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Vibration of Prestressed

Membrane Reflectors

S. Kukathasan and S. Pellegrino

CUED/D-STRUCT/TR194

European Space Agency Contractor Report

The work presented in this report was carried out under an ESA contract.

Responsibility for its contents resides with the authors.

ESA Study Manager: W.J. Rits

ESTEC Contract no. 11936/96/NL/FG

Release date: 16 March 2001

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y

oa

b

y

a

a

x

a

ox

y

a a

a

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A

1

3

1

2

PLAN

C

B

D

ELEVATION

axis of symmetry

axis of symmetry

0.1 m

0.1 m

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0.2 m

0.2m

0.1 m

0.2m

0.2 m

0.1 m

(a) (b)

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l l

l

Equivalent Truss

baMembrane Element

y

x

A

A

d

A1

A1

ba

A

A

c

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1

2

3 1

2

3

axis of symmetry

A

axis of symmetry

0.1 m

0.1 m

B

DC

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0.5 m

1 m long ribs

Membrane

0.5 m

Rigid base

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1

2

3

1

2

3

1 m

0.5 m

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1

2

3 1

2

3 1

2

3 1

2

3

1

2

3 1

2

3 1

2

3 1

2

3

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1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

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11.5 mm

137

in ABAQUS

Modelled Section

Actual CrossSection

o

1

2

3

1

2

3

1

2

3

1

2

3

Ribs Finite Element Model

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l/2

B

O

A C

O

A

B

C

r

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w Rib profile

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1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

Mode 3Mode 2

Mode 9Mode 8

Mode 6

Mode 1

Mode 4

Mode 7

Mode5

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Mode 6

Mode 7

Mode 4

Mode 1

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

Mode 8 Mode 9

Mode 5

Mode 2 Mode 3

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Mode 2 Mode 3Mode 1

Mode 4

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

Mode 7 Mode 9Mode 8

Mode 5 Mode 6

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Mode 6

Mode 1

Mode 4

Mode 7

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

Mode 8

Mode 3

Mode 5

Mode 2

Mode 9

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Mode 8

Mode 4

Mode 1

Mode 7

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

Mode 5

Mode 3Mode 2

Mode 9

Mode 6

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Mode 1

Mode 7

Mode 4

Mode 8

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

Mode 5

Mode 9

Mode 2Mode 3

Mode 6

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Mode 6

Mode 9Mode 8

Mode 5

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

Mode 2

Mode 3

Mode 7

Mode 1

Mode 4

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(Ave. Crit.: 75%)

S, S11

-8.403e+04-4.767e+04-1.131e+04+2.505e+04+6.141e+04+9.776e+04+1.341e+05+1.705e+05+2.068e+05+2.432e+05+2.796e+05+3.159e+05+3.523e+05

X

Y

Z

(Ave. Crit.: 75%)

S, S22

-2.422e+05

-2.216e+05-2.011e+05-1.805e+05-1.599e+05-1.394e+05-1.188e+05-9.821e+04-7.764e+04-5.707e+04-3.650e+04-1.593e+04+4.642e+03

X

Y

Z

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X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

(a) Mode 1 (12.86 Hz)

(d) Mode 4 (13.09 Hz) (e) Mode 5 (14.04 Hz) (f) Mode 6 (14.07 Hz)

(g) Mode 7 (15.53 Hz) (h) Mode 8 (15.53 Hz) (i) Mode 9 (17.10 Hz)

(b) Mode 2 (12.86 Hz) (c) Mode 3 (13.09 Hz)

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10 100

10

Fundamentalnaturalfrequency(Hz)

Membrane prestress (N/m)

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