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