3 - D Dynamics of a Satellite with Flexible Elements By Abdullah Ahmed Alhumaidan 422004549
Jan 04, 2016
3-D Dynamics of a Satellite with Flexible Elements
By
Abdullah Ahmed Alhumaidan
422004549
Overview
●Project Objectives
●Introduction
●Case Studies
●CASE STUDY - 1
Project Objectives
■ 3D satellite dynamics.
■Study the motion of satellite struck by a space meteorite
■The stresses developed at the base of a flexible antenna.
■Mathematical modeling and analysis of a vibration absorber fixed to a satellite
Introduction
●L.E.O (Low Earth Orbit) micro satellites (since 1957).
●Small satellites (less than 1,000 kg )
●microsatellite (less than 100 kg )
●nanosatellites (less than 10 kg)
●picosatellites (less than 1 kg)
The Flexible Antenna
●Function
● )s-band ,c-band , x-band , ku – band(
The micro-vibration of the satellite
Case Studies
●A satellite with a flexible antenna .
●A satellite with rigid antenna.
●Satellite with single axis vibration absorber
A satellite with a flexible antenna
Z
Y
X
L
m
Ө
A
K
A satellite with rigid antenna
Z
Y
X
x
y
z
Vo
mo
Satellite with single axis vibration absorber
Z
Y
X
x
y
z
m
k
yy,
CASE STUDY - 1
Z
Y
X
B = 0.3 m
L=0.15m
m
Ө
A
K=1000 N/m
Development of The Equation of Motion
AAA rmhM
)cossincos( 22 bllmlk
kblljlillmlM A )cossincos()sincos()cos( 222
kkjMiMM AyAxA
Time response of the antenna
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1time response of theta(t) omiga=0(rad/sec)
time
theta
(t)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
3time response of theta(t) omiga=50(rad/sec)
time
theta
(t)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
3time response of theta(t) omiga=80(rad/sec)
time
theta
(t)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5
3time response of theta(t) omiga=100(rad/sec)
time
theta
(t)
The influence of satellite spin rate on the
max. vibration amplitude Өmax.
Omiga vs. Thita
0
20
40
60
80
100
0 20 40 60 80 100 120
omiga (rad/sec)
Th
eta
(deg
)
The influence of satellite spin rate on the response frequency of the antenna
model
omiga vs. omiga response
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120
omiga (rad/sec)
om
iga
resp
on
se (
rad
/sec
)
the influence of satellite spin rate on the max. moment on a boom at point A
05000
100001500020000250003000035000400004500050000
0 20 40 60 80 100 120
omiga (rad/sec)
M (
N.m
)
MAx
MAy
Design of the antenna base
variation of the moment for one cycle
-1500
-1000
-500
0
500
1000
1500
0 0.05 0.1 0.15 0.2 0.25 0.3
t (sec)
M (
N.m
)
MAx
MAy
sincos
sin
2
22
mlM
mlM
Ay
Ax
X
Y
Z
1.12 KN.m
670 N.m
Design of the antenna base
1.5 C
1.5 C
2 C
2 C
Am
Stresses
34 175
192
192
175 C
M
C
CM
I
yM AyAyAy
32
32
49)
16
49)(
4(22 C
M
CCM
tA
M AxAx
m
Axavg
32
31
14.1186
06.451
C
C
The base dimensions based on Max. Shear stress theory
Factor of Safety=1.5
σy=400MPa
21
Ydn
)(018.0 mC
Work to be completed
●For the flexible antenna case study , the influence of changing precession and spin rates of the satellite on the antenna support design will be investigated.
●The effect of meteorite velocity and direction on the satellite attitude will be studied.
●For the rigid antenna case , the maximum stress developed at the antenna base will be calculated for several meteorite velocities
and directions .
●The dynamic response of the absorber attached to the satellite which is aligned in x-direction as shown in figure ( 6) will be evaluated
for several values of satellite spin and precession rates .
THANK YOU