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WIND TUNMEL I N ~ S T I ~ A T I O N OF SUPERSONIC WING-TAIL FZUTTER Lawrence J, H u t t s e l l , Thomas E, No11 and Donald E, Holsapple Air Force F l i g h t Dynamics Laboratory SUMMARY An experimental and a n a l y t i c a l study w a s undertaken t o e s t a b l i s h t h e f l u t t e r trends of a highly swept wing-tail configuration i n t h e low supersonic speed regime. Wind tunnel f l u t t e r d a t a w a s a l s o required f o r e v a l u a t i n g a new supersonic aerodynamic method f o r p r e d i c t i n g wing-tail i n t e r f e r e n c e . A f l u t t e r model, c o n s i s t i n g of a wing, h o r i z o n t a l t a i l , and s p l i t t e r p l a t e / f u s e l a g e mechanism, w a s t e s t e d i n the Arnold Engineering Development Center (AEDC) Pro- pulsion Wind Tunnel F a c i l i t y (PWT) &Foot Transonic Tunnel in t h e Mach number range'1.1 t o 1.3. Two types of f l u t t e r w e r e encountered d u r i n g the t e s t i n g ; a wing-tail f l u t t e r mode and a t a i l bending-torsion f l u t t e r mode. The wing-tail f l u t t e r speed w a s found t o b e a minimum at M = 1 . 2 f o r the configuration t e s t e d . Recorded model test d a t a w e r e d i g i t i z e d f o r a power s p e c t r a l d e n s i t y (PSD) a n a l y s i s and Random Decrement (Randomdec) a n a l y s i s e Comparisons between t h e frequency and damping obtained from the PSD p l o t s and t h e Randomdec signa- t u r e s agreed very w e l l . A l i m i t e d f l u t t e r a n a l y s i s w a s conducted using a Mach box unsteady aerodynamics method which accounted f o r i n t e r f e r e n c e and a i r f o i l thickness. A n a l y t i c a l comparisons w i t h experimental f l u t t e r speeds agreed very w e l l . The analyses assuming zero thickness predicted f l u t t e r speeds higher than those measured, ranging from 1 percent a t M = 1,12 t o 8 percent at M = 1.28.
With the a i r f o i l thickness included the c o r r e l a t i o n w a s improved such t h a t predicted f l u t t e r speeds f o r a l l cases i n v e s t i g a t e d were w i t h i n 2 percent of experimental speeds. F l u t t e r frequencies w e r e n o t as w e l l predicted generally being somewhat higher than measured.
SYMBOLS b wing semichord measured streamwise and i n t e r s e c t i n g t h e elastic axis line a t 75-percent wing span f f requen cy g s t r u c t u r a l damping c o e f f i c i e n t m wing mass p e r u n i t span M freestream Mach number t o t a l p r e s s u r e pT TI f Pees tream v e l o c i t y at f l u t t e r P air d e n s i t y m
model t o air m a s s r a t i o , -
1-I Tpb2 w f l u t t e r frequency wing f i r s t coupled cantilever bending frequency
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w8 uncoupled fuselage t o r s i o n frequency INTRODUCTION Today's advanced m i l i t a r y aircraft must be capable of undertaking multi- mission r o l e s . Variable sweep wings are used on some a i r c r a f t configurations f o r improving performance at d i f f e r e n t f l i g h t conditions. Low wing sweep angles are attractive during takeoff, landing, and long range c r u i s e when higher aspect r a t i o is required; high wing sweep angles, which reduce drag, are d e s i r a b l e f o r high speed f l i g h t .
I n i t i a l l y it w a s thought t h a t f l u t t e r speeds would increase a t t h e high sweep angles thus complementing t h e use of t h e v a r i a b l e sweep wing. However, i n 1966, Topp, Rowe, and Shattuck (Reference 1) conducted a t h e o r e t i c a l and experimental program which determined t h a t t h e r e are cases where t h i s does n o t occur. Model tests i n d i c a t e d t h a t f o r l o w sweep a n g l e s , t h e critical f l u t t e r mode involved t h e high frequency bending-torsion motion of t h e wing. As expected, t h e f l u t t e r speed increased as t h e wing w a s i n i t i a l l y swept back.
Near 58 degrees wing sweep, however, a new f l u t t e r mode involving t h e lower frequency modes of the wing, fuselage, and t a i l became evident. With f u r t h e r i n c r e a s e s i n wing Sweep, t h e f l u t t e r speed dropped r a p i d l y , and at 70 degrees, t h e f l u t t e r speed w a s lower than f o r t h e most forward swept case. The cause f o r t h e lower f l u t t e r speed and its rapid drop with i n c r e a s i n g wing sweep w a s n o t f u l l y understood at t h i s time. Since t h i s w a s a new unforeseen phenomenon, not p r e d i c t a b l e using a v a i l a b l e aerodynamic t h e o r i e s f u r t h e r t h e o r e t i c a l and experimental s t u d i e s were conducted i n t h e following years.
One of t h e f i r s t experimental programs i n t h e area following t h e e f f o r t by Topp, e t a l e , w a s sponsored by t h e A i r Force Flight Dynamics Laboratory (AFFDL).
2 ) designed, constructed, and t e s t e d a series of I n 1966, Balcerak (Reference constant chord 45 degree and 60 degree swept wing-horizontal t a i l f l u t t e r models, Wing and t a i l s u r f a c e s were i d e n t i c a l i n planform. Testing w a s accom- plished at Mach numbers ranging from 0.4 t o 1.24 and defined the e f f e c t s o f important wing-tail parameters on f l u t t e r . I n some cases t h e f l u t t e r speed continued t o decrease i n t o t h e low supersonic speed regime.
In 1968, t h e AFFDL continued t h e i r i n v e s t i g a t i o n by conducting subsonic wind tunnel tests and analyses on a semispan model of a r e p r e s e n t a t i v e v a r i a b l e sweep wing a i r c r a f t configuration (Reference 3) e Similar trends of f l u t t e r speed versus sweep angle were found. The AFFDL p a r a l l e l e d t h e experimental i n v e s t i g a t i o n with a d e t a i l e d t h e o r e t i c a l study. Both a d o u b l e t - l a t t i c e method (Reference 4 ) and a k e r n a l function method ( 5 and 6) w e ences t o p r e d i c t the aerodynamic i n t e r a c t i o n between t h e wing and tail, Both methods predicted t h e f l u t t e r frequencies extremely w e l l , F l u t t e r v a t i v e l y predicted ranging up t o 20 percent lower than t h e v e l o c i t i e s , Also, t h e theory p r e d i c t e d the f l u t t e r speed t o decrease w i i n c r e a s i n g subsonic Mach number.
Since t h e t r a n s o n i c tests of Reference 2 showed decreased as t h e Mach number increased, at least up t ment of a method t o p r e d i c t unsteady aerodynamic loads f o r i n t e r f e r i n g s u r f a c e s w a s required f o r t h e supersonic speed regime. Under AFFDL sponsorship, a Mach box method (References 7 and 8) w a s developed f o r supersonic i n t e r f e r i n g surfaces. This paper d e s c r i b e s supersonic f l u t t e r tests of a half-span f l u t t e r model which w a s dynamically s c a l e d from the model used i n t h e earlier subsonic e f f o r t (Reference 3 ) , and t h e l i m i t e d analyses which were conducted f o r veri- f y i n g t h e Mach box aerodynamic method.
SUPERSONIC WING-TAIL FLUTTER MODEL The A i r Force F l i g h t Dynamics Laboratory defined t h e general design of a half-span f l u t t e r model c o n s i s t i n g of a wing, h o r i z o n t a l tail, and s p l i t t e r p l a t e / f u s e l a g e mechanism. The d e t a i l design and construction of t h e model w a s performed by Atkins and Merrill Inc., Ashland, Massachusetts.
The supersonic model w a s designed t o f l u t t e r within t h e Arnold Engineering (AEDC) P W T &Foot Transonic Wind Tunnel by dynamically Development Center s c a l i n g the 60 degree sweep subsonic model of Reference 3, with the exception of t h e h o r i z o n t a l t a i l , The design fundamental frequency f o r t h e supersonic t a i l model w a s twice t h a t of t h e wing. Higher t a i l freque'ncies were n o t obtained because t h e high s t i f f n e s s c h a r a c t e r i s t i c s of t h e subsonic t a i l could n o t p r a c t i c a l l y b e s c a l e d due t o t h e very low m a s s requirements f o r t h e super- s o n i c model.
Figure 1 provides a photograph of t h e model showing t h e wing and t a i l sur- faces, t h e s p l i t t e r p l a t e / f u s e l a g e mechanism, and t h e t u n n e l mounting system.
The fuselage mechanism and t h e wing and t a i l attachments were enclosed within The model w a s the f a i r i n g between t h e s p l i t t e r p l a t e and t u n n e l c e i l i n g .
mounted from t h e t u n n e l c e i l i n g i n such a manner as t o simulate antisymmetric This w a s achieved by a t t a c h i n g the models t o a s h a f t assembly v i b r a t i o n modes.
which w a s supported by b e a r i n g s , thereby providing a r o l l degree of freedom.
A r o l l s t i f f n e s s w a s provided by a s m a l l s p r i n g mounted between t h e s h a f t Variation in t h e fuselage t o r s i o n a l s t i f f n e s s assembly and t h e s p l i t t e r p l a t e .
w a s obtained by changing t h e e f f e c t i v e l e n g t h of a constant cross-sectional bar which connected t h e f o r e and a f t s h a f t assemblies. The wing and t a i l could e i t h e r r o l l t o g e t h e r or d i f f e r e n t i a l l y s i n c e t h e s h a f t assemblies f o r t h e wing Variations and t a i l s u r f a c e s w e r e interconnected only through t h e t o r s i o n bar.
in t h e t o r s i o n b a r l e n g t h could b e accomplished without a f f e c t i n g t h e s e p a r a t i o n between t h e wing and t a i l , Two t a i l attachment p o i n t s were a l s o provided t o allow a v a r i a t i o n i n h o r i The wing and t a i l models were t i o n technique. This composite con epoxy s k i n s which were high-temperature cured under p r e s s u r e with a honeycomb core, S t r i p s of g r a p h i t e were added along t h e span of t h e wing and t a i l t o o b t a i n t h e required bending stiffness. The wing w a s attached t o t h e forward fuselage r o l l b a r by m e carry-through s t r u c t u r e with scaled t o r s i o n and bending s t i f f n as attached t o t h e a f t fuselage r o l l assembly by means of a carry-through s t r u c t u r e with h i g h s t i f f - ness.
Natural mode shapes and frequencies w e r e computed u s i n g classical lumped m a s s methods. Figure 2 shows t y p i c a l r e s u l t s f o r f o u r e l a s t i c modes used in the f l u t t e r a n a l y s i s . I n general, agreement between t h e wing aeasured and pre- d i c t e d node lines and frequencies was good. The f i r s t mode (not shown i n t h e f i g u r e ) involves r o l l motion about the model r o l l axis w i t h a measured f r e - quency of 17.8 Hz; t h e second mode involves primarily wing carry-through t o r s i o n coupled w i t h wing bending; t h e t h i r d mode involves t a i l bending and wing bending; t h e f o u r t h mode involves p r i m a r i l y wing second bending and carry- through t o r s i o n ; and the f i f t h mode i s p r i m a r i l y t a i l t o r s i o n .
WIND TUNNEL TESTS The tests w e r e conducted i n t h e A E D C P W T &Foot Transonic Wind Tunnel. A schematic of t h e d a t a monitoring and recording system used during t h e f l u t t e r tests is shown i n Figure 3. During t e s t i n g , s t r a i n gage bridges w e r e used t o monitor and record t h e response of t h e model. S t r a i n gage bridges were mounted j u s t outboard of t h e wing and t a i l r o o t s t o measure t h e bending and t o r s i o n strains. Others were mounted on s p r i n g s t o measure wing carry-through t o r s i o n and bending, t h e fuselage t o r s i o n , and t h e model r o l l motions. The e i g h t strain gage channels and a t i m e code were displayed on a Varian s t r i p recorder and copied on t a p e together with a voice t r a c k . Two X-Y oscilloscopes w e r e used t o monitor t h e coupling of t h e c r i t i c a l wing-tail modes; one of t h e o s c i l l o s c o p e s displayed f u s e l a g e t o r s i o n (FT) and wing carry-through t o r s i o n (CT) responses ; t h e second o s c i l l o s c o p e displayed wing carry-through bending (CB) and wing carry-through t o r s i o n (CT) responses. An on-line Time/Data analyzer w a s used t o d i s p l a y t h e frequency response (0-100 Hz) f o r e i t h e r t h e wing carry-through t o r s i o n , t h e wing carry-through bending, o r t h e fuselage t o r s i o n motion. The approximate frequency range of h i g h model response w a s determined from such a Modes of i n t e r e s t w e r e s e l e c t e d and processed through a 5 Hz band- display.
width t r a c k i n g f i l t e r t o d e f i n e t h e critical frequency.
The test Mach number w a s approached from a low t o t a l p r e s s u r e (low dynamic The t o t a l p r e s s u r e w a s increased at an e s s e n t i a l l y constant Mach pressure).
number u n t i l f l u t t e r occurred. A t s e l e c t e d test conditions, t h e response d a t a w a s recorded and t h e frequencies measured using t h e t r a c k i n g f i l t e r . Figure 4 presents the AEDC 4T wind t u n n e l standard operating envelope of t o t a l p r e s s u r e and dynamic p r e s s u r e versus Mach number, and shows t h e f l u t t e r points obtained test configuration, wing bending t o f o r each configuration tested. The f i r s t fuselage t o r s i o n frequency r a t i o (%/We) of 0.62, was t e s t e d at M = 1.2 up t o of 1 2 g e 3 W a (2700 psf) m a t o t a l p r e s s NQ f l u t t e r was enco t h e r e w a s s i g n i f i c a n t wing and t a i l motion, i n d i c a t i n g t h e proximity t o f l u t t e r .
The s t r u c t u r a l damping c o e f f i c i e n t (g) w a s estimated t o b e approximately 0.01.
Tunnel l i m i t a t i o n s prevented f u r t h e r t e s t i n g of t h i s configuration. The fuse- l a g e t o r s i o n a l s t i f f n e s s w a s then adjusted t o g i v e %/We = 0.32, and t h e model w a s again t e s t e d . Wing-tail f l u t t e r was obtained a t M = 1.12, 1.2, and 1.28.
The f l u t t e r frequency varied from 85 Hz at M = 1.12 t o 88 Hz at M = 1.28.
Figure 5 p r e s e n t s a s t r i p c h a r t recording f o r t h e M = 1.28 test configuration.
Both wing and t a i l responses are shown t o be diverging, i n d i c a t i n g t h a t t h e test condition w a s s l i g h t l y i n t o an unstable region. The f l u t t e r mode r e s u l t e d in c a t a s t r o p i c damage t o both s u r f a c e s as shown in Figure 6 .
A t a i l bending-torsion f l u t t e r mode w a s encountered a t M = 1.08 while reducing Mach number a t a constant t o t a l p r e s s u r e from t h e M = 1.12 wing-tail The frequency of t h e t a i l f l u t t e r mode w a s 176 Hz which is f l u t t e r point.
s l i g h t l y above t h e t a i l t o r s i o n mode shown in Figure 2. The time h i s t o r y response record f o r t h e wing and t a i l strain gages are shown i n Figure 7 f o r t h i s mode of f l u t t e r . The t a i l bending and t o r s i o n gages diverged very rapidly. The motion on t h e wing is very s m a l l i n comparison t o t h e t a i l motions f o r t h i s predominantly t a i l bending-torsion coupling. The t a i l s u r f a c e w a s r a p i d l y destroyed following f l u t t e r onset.
DATA REDUCTION Following t h e wind tunnel tests, s e l e c t e d f l u t t e r model response d a t a were played back from analog t a p e s and d i g i t i z e d u s i n g an I T 1 4900-Preston A/D sys- Low pass analog f i l t e r s (48 dB p e r octave r o l l - o f f ) w e r e used t o band t e m .
Both Power l i m i t t h e d i g i t i z e d response d a t a t o a frequency range of 0-200 Hz.
S p e c t r a l Density (PSD) and Random Decrement (Randomdec) analyses methods were used t o reduce t h e test data.
PSD Method Narrow band (0.46 Hz bandwidth) PSD analyses were performed using a Raytheon 704 F a s t Fourier Analyzer system. Thirteen transforms with sample s i z e of 2048 were averaged t o provide a spectrum which w a s p l o t t e d on t h e Raytheon/Gould 4800 p l o t t e r . Figures 8 and 9 present t h e r e s u l t s of t h e PSD a n a l y s i s of the random response d a t a f o r t h e model with Wh/We = 0.32 and M = 1.2 at two subcri- t i c a l test conditions ( t o t a l p r e s s u r e s of 95.8 kPa (2000 p s f ) and 105.3 kPa (2200 p s f ) ) . The response i n t h e 84-86 Hz mode (the critical wing-tail mode) A t a t o t a l pressure increased with t o t a l pressure as f l u t t e r was approached.
of 105.3 kPa (2200 p s f ) , the response i n a 176 Hz mode became more e v i d e n t .
The frequency and damping were estimated from the PSD p l o t s using standard tech- niques, and t h e r e s u l t s are presented i n Table I f o r t h e critical wing-tail mode a t t h e two test conditions discussed above and at two a d d i t i o n a l p o i n t s .
Randomdec Method The Randomdec method, invented by He A.
w a s applied in t h i s study t o analyze t h e r e s p of the modes of i n t e r e s t .
t i o n f o r determining the frequency and damping The Randomdec program used ensemble averaging of up t o 300 d i g i t a l samples of response d a t a (,07 seconds i n length). The program e x t r a c t e d the c h a r a c t e r i s - t i c response s i g n a t u r e , and t h e frequency and damping ratio from t h e random response d a t a (0-200 Hz). A t y p i c a l Randodec s i g n a t f o r Wh/wg = 0.32 is shown i n Figure 10 f o r M = 1.2 and PT = 2000 psf. This corresponds t o t h e PSD p l o t shown i n Figure 8. The Randomdec s i g n a t u r e is very c l e a n , and t h e s t r u c - t u r a l damping can be e a s i l y determined.
Comparison of Results Using PSD and Randomdec Methods The s t r u c t u r a l damping c o e f f i c i e n t and frequency f o r t h e critical wing- t a i l mode which w e r e obtained u s i n g PSD and Randodec methods are presented in All frequency comparisons are w i t h i n 2 percent. S t r u c t u r a l damping Table I.
comparisons between the two methods are within 0.012. A t a t o t a l p r e s s u r e of 110.1 kPa (2300 p s f ) , f l u t t e r onset h a s been s l i g h t l y exceeded as shown by a s m a l l negative damping whereas t h e PSD method is n o t capable of providing nega- tive damping.
ANALYSIS AND CORRELATION Limited f l u t t e r analyses w e r e conducted using t h e supersonic Mach box program described i n References 7 and 8. This method w a s developed t o analyze l i f t i n g s u r f aces in close proximity i n supersonic flow including aerodynamic i n t e r f e r e n c e . The analyses were conducted f o r the f l i g h t conditions at which wing-tail f l u t t e r occurred f o r "h/oe = 0.32. These analyses were conducted both with and without a i r f o i l thickness included. The Mach box method includes an option f o r thickness c o r r e c t i o n s t o t h e pressure d i s t r i b u t i o n based on second order p i s t o n theory.
Table I1 p r e s e n t s comparisons of c a l c u l a t e d f l u t t e r speeds and frequencies Without with corresponding measured values at Mach numbers 1.12, 1.2 and 1.28.
a i r f o i l thickness included, t h e analyses predicted f l u t t e r speeds ranging from approximately 1 percent at M = 1.12 t o 8 percent higher than t h e measured speeds a t M = 1.28. With t h e a i r f o i l thickness included i n t h e analyses, f l u t t e r speed p r e d i c t i o n s were improved. A t M = 1.2, t h e c a l c u l a t e d f l u t t e r speed w a s w i t h i n 1.5 percent of the measured f l u t t e r speed, a 5 percent improve- A t M = 1.28, t h e analyses ment over t h e analyses without a i r f o i l thickness.
included w a s within 1 percent of t h e measured f l u t t e r with a i r f o i l thickness speed, an improvement of approximately 7 percent. F l u t t e r frequencies were n o t as w e l l predicted. The c a l c u l a t e d f l u t t e r frequencies were 8 t o 18 percent higher than t h e measured values.
Both measured and c a l c u l a t e d f l u t t e r d a t a are presented i n Figures 1 1 and 12 i n the form of f l u t t e r parameters V/bwe fi and w/we versus Mach number.
The subsonic d a t a from Reference 3 are a l s o shown f o r comparison, I n Figure 11, t h e predicted subsonic t r e n d of V/bwe is decreasing with Mach number as shown f o r uh/we = 0.62, The t r e n d f o r % / W e = 0-32 is shown dashed, s i n c e analyses w e r e n o t conducted f o r the configuration but w e r e estimated based on o t h e r similar t r e n d s , These subsonic analyses i n d i c a t e t h a t V/bwe con- t i n u e s t o drop a t least up t o t r a n s o n i c speeds. The supersonic test r e s u l t s f o r %/we = 0,32 i n d i c a t e t h a t a minimum f l u t t e r speed w a s obtained at M = 1.2.
s i g n i f i c a n t l y lower than t h e M = 0 subsonic test r e s u l t s . A f u r t h e r This w a s i n c r e a s e i n Mach number t o M = 1.28 provided some a l l e v i a t i o n ; however, t h e f l u t t e r parameter s t i l l remains below t h e M = 0 test r e s u l t s . The supersonic analyses with o r without a i r f o i l thickness included, show i n c r e a s i n g f l u t t e r speeds with i n c r e a s i n g Mach number.
Figure 12 p r e s e n t s & / w e v e r s u s Mach number. T e s t r e s u l t s i n d i c a t e an i n c r e a s i n g value of W / W ~ as t h e Mach number increases, while t h e analyses p r e d i c t a minimum f l u t t e r frequency r a t i o a t approximately M = 1.2 followed by an i n c r e a s e at t h e higher Mach number t e s t e d (M = 1.28).
CONCLUDING REMARKS I n conclusion, t h e r e s u l t s of t h i s wind t u n n e l i n v e s t i g a t i o n of a wing- t a i l f l u t t e r phenomena i n t h e Mach number range 1 . 1 2 t 0 1 . 2 8 show less s t a b i l i t y (lower f l u t t e r speed parameter) than earlier corresponding subsonic d a t a .
the r e s u l t s i n d i c a t e some increase i n f l u t t e r s t a b i l i t y a t M = 1.28 as However, compared with M = 1.2 data. A l s o , t h e Mach box a n a l y s i s procedure with aero- dynamic i n t e r f e r e n c e and a i r f o i l thickness e f f e c t s included w a s found t o adequately p r e d i c t t h e wing-tail f l u t t e r speeds of t h i s phenomena.
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n a t i o n a l Congress of t h e Aeronautical Sciences, London, England, September 1966 e 2. Balcerak, J. C. : F l u t t e r T e s t s of Variable Sweep Configurations. AFFDL-TR- 68-101, September 1968.
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4 . Albano, E. and Rodden, W.P.: A Doublet Lattice Method f o r C a l c u l a t i n g L i f t D i s t r i b u t i o n s on O s c i l l a t i n g Surfaces i n Subsonic Flows. A I M Journal, Vol. 7 , No. 2 , February 1969, pages 279-285.
5. Laschka, B. and Schmid, H.: Unsteady Aerodynamic Forces on Coplanar L i f t - i n g Surfaces i n Subsonic Flow (ing-Horizontal T a i l I n t e r f e r e n c e ) .
Presented at AGARD S t r u c t u r e s and Materials P a n e l Meeting, O t t a w a , Canada, September 1967.
6. Albano, E. Perkinson, F., and Rodden, W.P. : Subsonic L i f t i n g Surface Theory Aerodynamics and F l u t t e r Analysis of I n t e r f e r i n g WinglHorizontal T a i l Configurations. AFJ?DL-TR-70-59, September 1970.
7. I T , J.M. Borland, C . J . , and Hogley, J.R. : P r e d i c t i o n of Unsteady Aero- dynamic Loadings of Non-Planar Wings and Wing-Tail Configurations i n Supersonic Flow, P a r t I, "Theoretical Development, Program Usage, and Application". AFFDL-TR-71-108 , March 1972.
8 . Kramer, G.D. and Keylon, G.E. : P r e d i c t i o n of Unsteady Aerodynamic Loadings of Non-Planar Wings and Wing-Tail Configurations i n Supersonic Flow, P a r t 11, I1 Computer Program Description". AFFDL-TR-71-108, March 1972.
9. Cole, H.A., Jr. : Method and Apparatus f o r Measuring Damping Characteris- tics of a S t r u c t u r e . United S t a t e s P a t e n t No. 3 , 620, 069, 16 November 1971.
of 10. Cole, H.A., Jr. : On-Line F a i l u r e Detection and Damping Measurement NASA CR-2205, Aerospace S t r u c t u r e s by Random Decrement Signatures.
March 1973.
Table I, - Damping Comparison f o r the Critical Wing-Tail Mode a t M = 1.2, %/We = Oe32.
PSD
f (Hz)
84,O 0 8 100
86,O 0,070
86,5 0,020
-
8 6 , l
Table 11. - A i r f o i l Thickness E f f e c t s on F l u t t e r Trends, %/we = 0.32.
Figure 1. - Supersonic Wing-Tail F l u t t e r Model.
----- ( f )
CALCULATED MODES (FREQUENCY IN Hz) f MEASURED MODES (FREQUENCY I N Hz) ROLL A X I S Figure 2.
- Calculated and Measured Vibration Node Lines and Frequencies, w ~ / w ~ = 0.32.
STAA I P I GAGE OUTPUTS
NOMENCLATURE
W R - WING BENDING
W T - WIPJG TORSION
T B - T A I L BENDING
T T - T A I L TORSION
F T - FUSELAGE TORSION
RB - ROLL SPRING
CB - WING CARRY-THROUGH BENDING
CT - W I PIG CARRY-THROUGH TORS ION
Figure 3 . - Wind,Tunnel T e s t Data Monitoring and Recording System.
N
+
\ u- 2400 I W
5 2000
c/) v) W e n
$ 1600
I - CJ
+
SO0 AEDC P STANDARD OPERATING ENVELOPE
0 I 2 8 4 ,6 18 l l 0 L 1 3 l , 4
MACH NUMBER Figure 4. Wind Tunnel Operating Envelope with Experimental F l u t t e r Data.
(1 l b / f t 2 = 47.88 Pa.
Figure 5 . - Model Response a t M = 1.28 and PT = 118.5 kPa (2475 l b / f t 2 ) , %/we 0.32.
= 0.32.
Figure 6 . - Model Damage from Wing-Tail F l u t t e r a t M = 1 . 2 8 , w /w
h 0
Figure 7 . - Model
/we
FREQUENCY' - HZ
Figure 8, - PSD P l o t f o r M =. 1.2 and PT = 95.8 kPa (2000 l b / f t 2 ) , W h / W e = 0.32.
Figure 9. - PSD P l o t f o r M = 1.2 and PT = 105.3 kPa (2200 l b / f t 2 ) , % / W e 0.32.
Figure 10. - Randomdec Signature for M = 1.2 and P = 95.8 kPa (2000 l b / f t 2 ) , %/me = 0.32. T
SULID SYMEOLS - ANALYSIS
OPEN SYMROLS - TEST
BOLS - ANALYSIS WITH THICKNESS
NEAR FLUTTER ONSET
- 112
L O
V
0,8
0,6
SUBSONIC DATA FROM FEFFPENGF 3
NOTE:
0 0,4 0,8 182 i , 6
MACH NUVBER
Figure 11. - V/bwg fi Versus Mach Number.
I S WITH TtiICI<
NEAR FLLITTEI? ONSET
-
0 0 8 4
!1ACH NUMBER
Figure 1 2 . - O/W Versus Mach Number.