of l i t e r a t u r e has been generated i n t h i s area, f o r instance, Alan Powell and T. J. B. Smith prepared a bibliography i n 1962 ( r e f . l ) , a t which time they noted 2,000 articles, and the first reference i n t h i s l i s t was a paper by Michael Faraday i n 1818, "On Sound Produced by Flames i n Tubes."

The basic work of Hans Liepmann as w e l l a s the d e f i n i t i v e experimental work of W. W. Willmarth are noted. Ribner of t h e University of Toronto and Maestrello of The Boeing Company ha.ve been active i n both the experimental and theoretical areas of t h e problem of boundary-la.yer noise.

Before discussing some analytical approaches, reference is made t o some c work done by D. A. Bies of Bolt Beranek and Newman ( r e f . 2 ) . H e examined recent l i t e r a t u r e concerning the measurement of the pressure fluctuations i n the boundary layer, and devised a nondimensionalizing parameter which would c o l l a t e the data i n t o a l o g i c a l pattern. After scanning t h e l i t e r a t u r e , he s e t t l e d on about 30 sources of data, and on figure 2 i s shown a summary of h i s r e s u l t s , where he selected f o r h i s ordinate, the quantity

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where U , = stream velocity = frequency spectra F ( f ) 4 = dynamic pressure f r i c t i o n coefficient Cf =

dC = boundary-layer displacement thickness

For the abscissa, he chose t h e Strouhal number where LD i s t h e frequency, V is t h e free-stream velocity, and 6* i s the boundary-layer momentum thickness. There is a very large s c a t t e r i n the data., so t h a t e i t h e r the correct parameter has not been found or the measurements themselves are not accurate. The l i n e i n the middle indicates a region he was able to identify as an area of concentration of r e s u l t s . It is apparent, then, t h a t there is work to be done i n the experimental determina,tion of these fluctuating pres- ...

sures, as t h e proper nondimensionalizing parameter has not been determined.

u Also, a definitive and satisfying theory of boundary-layer turbulence has not been determined. What i s the mechanism whereby the flow becomes turbulent? What i s the triggering mechanism, and i n what form does t h i s o s c i l l a t i o n e x i s t ? What a r e the nondimensionalizing parameters? In many places i n the l i t e r a t u r e a r e found statements that o f f e r no hope f o r a rational explanation, but t h i s i s a rather bleak outlook, and some day there w i l l be a. satisfying explanation. For instance, Theodorsen i n 1958 proposed a model f o r turbulence which consisted e s s e n t i a l l y of the forma.tion of horse- shoe vortices i n t h e boundary la.yer, and the subsequent growth and decay as t h e cause f o r t h e pressure fluctuations.

Black's hypothesis.- Following t h i s l i n e of attack, Thomas J. Black, "RACOR, has developed what may be t h e beginning of a rationale f o r boundary- layer noise ( r e f . 3 ) . At t h e present time, t h i s i s j u s t a physical model

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and t h e mathematics s t i l l must be developed. O n figure 3 i s shown the concept is plotted a velocity of t h e basic mechanism f o r turbulence generation, where

profil-e, but the velocity i s against a r e l a t i v e velocity, X - Ui, where Ui

i s the velocity of t h e disturbance, thus f o r an observer on the disturbance, t h e w a l l appears t o be moving upstream, while the f r e e stream is moving down- stream. Black postulates t h a t t h e velocity d i s t r i b u t i o n is i n i t i a l l y laminar, having t h e p r o f i l e as shown on t h e top r i g h t , but as the flow progresses certain nonlinear e f f e c t s cause the flow t o gradually deviate from t h i s i n i t i a l flow, as shown i n t h e figure. Below t h i s figure i s plotted the d i f - ference i n t h e o r i g i n a l purely viscous velocity distribution and t h e newer velocity d i s t r i b u t i o n caused by t h e nonlinear effects. The supposition i s now t h a t a vortex p a i r i s formed due t o the shearing action i n the laminar . .

sublayer, as shown on t h e bottom l e f t . The upper vortex w i l l then f l o a t up- ward due t o a l i f t i n g force similar t o the bound vortex on an a i r c r a f t wing.

A vortex must e i t h e r be i n f i n i t e i n extent, end on a s o l i d surface, o r c1os.e on i t s e l f . For t h i s case it w i l l form a complete c i r c u i t , such as shown on figure 4, and t h i s picture i s i d e n t i c a l t o t h a t depicted f o r a l i f t i n g wing.

Eventually, t h e vortex on t h e w a l l w i l l dissipate, and a.horseshoe vortex w a l l and extending off into the boundary layer w i l l remain.

attached t o t h e Another interesting facet t o t h i s physical model i s tha.t it i s possible t o s m a l l eruptions or j e t l i k e flows i n the w i n stream, explain t h e presence of which have been observed experimentally, and t h e explanation could be t h a t the induced velocity on t h e underside of t h e vortex resulting i n a flow which, when it reaches t h e edge of t h e boundary layer, would look l i k e s m a l l random j e t s . O f course, it i s presumed t h a t t h e strength of these vortices would

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be variable and thus provide random pressures. Further, Black points out t h a t t h e scaling distance f o r the smaller and higher frequency disturbances may be t h e laminar sublayer thickness, whereas t h e lower frequency, l a r g e r vortices may scale with t h e boundary-layer thickness. This attack should be pursued f u r t h e r to see if a mathematical model could be developed. Some of t h e questions to be determined are: A t what point i n t h e flow w i l l t h e vortices form, and what w i l l be t h e i r strength, and what determines t h e i r strength?

Houbolt 's method. - One more semianaJytica1 method f o r turbulent boundary-

l a y e r flows i s research recently done by Dr. John C. Houbolt of Aeronautical

Research Associates of Princeton (refs. 4 and 3 ) . The problem w a s t o deter-

- mine the fluctuating pressures i n the boundary layer at hypersonic speeds.

. . ' On figure 5 i s plotted t h e root-mean-square of the pressure fluctuation divided by the dynamic pressures plotted against Mach number. Here, it can be seen t h a t a rough configuration, such as t h e Mercury spacecraft, may have pressure fluctuations ranging around 5 percent of t h e free-stream dynamic f o r smooth shapes the pressure, which would be i n the buffet range, whereas order of magnitude i s around 1/2 percent of the dynamic pressure. Some vehicles enter t h e atmosphere at very high dynamic pressures and high Mach number, and u t i l i z i n g t h i s constant value f o r t h e same response would indicate extremely high values of t h e pressure fluctuations, enough so t h a t the vehicle would certainly be destroyed or seriously W a g e d , and experience has shown t h a t t h i s is not t h e case. So what Houbolt did was to derive a more r a t i o n a l variation of CT with Mach number. H e used as a basis t h e l o c a l mean density - 6 - of t h e flow i n t h e region of large velocity gradient i n the boundary layer.

With t h i s assumption, he derived an expression f o r t h e r m s pressure as shown on t h e top of figure 69 a = cp V where C i s a constant t o be determined, 1 0 p1 is t h e density a t t h e point of maximum velocity gradient, and Vo i s t h e free-stream velocity. Utilizing a recovery f a c t o r and f i t t i n g the expression t o the known subsonic and low supersonic results, he obtained = 0*0°7 2 ) 1 + 0.012 M Note t h a t f o r reduces t o 0.007, a value i n agreement with t h e M = 0, a/q experimental r e s u l t s previously shown.

Also, by assuming a model f o r convection velocity, he was able to derive an expression f o r the power s p e c t m , as follows: 1 2

0.00002 y q 6j"

c p ( 4 =

1 f t + ) 2

On the two p l o t s of figure 6 a r e shown t h e a/q against Ma.ch number and the s p e c t m f o r various velocities.

Note t h a t with the model Houbolt selected, does indeed drop o f f i n the high Mach number region. A s f a r as i s t h e a/q known, t h i s has not been confirmed experimentally, due principally to t h e d i f f i c u l t y of measuring fluctuating pressure under high-temperature conditions, O n the same figure are shown soge-s$ectra f o r several f l i g h t velocities. As t h e f l i g h t speed increases, t h e spectra a r e reduced i n magnitude, but a r e very f l a t and extend t o higher frequencies.

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Buff e t Buffeting of a i r c r a f t is a phenomenon related t o boundary-layer noise.

The scale lengths a r e much l a r g e r than the boundary-layer thickness and approach t h e dimensions of the body dimensions, such as the wing chord or body diameter.

With regard t o the aerodynamic input, there a r e no theoretical means f o r estimating the buffeting unsteady pressures, and thus r e s o r t i s made t o experimental methods, principally wind-tunnel t e s t s . o n scaled models.

O n figure 7 a r e shown some types of buffet problems which have arisen on aircra,ft. O n the top is a very common type which involves t h e vibration of t h e t a i l resulting from unsteady flow from the wing. Another type involves t h e f l o w around a body with unsteady incidence on a canard, such as happens on the B-70 f o r some subsonic f l i g h t conditions. Another type can occur i n , . .

cutouts o r bays, and t h i s is usually important s o l e l y f o r the design of the

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payload i n the bay, such as rockets and missiles. Another type can be due t o protuberance on a i r c r a f t , f o r instance, f o r camera windows or other necessary bumps.

T a i l buffet. - With regard t o tail-induced buffet, a dpamica.lly induced

aeroelastic model i n which both Reynolds number and Mach number are thus scaled can provide adequate prediction f o r full-scale a i r c r a f t as shown by A. G. Rainey (ref. 6 ) .

Cavity buffet.- With regard t o bay or cavity buffet, some excellent work w a s accomplished by Plumblee e t a l . (ref - 7).

Protuberances.- Protuberances on a i r c r a f t can cause a l o c a l flow break- down, and r e s u l t i n rather severe but area-restricted pressure fluctuations which can degrade or damage sensitive instruments. For instance, i n an

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investigation of t h e flow around a step protuberance on a model tested i n the Transonic Dynamics Tunnel at Langley Research Center, the measured rms buffeting pressures appeaz as shown i n figure 8 f o r two configurations.

The aerodynamic shapes are shown on t h e right of t h e figure, and t h e measured pressures plotted against Mach number. A n important f a c t o r i n t h i s figure is t h e f a c t that t h e phenomenon is more severe at subsonic Mach numbers peaking about M = 0.7, although t h e tests were extended t o the low super- sonic range.

The model was then reshaped t o remove t h e step by refairing the nose as shown ( t h e dotted l i n e s show t h e f i r s t shape), and the reduction i n buffeting loads i s dramatic; however, there is s t i l l a slight peak at M = 0.88.

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Response t o canard buffet.- Early i n the f l i g h t program, it became evident t h a t t h e XB-70 w a s experiencing s t a l l buffet of the canard a t low

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values o f dpamic pressure f o r subsonic f l i g h t . The following r e s u l t s represent unpublished work by Dr. Eldon Kordes of the NASA Flight Research Center.

I n order t o determine the effect of a strong disturbance applied through of the airplane response, t h e acceleration t h e canard structure on t h e nature at the center of gravity w a s analyzed f o r the condition of M = 0.4 ak 10,000 f e e t (3,048 meters) a l t i t u d e . The power spectral density estimates of the normal and lateral accelerations obtained from a 40-second record sample are shown i n figure 9 . The results f o r the normail acceleration show t h e response of several s t r u c t u r a l modes with a m a x i m u m s t r u c t u r a l response a t 13.4 cps which corresponds t o the first symmetrical bending mode of the canard. The response f o r t h i s f l i g h t condition contains a large amount of energy from s t r u c t u r a l modes above 6 cps and with a t o t a l rms value of 0.046g. The l a t e r a l acceleration response shows a r m s l e v e l of O.O25g with almost all of t h e energy between 5 and ll cps.

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Comparison of the power spectral density estimates of center-of-gravity accelerations w i t h t h e estimates shows t h a t whereas t h e primary s t r u c t u r a l response f o r canard buffet i s at 13.4 cps, t h i s frequency does not appear i n the gust response.

Even the acceleration response at t h e p i l o t ' s s t a t i o n does not contain s t r u c t u r a l response at 1 3 . 4 cps.

Unfortunately, t h e acceler- ometers at the p i l o t ' s s t a t i o n were not operating on t h e f l i g h t when canard buffet w a s experienced, so t h a t a d i r e c t comparison of the p i l o t ' s s t a t i o n response cannot be made w i t h the response i n turbulence.

Gust Response A history of the development of t h e gust c r i t e r i a over t h e years follows: O n figure 10 are shown s i x airplane types representing s i x identifiable time periods of development of t h e gust c r i t e r i a . O n the upper l e f t i s shown a - biplane i n the period of t h e 1920's. There is no information as t o how, i f

- a.t a l l , the response of loads t o gust w a s performed; the likelihood i s t h a t

About 1934, no attempt was made t o design the airplane f o r t h i s condition.

a sharp-edge gust c r i t e r i o n w a s developed by Rhode e t al. ( r e f . 8) which w a s used f o r several years.

About 1 9 4 2 a ramp gust w a s introduced, and some account w a s taken of the relieving f a c t o r of t h e v e r t i c a l acceleration of the airplane as well as t h e effects of unsteady aerodynamics.

A good summary of t h e status of gust work w a s made by P. Donely ( r e f . 9) at t h i s time.

In 1955 K. G. P r a t t ( r e f . 10) introduced t h e effective gust factor which he terms Kg.

I n t h i s case, a 1 - cos gust having a length of 25 chords and a maximum

velocity of 50 ft/sec, P r a t t provided tables of w i t h which the correction K g t o be made t o t h e older type of c r i t e r i a could be calculated.

About 1960,

when the present f l e e t of jets were being designed, t h e same 1 - cos gust

w a s used, with two changes: first, the length of the gust w a s made variable and calculations were made u n t i l t h e maximum response w a s obtained, and second, t h e f l e x i b i l i t y of t h e wings was taken into account.

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For the future, concepts of continuous random turbulence w i l l almost certainly become t h e design standard.

A t t h e present time, both t h e

1 - cos variable gust as w e l l as the random turbulence concepts are being

used. The random approach has been pioneered by Etkin ( r e f s . 1 1 and 2.2) i n

Canada, and Houbolt ( r e f . 14), Press ( r e f . 12), and Diederich ( r e f . 13)

i n t h e United States.

For t h e supersonic a i r c r a f t , such as the B-70 and SST, it is not the wing which i s t h e main contributing f a c t o r to turbulence, but rather t h e fuselage-wing combination, or more specifically, t h e complete airplane vibration modes, which f o r these long slender configurations contain a large degree of f l e x i b i l i t y i n t h e fuselage, as opposed t o t h e rather stiff

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fuselages a-nd f l e x i b l e wings of t h e present subsonic j e t s . O n figure 1 1 a r e shown t h e acce1era.tion spectrum f o r t h e p i l o t ' s s t a t i o n f o r the I XB-70 at M = 2.4 and a l t i t u d e 35,000 f t , and f o r a typical subsonic j e t .

The large response a.t the low frequency portion i s due to the r i g i d body "short-period" response, t y p i c a l o f a l l a i r c r a f t . However, the unusual response is at the higher frequency portion, and it w i l l be noted t h a t the XB-70 has two rather l a r g e peaks as compared to t h e subsonic j e t .

These two peaks correspond to t h e t h i r d and fourth airplane vibration modes. This r e s u l t s i n a rather rough r i d e f o r t h e p i l o t s , even i n extremely l i g h t turbu- lence. There have been times during the f l i g h t of t h e B-70 when t h e p i l o t reported l i g h t to severe turbulence, when the nearby chase airplane p i l o t reported no turbulence. I t i s apparent, then, t h a t some method f o r reducing these large responses i s needed and some work is now underway. One method would

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be t o automatically sense the motion of t h e a i r c r a f t and attempt t o dampen out the motion, including the f l e x i b l e mode of t h e airplane. This has actually been demonstrated on a B-32 airplane, and the results a r e shown on figure 12, from reference 13. Here is shown damping r a t i o p l o t t e d versus dynamic pressure f o r two modes: the Dutch roll mode and t h e fuselage side bending mode.

O f course, an increase i n damping means a corresponding decrease i n response of the a i r c r a f t .

There is a large increase i n damping f o r both modes f o r the system on, as compared t o t h e system off. Also shown are t h e r e s u l t s of f l i g h t tests of the a c t u a l automatic system and the agreement is excellent. Thus, it appears that t h e t o o l s necessary t o reduce t h e response of these very f l e x i b l e airplanes t o random turbulence a r e i n hand.

F l u t t e r . - F l u t t e r is a self-induced o s c i l l a t i o n of a surface which can

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result i n t h e destruction of the surface.

The first recognized f l u t t e r - a World War I bomber, and the solution was occurred on obtained by Lancaster and Bairstow who advised an increase i n torsional s t i f f n e s s of the t a i l surface.

Since that time, there have been rapid advances made i n t h e state of the science.

The f l u t t e r speed of wings throughout t h e subsonic range as w e l l as t h e supersonic range can be analytically predicted. The one remaining gap lies i n the transonic speed range, where t h e theories a r e s t i l l not adequate, and wind-tunnel t e s t i n g is mandatory. For t h i s range, model tests are run and the Transonic Dynamics Tunnel at Langley Research Center has been used t o proof-test every m i l i t a r y a i r c r a f t of recent vintage.

To provide a graphical view of the transonic problem, on figure 13 is Here is shown t h e true airspeed f o r f l u t t e r plotted against Mach number.

noted a. very small variation i n speed, u n t i l approaching M = 1, where

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there i s a rather large reduction i n f l u t t e r speed and, f i n a l l y , a rapid increase upon entering the supersonic region. (It is interesting t o note t h a t t&is curve i s very similar t o the reciprocal of t h e slope of the l i f t curve, when plotted against Mach number. ) To round out t h e f l u t t e r picture, a plot i l l u s t r a t i n g one other area t h a t requires additional work, nskmely, t h e coplanar case, and some experimental r e s u l t s are i l l u s t r a t e d i n figure 1 4 ( r e f . 1 5 ) . A t the top is shown the configu- ration when t h e main wing i s pivoted, and f l u t t e r speed is plotted against sweep angle. A s t h e angle of sweep increases f o r t h e wing alone, the usual increase i n speed with increasing sweep angle i s noted; however, when a fixed t a i l i s placed on t h e a i r c r a f t , the f l u t t e r speed suddenly decreases.

Sonic Fatigue By sonic fatigue is meant the damaging of a small section of t h e air- or due t o the c r a f t by noise genera-ted mainly by the exhaust of jets boundary layer i t s e l f , although similar results on fuselage areas near t h e result. There are essentially three problem plane of t h e propeller can areas: namely, what are t h e noise spectrum and orientation generated by t h e jet? What is t h e response of t h e panel due t o t h i s noise? And f i n a l l y , what is t h e fatigue l i f e of t h e jet? Two conferences were held on t h i s subject: one i n 1966 at the University of Minnesota and published i n WADC TR 39-676 {ref. 16), and a second a t Dayton, Ohio, t h e proceedings of which were published i n a book e n t i t l e d "Acoustical Fatigue i n Aerospace Structures" ( r e f . 17).

J e t noise. - The famous work of Lighthill ( r e f . 18), set the pattern f o r

theoretical j e t noise prediction, wherein he s t a t e d t h a t t h e noise produced by a j e t was essentially due t o shearing ac-bion on the j e t boundary, and the

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noise w a s proportional t o t h e v8.

This velocity dependence has been rather well substantiated i n the past; however, some recent work has shown regions vhere t h i s may not be e n t i r e l y t h e f u l l story. O n figure 13 t h i s problem i s i l l u s t r a t e d qualitatively. H e r e , noise is plotted against j e t exhaust velocity. The central part of t h e curve seems t o follow nicely the 8 t h power law. However, it has been observed i n experimental work of actual configu- rations that the noise reduction i n t h e low velocity range does not decrease as rapidly as predicted by t h e Lighthill theory, and is somewhere between t h e 4-6th power. Similarly, f o r t h e higher jet velocities the noise does not seem t o be as great as t h e 8th power indicates. For the lower velocity range, t h i s problem has been experimentally studied by Gordon and Maidanik of Bolt Beranek and Newman (ref. 19). It is t h e i r conclusion that noise generated inside the pipe by obstruction as well as rotor noise may cause a noise which i s proportional t o the 4-6th power, and can be explained by t h e use of dipole o r doublet distributions, t h a t is, a s o r t of l i f t i n g surface i n the pipe.

With regard t o panel response, Alan P o w e l l (ref. 20) has proposed t h e more or less c l a s s i c a l procedure of calculating t h e response o f a panel u t i l i z i n g many vibration modes and the complete noise f i e l d over the panel with all the attendant correlation of the pressure f i e l d . This is quite an imposing job, and B. L. Clarkson has proposed what may be an easier out, wherein he focuses on one vibration &e (ref. 21). I n t h a t paper, Clarkson points out t h a t from experiments most of t h e panel response i s i n a single vibration mode, and it is usually t h e lowest mode. With t h i s concept then,

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he u t i l i z e s a result of Miles f o r the response of a single-degree-of-freedom system t o random noise. Specifically, the equation, shown a t the top of figure 16, is CT = vision damping r a t i o = frequency of predominant mode fr G (f ) = spectral density of pressure at fr P r = s t r e s s a t point of i n t e r e s t due t o a uniform s t a t i c gressure “ 0 of u n i t magnitude To i l l u s t r a t e the adequacy of the method, r e s u l t s taken from Clarkson’s I report i l l u s t r a t e t h e r e s u l t s of a number of experiments versus the analytical estimates, where the measured rms stress i s plotted on the ordinate. This is quite remarkable agreement, and it should constitute the beginning of a semirational approach. O f course, the next step i s t o estitmte t h e fatigue l i f e , and experimental data are lacking, since it would be necessary t o have S-M curves from random input having a Rayleigh d i s t r i b u t i o n of s t r e s s and having ms stress and t h e number of reversals as ordinates. A considerable amount of experimental work would be necessary t o gather these data.

Helicopter Vibration Problems The helicopter has by far the most severe vibration problems of any aircraft, resulting from t h e f a c t that the main l i f t i n g surfaces operate i n a completely nonuniform flow f i e l d . Some of the aerodynamic sources of

the vibration a r e shown on figure 17 along w i t h a conceptual p l o t of the

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A t the lower speeds, there is vibration l e v e l plotted against forward speed.

a rather severe vibration due t o interaction of the t i p vortex generated by a blade on t h e following blade. This This noise i s usually termed blade slap.

phenomenon is surprising, since it has usually been assumed t h a t the t i p vortex i s normally deflected down and t h a t it could pass under the following blade.

This i s s t i l l a research problem, and the f i x e s a r e being worked on. A t t h e higher f l i g h t speeds, there a r e a number of problems such as stall, compressibility effects, s t a l l f l u t t e r , and blade-motion i n s t a b i l i t y . To obtain a b e t t e r idea of how the blade operates, figure 18, taken from a paper by Al Gessow of NASA (ref. 2 2 ) , i l l u s t r a t e s t h e f l o w f i e l d . Looking down on t h e blade f i e l d , t h e The a i r f l o w i s portion of t h e rotational f i e l d shows certain important factors.

- from top t o bottom. Regions of s t a l l and high Mach number operation are shown.

For instance, a blade t i p w i l l be at on the advancing side, whereas M = 0.9 - the blade root is a t M = 0.3. When the blade is on the retreating side, the blade t i p i s a.t M = 0.3 and t h e root i s p r a c t i c a l l y a t M = 0, and t h e whole event occurs once per revolution. O n t h e other hand, t h e angle-of-attack ranges from -2 at t h e t i p on t h e advancing blade t o h0-50 a t t h e root, but on the

retreating side can go as high as 1 4 . The hatched area shows t h e area of

importance from the standpoint of s t a l l and s t a l l f l u t t e r . S t a l l i n g of the blade r e s u l t s i n a more or l e s s random input, whereas s t a l l f l u t t e r involves a sinusoidal o s c i l l a t i o n a t t h e natural torsional frequency of the blade and is more or l e s s Therefore, a possible proportional t o t h e square root of t h e torsional frequency.

f i x i s t o increase t h e s t i f f n e s s of the system. O f course, using a i r f o i l shapes t h a t w i l l stall a t a higher angle of attack w i l l be beneficia3 as w e l l as boundary- The s t a l l i n g e f f e c t is one of t h e principal effects t h a t limits layer control.

the f l i g h t speed of a helicopter.

- 16 -

Concluding Remarks This paper has been principally aimed at pointing out some major aerodynamically induced vibration problems of a i r c r a f t , and t o provide sone insight into the progress being made. Specifically, t h e paper has covered the following areas : (1) boundary-layer noise, (2) buff et, ( 3 ) gust response, ( 4 ) canard buffet, ( 5 ) f l u t t e r , (6) sonic fatigue, and (7) helicopter vibration.

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