Vibration effects of simple curved panels to high intensity random and discrete frequency nois

Rucker, C. E.

English

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I O N  RESPONSES OF SIMPI;E CURVED PANELS TO 
HIGH-INTENSITY RANDOM AND DISCRETE 
FREQUENCY NOISE 
C a r l  E. Rucker 
NASA Langley Research Center 
Langley Station, Ha.mpton, Va. 
Presented a t  the 38th Shock and Vibration Symposium 
St. Louis, Missouri 
~ a y  1-2, 1968 
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VIBRATION RESPONSES OF SIMl?I;E CURVED PANELS TO 
HIGH-INTENSITY FiANDOM AND DISCRETE 
FREQUENCY NOISE 
Carl E. Rucker 
NASA Langley Research Center 
ABSI'RACT 
Unexpectedly short times to failure for curved panels under acoustic 
loading led to detailed studies of their dynamic response characteristics with 
the objective of exploring the reasons for such short times to failure. 
linear response characteristics were observed involving significant low- 
frequency motions due to buckling. 
centage of large strain amplitudes than would be predicted for a normal strain 
Non- 
Such behavior resulted in a much higher per- 
amplitude distribution. 
butions for significant time durations was greatly facilitated by the use of a 
pulse height analyzer which digitized, classified, stored, and displayed large 
amounts of information. 
The acquisition of joint strain-sound pressure distri- 
INTRODUCTION 
The responses of aircraft or spacecraft structures to complex noise inputs 
involves such important variables as the structural materials, the fabrication 
techniques, and the related environmental conditions. Analytical procedures 
have generally not been adequate for predicting such responses, and hence, much 
reliance has been placed on experiments. 
As part of a series of basic research studies of panel responses to noise, 
the effects of panel curvature have been documented. The purposes of this paper 
5-5769 1 
are to present some of the recent panel test analysis results and to briefly 
describe a unique method of collecting statistical data. 
SONIC FATIGUE FAILURES 
Sonic fatigue data are shown in figure 1 for three different panel curva- 
tures for comparison. 
edge is plotted as a function of time to failure in minutes. 
was a broadband random noise from an air jet. 
was 155 decibels and the spectrum peaked sharply at about 100 Hz (see refs. 1 
and 2). 
tures with lap attachments. 
Root-mean-square strain for a strain gage near the panel 
The excitation 
Its overall sound pressure level 
Identical 20- by 20-inch sheets of material were formed to curved fix- 
Three-sixteenth-inch A&N bolts and nuts adjusted to 
1 
2 
a given torque were spaced on 1- - inch centers with 5/8-inch edge distance. By 
this means, an attempt was made to minimize the edge-attacbment condition dif- 
ferences for the test panels. 
One of the main results of the above study was the relatively short times 
to failure of the 4-foot-radius panels even though the measured strain levels 
were markedly lower than for the other curvatures. 
that significantly different stress concentration factors may have existed. 
present paper, however, contains results of other studies relating to the 
dynamic behavior of the 4-foot-radius panel and which may also be significant 
in causing shorter times to failure. 
It was originally suggested 
The 
Figure 2 is a photograph of a panel which failed due to sonic fatigue while 
formed into a 4-foot-radius configuration. 
resulted from test conditions for which the panel was buckled. 
It is believed that this failure 
Since buckling 
is a strong indicator of nonlinear behavior, the panel response was studied for 
other evidence of nonlinearities. 
2 
SlTRAIN RESPONSES 
A se r ies  of dynamic response studies involving different  in tens i t ies  of 
acoustic loading were conducted, and some representative results are presented 
i n  figure 3 .  
discrete driving frequency f o r  sound-pressure levels  of 115 and I25 dB impinging 
on the lower surface of the panel. 
appeared t o  be responding generally as a l i nea r  system. 
however, there w a s  def ini te  evidence of nonlinear response. The skewness of 
the response peaks toward lower frequencies represents a sof t  spring effect;  
tha t  is, the panel becomes less stiff a t  large vibration amplitudes. 
Overall root-mean-square s t ra ins  are plot ted as a function of 
A t  the  lower excitation l eve l  the  panel 
A t  the  higher level,  
The mode shape sketches on the figure i l l u s t r a t e  qual i ta t ively the modal 
pattern variation f o r  these two levels  of excitation. The sketch a t  the top 
suggests a buckling condition such that the center portion of the panel experi- 
ences re la t ive ly  large amplitude motions a t  frequencies other than the driving 
frequency. 
Both analyticalcand experimental studies have been made f o r  the modal 
response of t h i s  panel, and the resu l t s  are presented i n  figure 4. 
i n  Hz i s  shown f o r  various modal numbers (number of antinodes). 
calculations assuming both clamped and simply supported boundary conditions 
(ref. 3 )  are represented by the so l id  and dashed curves, respectively. Experi- 
mental data obtained using discrete  frequency excitation are  represented by the 
c i r c l e  points. 
modal numbers and close t o  the clamped values a t  high modal numbers. Note that 
the frequency f o r  the fundamental mode corresponds closely t o  that of the s ix th  
mode. 
about U5 dB, whereas a t  a 120-dB l eve l  and higher, the panel snapped in to  a 
Frequency 
Theoretical 
They seem t o  f a l l  close t o  the simply supported values a t  low 
A s  indicated i n  figure 3, the s ix th  mode only w a s  excited a t  a leve l  of 
3 
buckled condition f o r  which the  fundamental and s ix th  modes a re  superimposed 
(see upper sketch of f ig .  3 ) .  
Additional panel response data f o r  high levels  of noise excitation are  
presented i n  figures 5 and 6.' I n  figure 5 the mean square bending s t ra ins  a re  
shown as a function of frequency. 
145-D level) w a s  provided by a s i r en  f o r  which the  harmonic content w a s  a t  
l e a s t  40 dB lower i n  level than the excitation frequency of the figure. 
data shown were obtained by means of a 19-second tape loop and narrow band 
fi l ters.  
c ies  lower than the exciting frequency. 
The discrete  frequency excitation (at a 
The 
Note tha t  re la t ive ly  strong responses of the panel occur at frequen- 
The'response of the panel t o  broadband noise i s  shown i n  f igure 6. Again, 
mean-square bending s t r a in  per un i t  bandwidth is plot ted as a function of fre- 
quency. The spectrum shape of the 190-dB leve l  random noise i s  shown a t  the 
top of the figure. 
erated by a unique j e t  turbulator nozzle represented by the sketch a t  the right.  
A number of re la t ively strong responses are observed a t  the  low frequencies 
even i n  the range where the input spectrum tends t o  drop off. These l a t t e r  
response data are thus consistent with those of figure 5. 
Note that this nearly f la t  random noise spectrum w a s  gen- 
AMPLI!J!UDE DISTRIBUTIONS 
I n  order t o  study the s t a t i s t i c a l  behavior of the panel, a unique method 
was made use of t o  col lect  and analyze appropriate sound pressure and associated 
s t r a i n  data. 
the main results. 
Figures 7 and 8 i l l u s t r a t e  the method used, and figure 9 contains 
Included i n  figure 7 are schematic representations of the root-mean-square 
sound pressure and t o t a l  panel s t r a in  t i m e  histories.  
4 
In  the course of t h i s  
study the amplitude dis t r ibut ions were obtained a t  several  arbi t rary input 
noise loading levels. 
oscillograph records a t  the proper times, as indicated schematically i n  figure 7. 
In  order t o  automate the process of accumulating data of this ty-pe, however, a 
pulse-height analyzer w a s  used i n  the manner suggested by the diagrams of fig- 
ure  8. 
second during t h e i r  80-minute durations ( t i m e  t o  f a i lu re  of the panel). 
analyzer operates i n  such a way tha t  a l l  s t r a in  values associated w i t h  a given 
sound pressure are  grouped together. Thus, it i s  possible t o  determine ampli-  
tude dis t r ibut ion direct ly  from the analyzer. 
Such a procedure could be accomplished by the reading of 
Records such as those of figure 7 were digi t ized about 300 times per 
The 
Such a display i s  i l l u s t r a t ed  i n  figure 8 which contains a cathode ray 
oscilloscope presentation of the s t r a in  and sound-pressure data. 
represents panel s t ra in ,  the zero value being i n  the  center and the negative 
and posit ive values being t o  the  l e f t  and r ight ,  respectively. 
root-mean-square sound pressure; the ve r t i ca l  coordinate represents the number 
of measurements fo r  given values of sound pressure and panel strain.  Thus, a t  
a given sound-pressure value, the display indicates the number of s t r a in  samples 
a t  each s t r a i n  value f o r  the en t i re  t i m e  of the data recording. The ty-pe of 
display i l l u s t r a t e d  i n  the figure i s  useful quali tatively,  but the numerical 
data are  obtained direct ly  from the tabulation c i rcu i t s .  
The abscissa 
The ordinate i s  
Sample s t r a in  amplitude dis t r ibut ion data as measured w i t h  the pulse- 
height analyzer are presented i n  figure 9 f o r  the 4-foot-radius panel. 
dis t r ibut ion shown i s  f o r  a sound-pressure leve l  of 157 dB and contains over 
79,000 samples. 
distribution. 
s t r a in  i s  plot ted on the ve r t i ca l  scale f o r  various multiples of standard 
The 
Also shown i s  a so l id  curve representing a normal or  gaussian 
The probability of being equal t o  or  l e s s  than a given value of 
5 
deviation (a). It can be seen tha t  the measured data generally follow the 
normal distribution curve up t o  nearly 2a and then deviate from the normal 
distribution curve a t  higher values. 
centage of the panel l ifetime i s  spent a t  s t r a in  values above 30 than would be 
the case for a normal distribution of s t ra in  amplitudes. 
the figure, similar data f o r  the other two panel curvatures of figure 1 f e l l  
generally along the gaussian curve a t  the higher CT values. The implication 
from these data i s  tha t  the &-foot curvature panel, probably because of i t s  
nonlinear behavior characterist ics,  experienced an abnormally high number of 
high s t r a in  values. These s t r a in  peaks may account f o r  the shorter times t o  
fa i lure  of these panels. 
This resu l t  implies that a greater per- 
Although not shown on 
Unexpectedly short 
loading led t o  detailed 
CONCLUDING 
times t o  fa i lure  
studies of t he i r  
REMARKS 
f o r  curved panels under acoustic 
dynamic response characteristics. 
Nonlinear response characterist ics were observed involving significant low- 
frequency motions due t o  buckling. Such behavior resulted i n  a much higher 
percentage of large s t r a in  q l i t u d e s  than would be predicted f o r  a normal 
s t r a in  amplitude distribution. 
6 
REFERENCES 
1. Carl E. Rucker, "Some Experimental Effects of Curvature on Response of 
Simple Panels t o  Intense Noise," Presented at  the 67th Meeting of the 
Acoustical Society of America (New York), May 1964. 
2. P. M. Edge, Jr., and Carl E. Rucker, "Response-to-Noise Studies of Some Air- 
craf t  and Spacecraft Structures," Acoustical Fatigue i n  Aerospace Structures, 
W. S. Trapp and D. M. Forney, Jr., eds., Qracuse Univ .  Press, 1965, 
pp. 404-408. 
3 .  John L. Sewall, "Vibration Analysis of Cylindrically Curved Panels With 
Simply Supported o r  Clamped Edges and Comparisons With Some Experiments," 
NASA TN D-3791, Table IVb, p. 38, and Figure 5 ,  p. 49, 1967. 
7 
LIST OF FIGURES 
Figure 1.- Time t o  failure f o r  0.020-inch-thick aluminum-alloy panels of three 
cumatures i n  a random noise f i e l d  having an overal l  sound-pressure l eve l  of 
160 a. 
Figure 2. - Photograph of 0.020-inch-thick aluminum-alloy panel of 4-foot radius 
a f t e r  sonic fatigue failure due t o  s i ren excitation. 
Figure 3.- overall s t r a i n  responses of a 4-foot-radius pme1 as a function of 
driving frequency f o r  two different  levels  of discrete frequency excitation. 
Figure 4.- Some modal responses of curved aluminum panel (R = 4 f t )  excited by 
discrete  frequency noise. 
Figure 5.- Spectrum of bending s t r a in  response of 4-foot-radius curved panel 
due t o  discrete frequency excitation a t  143-dB sound-pressure level. 
Figure 6.- Bending s t r a in  response spectrum of a 4-foot-radius panel due t o  
random noise input from a four-branch a i r j e t  noise source. 
Figure 7.- Schematic diagram of the time h is tor ies  of the root-mean-square 
sound pressure and associated t o t a l  panel s t ra in .  
indicate points a t  which s t r a i n  values were determined f o r  an arbi t rary 
sound-pressure load value. 
Vertical  dashed l i nes  
Figure 8. - Photograph of oscilloscope display of a pulse-height analyzer used 
f o r  accumulation of jo in t  probability data. 
Figure 9.- Total s t r a in  amplitude dis t r ibut ion f o r  4-foot-radius panel due t o  
random noise loading compared t o  a normal distribution. 
8 
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Vibration Responses of Simple Curved Panels to High-intensity Random and Discrete Frequency Noise

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