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426 Structural Dynamics. Emergency tutorial Nov. 12, 2012. Provisional Layout – perspective view. z. Point mass 3. Rigid body 2. Point mass 1. Cable r1-1. Cable r1-3(a). Cable r1-3(b). x. Rigid body 1. Point mass 4. Point mass 2. Point mass 5. y.

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426 structural dynamics

426 Structural Dynamics

Emergency tutorial

Nov. 12, 2012

provisional layout perspective view
Provisional Layout – perspective view

z

Point mass 3

Rigid body 2

Point mass 1

Cable r1-1

Cable r1-3(a)

Cable r1-3(b)

x

Rigid body 1

Point mass 4

Point mass 2

Point mass 5

y

Note: cables are labeled by the point masses & rigid bodies they connect. Same for columns

provisional layout x y projection
Provisional Layout – x-y projection

Pm 1

rb 1

rb 2

Pm 3,4,5

y

Pm 2

x

provisional layout y z projection
Provisional Layout – y-z projection

z

Pm 3

rb 1

rb 2

Pm 4

2L

y

Pm 5

R

modal analysis insight and simplification
Modal Analysis: Insight and Simplification
  • The system has symmetries with respect to the x-z, y-z, and x-y planes
  • Mode shapes are approximately in pairs of symmetric and antisymmetric motions with nearly equal modal frequencies. Mode frequency splitting due to Coriolis ~0.03Hz (if  = 3.5 rpm)
  • The lowest frequency modes involve motion of the rigid-body hab modules and the various point masses
    • Mostly, the participation of one pair of masses predominates
    • Tension in cables is statically determinate and the effective modal stiffness is relatively easy to calculate
  • Special interest: modes involving motion of the hab modules. To prevent motion sickness, we must avoid:
    • Frequencies from 0.05 to 0.8 Hz, especially 0.167Hz
    • 8Hz modes
estimate of lowest mode hab module x translation
Estimate of lowest mode: Hab Module x Translation

Pm 1

Cable r1-1

Cables r1-3(a)

r1-5(a)

rb 1

y

Cables r1-3(b)

r1-5(b)

Cable r1-2

Pm 2

x

selection of cable radius
Selection of cable radius

Forbidden Range of Frequencies

radial modes example y translation
Radial Modes – Example, y translation

z

Pm 3

Cables r1-3(a, b)

rb 1

2L

Pm 4

y

Cables r1-5(a, b)

Pm 5

R

selection of cable radius for r1 3 a b and r1 5 a b
Selection of cable radius for r1-3(a,b) and r1-5(a,b)

Thus: These cables can be half the thickness of the circumferential cables

Forbidden Range of Frequencies

hab rocking modes rotation about x axis
Hab Rocking Modes: Rotation about x axis

z

Cables r1-3(a, b)

y

L

Cables r1-5(a, b)