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SOME EXPERIENCE USING SUBCRITICAL RESPONSE METHODS I N WIND-TUNNEL FLUTTER MODEL STUDIES Jerome T , Foughner, Jr.
NASA Langley Research Center SUMNARY Experiences obtained with f o u r methods t o p r e d i c t f l u t t e r of wind-tunnel models from s u b c r i t i c a l response d a t a are described. The four methods are: co/quad, randomdec, power s p e c t r a l d e n s i t y , and t h e peak-hold spectrum. Model e x c i t a t i o n techniques included both forced ( s i n u s o i d a l sweep) and random ( t u n n e l turbulence). These methods w e r e s u c c e s s f u l l y used t o measure t h e frequency and damping (or an i n v e r s e response amplitude proportional t o t h e damping) i n t h e predominant f l u t t e r modes. Implementation and a p p l i c a t i o n of Some r e s u l t s and comparisons between methods are each method are discussed.
presented.
INTRODUCTION Transonic f l u t t e r model t e s t i n g has become a n i n t e g r a l p a r t of t h e develop- m e n t of high-speed a i r c r a f t such as t h e Grumman F-14, Rockwell B-1, Boeing 747, and Lockheed C-5A. Wind-tunnel s t u d i e s t o e s t a b l i s h t r a n s o n i c f l u t t e r clear- ances and t o provide d a t a f o r c o r r e l a t i o n w i t h a n a l y s i s and with f l i g h t tests are made using dynamically scaled a e r o e l a s t i c models. Some examples of corre- l a t i o n between f l i g h t and wind-tunnel model tests i n t h e Langley t r a n s o n i c dynamics tunnel (TDT) are given i n r e f e r e n c e 1. These models simulate t h e com- p l e t e a i r c r a f t under near f r e e - f l y i n g conditions and are q u i t e s o p h i s t i c a t e d and expensive. Since f l u t t e r can b e an explosive-type9 d e s t r u c t i v e i n s t a b i l i t y , t h e r e is a s u b s t a n t i a l r i s k of damaging t h e model when f l u t t e r is encountered.
Consequently, t h e r e is a need t o develop methods t o p r e d i c t t h e f l u t t e r condi-
I
t i o n without having t o a c t u a l l y experience f l u t t e r . The requirements are similar t o those i n f l i g h t f l u t t e r t e s t i n g , namely, t o i d e n t i f y t h e v i b r a t i o n modes critical t o f l u t t e r and t o measure and t r a c k t h e frequency and damping i n t h e s e modes as t h e test conditions are v a r i e d , and t h e f l u t t e r boundary is approached.
The state of t h e a r t of s u b c r i t i c a l f l i g h t f l u t t e r t e s t i n g w a s surveyed i n late 1972 ( r e f . 2). A t t h e time of t h i s survey, United S t a t e s i n d u s t r y r e l i e d almost exclusively on s i n u s o i d a l e x c i t a t i o n provided by a u x i l i a r y aerodynamic vanes, i n e r t i a shakers, o r t h e power c o n t r o l system. Random e x c i t a t i o n techni- ques had not been used f o r f l i g h t f l u t t e r t e s t i n g . For a number of y e a r s t h e s t a f f of t h e TDT has used v a r i o u s s u b c r i t i c a l response methods i n wind-tunnel f l u t t e r model s t u d i e s . I n some cases e x t e r n a l e x c i t a t i o n of t h e model has been used, s i m i l a r t o f u l l - s c a l e f l i g h t f l u t t e r t e s t i n g . However, t h e methods of e x c i t a t i o n of models are u s u a l l y more r e s t r i c t e d , For i n s t a n c e , t h e model c o n t r o l system is normally provided f o r t r i m and is n o t capable of high- frequency i n p u t s , Space and weight are a l s o u s u a l t o o l i m i t e d t o a l l o w i n t e r n a l shaker equipment Consequently, m f t h e model s u b c r i t i c a l damping work a t Langley h a s been a s s o c i a t e d w i t h methods t h a t u s e n a t u r a l wind-tunnel t u r b u l e n c e as t h e e x c i t a t i o n f o r c e .
The purpose of t h i s paper is t o d e s c r i b e some experiences i n t h e applica- t i o n of f o u r s u b c r i t i c a l r e s p o n s e methods t o p r e d i c t model f l u t t e r c h a r a c t e r i s - t i c s i n t h e Langley TDT. The f o u r methods examined are co/quad, which r e q u i r e s s i n u s o i d a l f o r c e d e x c i t a t i o n , randomdec and power s p e c t r a l d e n s i t y (PSD), which r e q u i r e only random e x c i t a t i o n , and t h e peak-hold spectrum method, which is a p p l i e d t o b o t h a forced and random e x c i t a t i o n system. The implementation of each method is d e s c r i b e d , and r e s u l t s from t h e a p p l i c a t i o n of a l l f o u r methods t o a c a n t i l e v e r , delta-wing model i n t h e TDT are presented. Since t h i s model w a s designed and b u i l t f o r active f l u t t e r s u p p r e s s i o n s t u d i e s and w a s equipped w i t h f a s t a c t i n g o s c i l l a t i n g c o n t r o l s , it provided a unique o p p o r t u n i t y f o r determining s u b c r i t i c a l r e s p o n s e d a t a where s i n u s o i d a l f o r c e d e x c i t a t i o n is r e q u i r e d f o r comparison w i t h damping d a t a obtained u s i n g random e x c i t a t i o n produced by turbulence. Also, co/quad and randomdec r e s u l t s o b t a i n e d by u s i n g a complete, cable-mounted B-52 model are discussed.
FOUR PREDICTION METHODS The f o u r methods used t o measure t h e s u b c r i t i c a l (below t h e a c t u a l f l u t t e r speed) r e s p o n s e c h a r a c t e r i s t i c s are r e f e r r e d t o h e r e i n as co/quad, randomdec, PSD, and peak-hold spectrum methods. These methods w e r e used t o measure t h e frequency and damping ( o r a n i n v e r s e r e s p o n s e amplitude p r o p o r t i o n a l t o t h e damping i n t h e peak-hold spectrum case) i n t h e predominant o r c r i t i c a l v i b r a t i o n modes.
By s u i t a b l y p l o t t i n g and e x t r a p o l a t i n g t h e s u b c r i t i c a l damping i n t h e v i b r a t i o n mode o r modes of i n t e r e s t , t h e f l u t t e r p o i n t c a n u s u a l l y b e estab- l i s h e d . With each method, it w a s assumed t h a t t h e r e s p o n s e can b e approximated by t h a t of a single-degree-of-freedom system. The r e s p o n s e d a t a c o n s i s t e d of a n accelerometer on t h e model under e i t h e r a forced e x c i t a t i o n o r t h e random e x c i t a t i o n from t h e t u n n e l turbulence. A l l of t h e s e methods can b e used on-line, t h a t is, used t o t r a n s l a t e t h e response time h i s t o r y samples i n t o q u a n t i t a t i v e information f o r t h e test e n g i n e e r w h i l e t h e test is i n progress.
B r i e f l y , t h e co/quad method measures t h e in-phase and out-of-phase compo- n e n t s of t h e f o r c e d response generated by t h e s i n u s o i d a l frequency sweep tech- nique. The randomdec method, a r e l a t i v e l y new method d e s c r i b e d i n r e f e r e n c e 3 , makes u s e of ensemble averaging of t r a n s i e n t response t o random e x c i t a t i o n .
The PSD method is a well-known procedure f o r t h e a n a l y s i s of random response d a t a . It i s o b t a i n e d d i r e c t l y from an ensemble a v e r a g e of t h e s q u a r e of t h e magnitude of t h e F o u r i e r t r a n s f o r m of a number of segments of t h e time h i s t o r y - I n t h e peak-hold spectrum method, F o u r i e r components of a number of time h i s t o r y segments are determined and t h e envelope of t h e peak v a l u e s of t h e s e components i s obtained as a f u n c t i o n of frequency.
DESCRIPTION AND IMPLEMENTATION Co/quad Method The co/quad method involved measuring t h e forced response of a model t o an input f o r c e such as t h a t generated by a trailing-edge c o n t r o l s u r f a c e as i l l u s - t r a t e d schematically i n f i g u r e 1. I f a t r a n s f e r f u n c t i o n r e l a t i n g t h e response t o t h e input f o r c e is determined as a function of frequency, then t h e damping i n each mode can be obtained. For t h e model a p p l i c a t i o n s presented herein, t h e e x c i t a t i o n f o r c e w a s provided by o s c i l l a t i n g a n aerodynamic c o n t r o l s u r f a c e , and t h e model dynamic response h w a s measured with an accelerometer. Since t h e measured a c t u a t o r phase l a g and amplitude v a r i a t i o n over t h e frequency range of i n t e r e s t w a s s m a l l and t h e aerodynamic phase l a g s of t h e c o n t r o l s u r f a c e w e r e assumed t o be s m a l l , t h e c o n t r o l s u r f a c e a c t u a t o r command s i g n a l 6, w a s used as a measure of t h e e x c i t a t i o n force. Cross spectrum between t h e c o n t r o l sur- f a c e command s i g n a l and t h e model dynamic response w a s determined with a S p e c t r a l Dynamics SD109B co/quad analyzer. This analyzer p r e s e n t s two outputs i n t e r m s of in-phase (called co f o r coincident) and out-of-phase ( c a l l e d quad f o r quadrature) components between s i g n a l s . Several means of c a l c u l a t i n g t h e damping are a v a i l a b l e d i r e c t l y from a co and quad type of presentation. A s indicated i n f i g u r e 1, t h e damping of a mode w a s estimated from t h e out-of-phase component by t h e frequencies l a b e l e d fA and fB. These are t h e frequencies a t t h e half-power p o i n t s and t h e s t r u c t u r a l damping g can be expressed i n t e r m s of these frequencies ( f i g . 1 ) .
Randomdec Method To obtain a randomdec s i g n a t u r e , one simply c o l l e c t s a number of segments of t h e random response s i g n a l , each segment having t h e same i n i t i a l amplitude, and ensemble averages them. I f t h e s y s t e m is l i n e a r and t h e e x c i t a t i o n random, t h e ensemble average converges t o t h e t r a n s i e n t response of t h e system due t o t h e s e l e c t e d set of i n i t i a l conditions.
The implementation of randomdec as used i n t h i s paper is shown schemati- The response t i m e h i s t o r y shown i n f i g u r e 2 contains many c a l l y i n f i g u r e 2.
modes and is normally recorded on analog tape. For t h e on-line randomdec process, a band-pass analog f i l t e r w a s used f o r mode i s o l a t i o n and n o i s e reduc- t i o n . The s t a r t i n g p o i n t of each ensemble member w a s s e l e c t e d with t h e gating c i r c u i t (a standard laboratory oscilloscope t r i g g e r i n g c i r c u i t w a s used). A Technical Measurement Corporation 400C computer of average t r a n s i e n t s w a s used f o r ensemble averaging. A s t h e s i g n a t u r e develops, it i s monitored on a n oscilloscope. An e l e c t r o n i c counter records t h e number of segments averaged and a X-Y p l o t t e r provides a hard copy of t h e f i n a l s i g n a t u r e . S t r u c t u r a l damping r a t i o may be determined d i r e c t l y as indicated on f i g u r e 2.
With t h e implementation as described ( f i g . 2 ) , t h e d i f f e r e n t time segments w e r e averaged s e q u e n t i a l l y . That is, t h e computer processed a l l t h e r e s u l t s f o r one t i m e segment before beginning t o c o l l e c t and average d a t a f o r t h e next segment. Also, i n t h e implementation as described, t h e averaging process f o r each time segment w a s obtained by taking only segments which c r o s s t h e s e l e c t e d t r i g g e r l e v e l w i t h a p o s i t i v e slope. Thus, t h e randomdec s i g n a t u r e r e p r e s e n t s t h e system t r a n s i e n t response due t o an i n i t i a l amplitude and v e l o c i t y , PSD and Peak-Hold Spectrum Methods The PSD and t h e peak-hold spectrum methods w e r e implemented as shown i n f i g u r e 3. Both methods w e r e implemented using a S p e c t r a l Dynamics SD330A Spectrascope. This analyzer employs time compression techniques t o achieve minimum a n a l y s i s t i m e for t h e frequency-tuned band-pass f i l t e r t o convert t h e i n p u t s i g n a l from t h e t i m e domain t o t h e frequency domain. Following compres- s i o n , t h e input s i g n a l is frequency analyzed using 250 synthesized f i l t e r loca- t i o n s t h a t are tuned by a b u i l t - i n sweep generator. With operator-selected modes of operation, t h i s analyzer i s highly f l e x i b l e . When t h e averaging mode of operagion is s e l e c t e d , t h e average spectrum c h a r a c t e r i s t i c s of t h e random s i g n a l h a r e o b t a i n e d . The averager examines successive ensembles of spectrum f u n c t i o n s and computes t h e averaged sum over a predetermined length of time.
Shown on t h e l e f t of f i g u r e ' 3 is a t y p i c a l PSD obtained from t h e model dynamic response h. The r e s u l t i n g s i g n a t u r e has a peak f o r each s t r u c t u r a l mode and, f o r well-separated peaks, t h e damping r a t i o may be obtained.
A s i n d i c a t e d i n f i g u r e 3, t h e s t r u c t u r a l damping is equal t o t h e frequency bandwidth, taken a t t h e half-power p o i n t , and divided by t h e mode frequency.
An a d d i t i o n a l mode of o p e r a t i o n of t h e Spectrascope allows f o r d e t e c t i o n and s t o r a g e of t h e peak v a l u e s f o r each of 250 frequency windows. I n t h i s mode of operation, a n ensemble spectrum composed of 250 frequency windows i s obtained.
Upon r e c e i p t of each subsequent spectrum, peak f i l t e r response a t each l o c a t i o n is updated i n a p o s i t i v e d i r e c t i o n . That is, only a n i n c r e a s e i n v a l u e causes an update t o t h e new higher value. On t h e r i g h t of f i g u r e 3 , a t y p i c a l peak- hold spectrum is shown. With t h i s method t h e damping parameter is not obtained.
However, t h e r e c i p r o c a l of t h e peak spectrum amplitude 1/P is proportional t o t h e damping r a t i o and is used as a measure of system s t a b i l i t y . The peak-hold method w a s applied using two forms of e x c i t a t i o n , model response t o tunnel turbulence and model response t o s i n u s o i d a l f o r c e .
APPLICATIONS TO WIND-TUNNEL MODEL TESTING The four s u b c r i t i c a l response methods w e r e applied t o f l u t t e r test d a t a of Further a p p l i c a t i o n of t h e co/quad and randomdec a delta-wing r e s e a r c h model.
Some r e s u l t s and methods were made using a B-52 f l u t t e r suppression model.
comparisons are presented i n f i g u r e s 4 t o 7.
Delta-Wing F l u t t e r Model The t r a i l i n g - A photograph of t h e delta-wing model is shown i n f i g u r e 4.
A d e t a i l e d edge c o n t r o l s u r f a c e w a s used t o provide t h e forced e x c i t a t i o n .
d e s c r i p t i o n of t h i s wing is given i n r e f e r e n c e 4. The f l u t t e r motion of t h i s model involves primarily t h e second n a t u r a l v i b r a t i o n mode coupled with some primary bending.
The s u b c r i t i c a l f l u t t e r c h a r a c t e r i s t i c s of t h i s model i n t h e TDT a t a Mach Two sets of t h e model d a t a are shown. number of 0,90 is presented i n f i g u r e 5.
Figure 5(a) p r e s e n t s t h e v a r i a t i o n of s t r u c t u r a l damp f l u t t e r mode w i t h dynamic pressure. The damping r e s u l t s obtained with t h e co/quad, randomdec, and PSD methods are i n d i c a t e d with t h e open symbols. The model f l u t t e r e d a t a dynamic p r e s s u r e of 5.89 kPa (123 l b f / f t 2 ) as i n d i c a t e d with t h e closed symbol. The s o l i d l i n e i n t h e f i g u r e is f a i r e d through t h e randomdec d a t a which, of t h e t h r e e methods shown, a p p e a r s t o g i v e t h e most c o n s i s t e n t f o r e c a s t of the f l u t t e r point.
A s a word of caution, it should be noted t h a t frequency sweep methods, when used c l o s e t o a f l u t t e r condition, may l e a d t o dangerously l a r g e amplitude response as t h e f o r c i n g frequency sweeps through t h e f l u t t e r mode frequency.
A p l o t of t h e inverse amplitude of t h e peak spectrum (used as t h e s t a b i l i t y c r i t e r i a ) is presented i n f i g u r e 5(b) as a f u n c t i o n of dynamic pressure. Shown are r e s u l t s from forced e x c i t a t i o n (same e x c i t a t i o n system as used i n co/quad method) and r e s u l t s from random e x c i t a t i o n (model response t o tunnel turbulence).
The b e s t r e s u l t s w e r e obtained with the forced e x c i t a t i o n ( f a i r e d d a t a ) while t h e response-only d a t a showed some s c a t t e r . Although experience is l i m i t e d i n t h e u s e of t h i s method, i t is included s i n c e it appears promising as a f l u t t e r i n d i c a t o r .
Further i l l u s t r a t i o n of t h e type of d a t a generated with t h e u s e of t h e four s u b c r i t i c a l methods is presented i n f i g u r e 6. Shown are t h e d a t a p l o t s from which t h e damping levels presented i n f i g u r e 5 w e r e obtained. The wind-tunnel conditions w e r e t h e same f o r each method (Mach number M = 0.90; dynamic pres- I n t h e implementation of t h e co/quad method, s u r e q = 5.42 kPa (113 l b f / f t 2 ) ) .
a 3.33-minute logarithmic sweep from 5 t o 25 Hz w a s used. A damping level of 0.037 a t a frequency of 10.8 H z is indicated. Approximately 40 seconds of d a t a w e r e taken f o r t h e randomdec method giving a damping level of 0.048 f o r a f r e - quency of 10.6 Hz. Forty seconds of data w e r e used f o r t h e PSD and peak-hold spectrum methods (3.33 minutes f o r t h e peak-hold forced e x c i t a t i o n procedure).
A frequency of 10.7 Hz and a damping l e v e l of 0.037 is indicated f o r t h e PSD method. The f l u t t e r mode frequency f o r t h e peak-hold spectrum is 10.6 Hz.
B-52 Model Further experience with t h e co/quad forced response method and t h e random- dec method w e r e obtained using a 1/30-scale, dynamic model of a B-52. The model w a s equipped w i t h fast a c t i n g c o n t r o l s u r f a c e s f o r f l u t t e r suppression s t u d i e s which are described i n r e f e r e n c e 5. For t h i s model, shown on t h e r i g h t of f i g u r e 7 , t h e a i l e r o n s w e r e used t o generate t h e forcing function. Thus, f o r t h e co/quad method, t h e damping w a s estimated by determining t h e r a t i o of the outboard-accelerometer response t o t h e a i l e r o n command f o r a frequency range of 4 t o 24 Hz. The s u b c r i t i c a l f l u t t e r c h a r a c t e r i s t i c s of t h i s model i n t h e TDT are presented i n f i g u r e 7. The damping r e s u l t s obtained with t h e co/quad and t h e randomdec methods are indicated with t h e open symbols. Both of t h e s e methods s a t i s f a c t o r i l y p r e d i c t t h e measured f l u t t e r p o i n t a t a dynamic pressure of 2.65 kPa (55.4 l b f / f t 2 ) as indicated by t h e closed symbol.
OBSERVATIONS Although a l l f o u r methods assumed t h a t t h e response can be c h a r a c t e r i z e d by a single-degree-of-freedom system, they s u c c e s s f u l l y provided a measure of t h e s u b c r i t i c a l damping l e v e l . Each method can be implemented with commer- c i a l l y a v a i l a b l e instrumentation. The randomdec and PSD methods which depend on random unknown e x c i t a t i o n , i.e., turbulence and b u f f e t i n g , comp forced sweep co/quad method. Both types of e x c i t a t i o n i n p u t s have t h e i r advan- tages. What is "noise" f o r co/quad is "input" f o r randomdec. Randomdec works b e s t when t h e r e i s l a r g e response t o turbulence o r b u f f e t e x c i t a t i o n - t h e r e g i o n where co/quad d a t a are least r e l i a b l e . One l i m i t a t i o n of t h e random e x c i t a t i o n methods is when t h e f l u t t e r c o n d i t i o n involves high frequency modes t h a t may not b e e x c i t e d by random e x c i t a t i o n such as turbulence and b u f f e t i n g .
I n t h i s i n s t a n c e t h e forced sweep method should be used.
D i f f i c u l t i e s t h a t may b e encountered w i t h t h e u s e of s u b c r i t i c a l response methods include unwanted n o i s e and c l o s e l y spaced resonant frequencies. Methods ( c u r r e n t l y used i n f l i g h t f l u t t e r t e s t i n g ) f o r e l i m i n a t i n g o r masking n o i s e e f f e c t s have been evaluated and s e v e r a l new techniques suggested i n r e f e r e n c e 6.
Several system i d e n t i f i c a t i o n schemes w e r e a l s o developed i n r e f e r e n c e 6 t o handle t h e s i t u a t i o n where two o r more f r e q u e n c i e s of t h e system are c l o s e together.
A s a r e s u l t of experience gained during t h i s e a r l y implementation of t h e randomdec method, f u r t h e r development of t h i s method w a s undertaken. A c u r r e n t implementation ( u t i l i z i n g thenew TDT d a t a system) of t h e randomdec procedure is presented i n r e f e r e n c e 7. The f e a s i b i l i t y of using t h e randomdec method i n conjunction w i t h a s i g n a t u r e a n a l y s i s procedure t o determine t h e damping and frequency v a l u e s of a two-mode a e r o e l a s t i c system w a s e s t a b l i s h e d i n r e f e r e n c e 8.
The s i g n a t u r e a n a l y s i s procedure w a s based on a least-squares curve f i t t i n g of t h e randomdec s i g n a t u r e . The randomdec method w a s applied during t h e YF-16 f l i g h t f l u t t e r tests and f o r t h i s a p p l i c a t i o n provided a s a t i s f a c t o r y a l t e r n a t e t o more c o s t l y conventional s u b c r i t i c a l methods ( r e f . 9 ) .
The r e a d e r is cautioned t h a t f o r a case where a few knots i n c r e a s e i n speed s p e l l s t h e d i f f e r e n c e between a well-damped response and v i o l e n t f l u t t e r , sub- critical damping techniques may n o t be a p p l i c a b l e t o p r e d i c t t h e f l u t t e r condi- w i l l still be of v a l u e i n t i o n . However, i n t h i s case, s u b c r i t i c a l techniques c o r r e l a t i o n w i t h s u b c r i t i c a l a n a l y t i c a l d a t a and f o r u s e i n parameter i d e n t i f i - the system mathematical model.
c a t i o n techniques t p d e f i n e CONCLUDING REMARKS Four s u b c r i t i c a l response methods w e r e applied t o f l u t t e r test d a t a f o r t h e same model, a c a n t i l e v e r d e l t a wing. E x c i t a t i o n methods included forced excita- t i o n (co/quad and peak-hold spectrum) and random e x c i t a t i o n (randomdec, PSD, and peak-hold spectrum). F u r t h e r experience with t h e co/quad and t h e randomdec methods w a s obtained with f l u t t e r test d a t a of a complete cable-mounted B-52 f l u t t e r model, With b o t h f l u t t e r models, t h e s u b c r i t i c a l methods t e s t e d i n t h e paper s a t i s f a c t o r i l y p r e d i c t e d t h e measured f l u t t e r p o i n t s e REFERENCES 1. R e e d , Wilmer H . , 111: C o r r e l a t i o n With F l i g h t of Some A e r o e l a s t i c Model S t u d i e s i n t h e NASA Langley Transonic Dynamics Tunnel. NASA Symposium of F l u t t e r T e s t i n g Techniques, O c t . 1975. (Paper No. 1 0 of t h i s compilation.)
2. Rosenbaum, Robert: Survey of A i r c r a f t S u b c r i t i c a l F l i g h t F l u t t e r T e s t i n g Methods. NASA CR-132479, 1974.
3 . Cole, Henry A., Jr.: On-Line F a i l u r e D e t e c t i o n and Damping Measurement of Aerospace S t r u c t u r e s by Random Decrement S i g n a t u r e s . NASA CR-2205, 1973.
4 . Sandford, Maynard C . ; Abel, I r v i n g ; and Gray, David L.: Transonic Study of Active F l u t t e r Suppression Based on a n Energy Concept. J. Aircr., v o l . 12, no. 2, Feb. 1975, pp. 72-77.
5. Redd, L. T . ; Gilman, J., Jr.; Cooley, D. E.; and Sevart, F. D.: Wind- a B-52 Model F l u t t e r Suppression System.
Tunnel I n v e s t i g a t i o n of J. Aircr., v o l . 11, no. 11, Nov. 1974, pp. 659-663.
6. Houbolt, John C.: S u b c r i t i c a l F l u t t e r T e s t i n g and System I d e n t i f i c a t i o n .
N A S A CR-132480, 1974.
7. Hammond, C h a r l e s E.; and Doggett, Robert V . , Jr.: Determination of Sub- c r i t i c a l Damping by Moving-Block/Randomdec A p p l i c a t i o n s . NASA Symposium O c t . 1975. (Paper No. 3 of t h i s of F l u t t e r T e s t i n g Techniques, e ) compilation 8. Chang, C. S.: Study of Dynamic C h a r a c t e r i s t i c s of A e r o e l a s t i c Systems U t i l i z i n g Randomdec S i g n a t u r e s . NASA CR-132563, 1975.
9. Brignac, W. J.; Ness, H. B . ; and Smith, L. M.: The Random Decrement Tech- nique Applied t o t h e YF-16 F l i g h t F l u t t e r T e s t s . AIAA Paper No. 75-776, May 1975.
1 8 7 FREQUENCY, Hz Figure 1 . - Implementation of co/quad method.
~lilG,,,w-J CONDITIONER RESPONSE TIME HISTORY
c
t
TMC MODEL 400 C AVERAGER r----- 1 TIME- PLOTTER COUNTER Figure 2 . - Implementation of randomdec method.
MODEL RESPONSE PEAK HOLD SPECTRUM PS D PSD fO FREQUENCY FREQUENCY Figure 3 . - Implementation of spectrum methods.
Figure 4 . - Delta-wing model.
METHOD 0 CO-QUAD -0- RANDOMDEC .04 FLUTTER
:~~
(a) Co/quad, randomdec, PSD results.
EXCITATION *FORCED b RANDOM
-+ li-i**; 4.0 4.4 4.8 5.2 5.6 6.0 FLUTTER
DYNAMIC PRESSURE, kPa (b) Peak-hold spectrum results.
Figure 5.- Comparison of subcritical methods, delta-wing model (M = 0.90).
r IN-PHASE g = 0 . 0 3 7 h
- h"2
Hz bC I I I I 10 15 20 25 0 4 8 12 16 20 24 FREQUENCY. Hz FREQUENCY, Hz (a) Co/quad. (c) PSD.
PEAK " AMPLITUDE f = 1 0 . 6 Hz h 0 4 8 12 16 20 24 0.5 1.0 0 FREQUENCY, Hz TIME, seconds (b) Randmdec. (d) Peak-hold spectrum.
6.- Illustration of subcritical methods.
Figure q = 5.42 kPa (113 lbf/ft2).
M = 0 . 9 0 ; OUTBOARD A I L E R O N ER
-
.02 0 1 . 6 2.0 2.4 2.8 D Y N A M I C PRESSURE, kPa F i g u r e 7.- S u b c r i t i c a l response of B-52 model.
1 9 1