The primary concern for verification is the dynamic characteristics of the space structure related to the control and sensor/actuator location. Properties such as modal density, range of natural frequencies, and modal displacements at the sensor/actuator location are considered and are simulated for the verification of the structure/control closed loop system. A space beam is studied in zero gravity environment and in a 1 G gravity environment, along with their governing equations

Chen, J.

Garba, J.

Welsh 

NASA Technical Reports Server

VERIFICATION FOR LARGE SPACE STRUCTURES 
J. Chen and J. Garba 
J e t  Propuls ion Laboratory 
C a l i f o r n i a  I n s t i t u t e  of Technology 
Pasadena, Cal i f o r n i  a 
Appl i e d  Mechanics Techno1 ogy Sec t ion  
Large Space Antenna Systems Technology - 1984 
December 4-6, 1984 
39 3 
https://ntrs.nasa.gov/search.jsp?R=19850015525 2020-03-22T18:47:57+00:00Z
T r a d i t i o n a l l y ,  most aerospace s t r u c t u r a l  systems must be sub jec ted  t o  some form 
o f  v e r i f i c a t i o n  p r i o r  t o  f l i g h t .  The v e r i f i c a t i o n  procedure o f t e n  i n c l u d e s  t h e  
exper imenta l  i d e n t i f i c a t i o n  o f  s t r u c t u r a l  c h a r a c t e r i s t i c s  such as t h e  n a t u r a l  
f requenc ies  and normal modes u s i n g  modal t e s t s .  It may a l s o  i n c l u d e  a d i r e c t  
s t r u c t u r a l  i n t e g r i t y  v e r i f i c a t i o n  under s imu la ted  dynamic environments. I n  t h e  past  
t h e  design c r i t e r i a  f o r  t h e  s t r u c t u r a l  systems were r e q u i r e d  t o  s u r v i v e  o n l y  t h e  
launch loads, hence these v e r i f i c a t i o n  procedures were performed under a 1-g 
env i  ronment and posed no p a r t i c u l a r  concern. 
FOR CONVENTIONAL AEROSPACE STRUCTURES 
0 STRUCTURAL V E R I F I C A T I O N  P R I O R  TO F L I G H T  
0 E X P E R I M E N T A L  I D E N T I F I C A T I O N  OF STRUCTURAL D Y N A M I C  C H A R A C T E R I S T I C S  - 
L O A D S  MODEL V E R I F I C A T I O N  
0 S I M U L A T E D  D Y N A M I C  ENVIRONMENTS FOR STRUCTUHAL I N T E G R I T Y  
o D E S I G N  C R I T E R I A  - LAUNCH LOADS I N  1.0 G 
I 39 4 
For t r u e  space s t r u c t u r e s  e r e c t e d / f a b r i  cated/deployed i n  o r b i t ,  t h e  envi  ronment 
i n  space i s  q u i t e  benign, t h e  a p p l i e d  loads are  apt  t o  be smal l ,  and t h e  s t r e n g t h  o f  
t h e  s t r u c t u r e  i s  not  a pac ing f a c t o r .  On t h e  o ther  hand, t h e  demands p laced on 
antenna s t r u c t u r e s  and s o l a r  r e f l e c t o r s  f o r  accurate p o s i t i o n i n g  and t h e  
requirements o f  adequate s t i f f n e s s  t o  avo id  undes i rab le  s t r u c t u r a l  d i s t o r t i o n s  are 
o f t e n  ser ious  and thereby d i c t a t e  t h e  design. 
For  l a r g e  space s t r u c t u r e s ,  t h e  design c r i t e r i a  a re  d i f f e r e n t .  The o p e r a t i o n a l  
environments such as maneuver, deployment, docking, etc., are t h e  events t h a t  are 
expected t o  generate t h e  c r i t i c a l  loads. 
FOR LARGE SPACE STRUCTURES 
0 DESIGN C R I T E R I A  - MANEUVER, DEPLOYMENT, DOCKING, ETC. 
0 STIFFNESS FOR ACCURATE POSIT IONING AND SHAPE REQUIREMENTS 
0 ACCURATE DYNAMIC CHARACTERISTICS FOR ACTIVE CONTROL 
0 ZERO GRAVITY REQUIREMENT 
0 GROUND TEST V E R I F I C A T I O N  
39 5 
The dynamic c h a r a c t e r i s t i c s  o f  t h e  space s t r u c t u r e  r e l a t e d  t o  t h e  c o n t r o l  and 
sensor /actuator  l o c a t i o n  become t h e  pr imary concerns f o r  t h e  v e r i f i c a t i o n .  
Therefore, i n s t e a d  o f  v e r i f y i n g  t h e  l o a d  c a r r y i n g  c a p a b i l i t y  o f  t h e  s t r u c t u r e ,  
p r o p e r t i e s  such as modal dens i ty ,  range o f  n a t u r a l  f requencies,  and modal 
displacements a t  t h e  p o t e n t i a l  sensor /actuator  l o c a t i o n  are impor tant  and must be 
s imulated f o r  t h e  v e r i f i c a t i o n  o f  t h e  s t r u c t u r e / c o n t r o l  c losed- loop system. 
GROUND TEST CONSIDERATION 
0 G K A V I T Y  E F F E C T S  ON D Y N A M I C  C H A R A C T E R I S T I C S  
0 V E K I F I C A T I O N  OF LOAD C A R R Y I N G  C A P A B I L I T Y  NOT REblU IRED 
0 D Y N A M I C  C H A R A C T E R I S T I C S  RELATED TO CONTROL REOUIREI )  
0 MODAL D E N S I T Y ,  FREQUENCY RANGES, MODAL D I S P L A C E M E N T S  AT 
SENSOR/ACTUATOR L O C A T I O N S ,  ETC.  
39 6 
The gener ic  s t r u c t u r a l  element chosen f o r  t h e  study i s  a space beam which i s  a 
beam w i t h  a l a r g e  slenderness r a t i o .  For s i m p l i c i t y ,  t h e  c o n d i t i o n s  o f  s imple beam 
t h e o r y  w i l l  be assumed. The f i g u r e  shows t h e  v i b r a t i n g  beam i n  a zero g r a v i t y  
env i  ronment and a 1-g g r a v i t y  env i  ronment. 
I n  what f o l l o w s ,  t h e  governing equat ion f o r  t h e  v i b r a t i n g  beam i n  a 1-g 
environment w i l l  be examined. The zero g r a v i t y  c o n d i t i o n  w i l l  be t r e a t e d  as a 
spec ia l  case i n  which t h e  e f f e c t s  o f  t h e  g r a v i t y  w i l l  be e l iminated.  
' 
A SPACE BEAH 
0 BEAM W I T H  LARGE SLENDERNESS R A T I O  
0 G R A V I T Y  E F F E C T S  ON D Y N A M I C  C H A R A C T E R I S T I C S  AS F U N C T I O N  OF 
N O N - D I M E N S I O N A L  PARAMETERS 
Y 
I 
9 '  1.0 
39 7 
It i s  p o s t u l a t e d  t h a t  t h e  response can be d i v i d e d  i n t o  two par ts ,  namely, t h e  
s t a t i c  d e f l e c t i o n  due t o  g r a v i t y  and t h e  v i b r a t i o n a l  response. However, t h e  induced 
a x i a l  f o r c e  P remains unknown and t h e  s o l u t i o n  i s  a f u n c t i o n  o f  P. The f a c t  t h a t  P 
i s  no t  zero i n d i c a t e s  t h a t  both end supports a re  not  movable and t h e  beam must be 
s t r e t c h e d  t o  accommodate t h e  l a t e r a l  deformation. This e longat ion  a long t h e  a x i a l  
d i r e c t i o n  should be a f u n c t i o n  o f  t h e  r e a c t i o n  f o r c e  P. It i s  obvious t h a t  t h e  
l e n g t h  increment can be r e l a t e d  t o  t h e  curva ture  due t o  l a t e r a l  d e f l e c t i o n .  
GOVERNING EOUAT IONS 
4 2 2 
E 1  - p 3 + p .?-Y = -pg 
ax ax a t 2  
39 8 
The s t a t i c  d e f l e c t i o n  due t o  g r a v i t y  s a t i s f i e s  t h e  s imply  supported end 
For s i m p l i c i t y ,  
1 
c o n d i t i o n s  and was obta ined by t h e  G a l e r k i n ’ s  approximat ion method. 
t h e  magnitude of t h e  f i r s t  d e r i v a t i v e  i s  l i m i t e d  t o  be small .  
ASSUHPT IONS 
4 -1 
76.5 + 7.75(p!L2/EI) ys =( 
0 NON-DIMENSIONAL PARAMETERS 
pgR NON-DIMENSIONAL WEIGHT a =  AE 
SLENDERNESS RAT 10 B = F , r 2 = K  R I 
P NON-DIMENSIONAL AXIAL FORCE q = 
2 
4 2  
WEIGHT-LENGTH PARAMETER Y = %n*B 
2 wq NON-D IMENS IONAL FREQUENCY 1 = -  
FREQUENCY RAT I O  
b l  
rl E1 
Q = -  4-l 
39 9 
From t h e  a x i a l  e l o n g a t i o n  c o n d i t i o n ,  t h e  a x i a l  f o r c e  can be r e l a t e d  t o  t h e  
g r a v i t y  l o a d i n g  and slenderness r a t i o  o f  t h e  beam. 
NON-DIMENSIONAL AXIAL FORCE 
SLENDERNESS RATIO p 
400 
The e igenvalue and e igenvec tor  a re  f u n c t i o n s  o f  a s i n g l e  non-dimensional 
parameter. For a s imply  supported case, t h e  e igenvec tor  i s  an i n v a r i a n t ,  
independent o f  t h e  beam geometry. 
I 
E l  GEWVALUES AND E1 GEWVECTORS 
SIMPLY SUPPORTED CASE : 
X 
Qq = a s i n  (qn-) R
B U I L T - I N  CASE: 
= (1 - cos 0 cosh 1-1 ) + y s i n  u s i n h  1-1 = 0 
rl rl rl rl 
0 ' sinh(1-1 5) Q = s i n ( a  -) - -X 
rl n lJn n R  
401 
Once t h e  geometry and t h e  m a t e r i a l  p r o p e r t i e s  o f  t h e  beam a re  given, t h e  
we igh t - l eng th  parameter can be determined. On t h e  o t h e r  hand, f o r  a g i v e n  
we igh t - l eng th  parameter, one may f i n d  a v a r i e t y  o f  beams w i t h  d i f f e r e n t  geometr ic 
and m a t e r i a l  p r o p e r t i e s  t h a t  w i l l  have t h e  same parameter value. 
ME 16HT LENGTH PARAMETER 
35 
30- 
- 
20- - 
100 150 200 BO 3 0  350 400 450 500 
SLENDERNESS RATIO p 
402 
Unl ike  t h e  case o f  s imply  supported boundary cond i t ions ,  t h e  mode shapes f o r  
t h e  beams w i t h  b u i l t - i n  ends a r e  a f u n c t i o n  o f  t h e  we igh t - length  parameters. 
However, t h e  mode shapes f o r  0-g and 1-g are very s i m i l a r .  
RODE SHAPE COMPARISON 
n =  * I I I I I A x  
0 0.2 0.4 0.6 0.8 LO 
I I - 
n =  I I I f I I I I I 
- 'Y= O(ZER0 GRAVITY) 
I5 ---e 
4 03 
For a s imply  supported case, i t  i s  found t h a t  f o r  lower modes w i t h  l a r g e r  
we igh t - l eng th  parameters t h e  frequency r a t i o  i s  q u i t e  d i f f e r e n t  from t h a t  o f  t h e  0-g 
case. I n  o t h e r  words, t h e  h i g h e r  f requency modes are e a s i e r  t o  s i m u l a t e  by a s c a l e  
model t e s t  than t h e  lower  f requency modes. Un fo r tuna te l y ,  i t  i s  t h e  l a t t e r  t h a t  a r e  
i n  general,  more impor tant .  
~ 
FREQUENCY R A T I O  FOR SIMPLY SUPPORTED CASE 
4. 
c2= 
3. ( 
2. c 
I I I I 
-P 0 (ZERO GRAVITY) 
10 
20 
--- I 
-om- = 
I I I I I 
1 2 3 4 5 6 
1. a 
WAVE NUMBER n 
I 404 
For t h e  case o f  b u i l t - i n  boundary condi t ions ,  s i m i l a r  r e s u l t s  a r e  found f o r  t h e  
frequency r a t i  0. 
FREQUENCY RATIO FOR BUILT-IN CASE 
3. (I 
2.5 
c 
2.0 
1.5 
L O  
I I I I I 
- Y =  0 (ZERO GRAVITY) 
10 
20 
-.II- I 
-m-m = 
1 2 3 4 
WAVE NUMBER n 
5 6 
405 
U 
For ground t e s t i n g  v e r i f i c a t i o n  o f  l a r g e  space s t r u c t u r e s  t h e  f e a s i b i l i t y  o f  
i n g  a sca le  model i s  dependent no t  on ly  on t h e  s t r u c t u r e  i t s e l f ,  but  a l s o  on t h e  
c o n t r o l  systems. Accurate modal displacements and modal dens i ty  d i s t r i b u t i o n s  are 
t h e  impor tant  parameters t o  be considered. For l a r g e  complex space s t r u c t u r e s  t h e  
ground t e s t  may be very expensive and t i m e  consuming, such t h a t  t h e  t e s t  
cons idera t ion  may become p a r t  o f  the  design requirement. However, s ince  very l i t t l e  
exper ience i s  a v a i l a b l e  i n  t h i s  respect,  a more systemat ic  study i n  r e a l i s t i c  l a r g e  
space s t r u c t u r a l  systems should be performed. 
CONCLUDING REHARKS 
0 FOR A GIVEN SPACE BEAM WITH I T S  WAVE-LENGTH PARAMETER, THE FREQUENCY 
DENSITY DEVIAT ION DUE TO 1 G CAN BE READILY FOUND. 
0 FOR A GIVEN ERROR TOLERANCE I N  MODAL DENSITY, THE F E A S I B I L I T Y  OF PERFORMING 
GROUND TESTING FOR VERIF ICATION CAN BE DETERMINED. 
0 OTHER CHARACTERISTICS WILL BE INVESTIGATED. 
0 STUDIES ARE EXTENDED TO OTHER LARGE SPACE STRUCTURES. 
0 V E R I F I C A T I O N  OF STRUCTURES/CONTROL CLOSED LOOP SYSTEM WILL BE INVESTIGATED. 
I 406 


Verification for large space structures

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