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426 Structural Dynamics

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

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  1. 426 Structural Dynamics Emergency tutorial Nov. 12, 2012

  2. 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

  3. Provisional Layout – x-y projection Pm 1 rb 1 rb 2 Pm 3,4,5 y Pm 2 x

  4. Provisional Layout – y-z projection z Pm 3 rb 1 rb 2 Pm 4 2L y Pm 5 R

  5. Equations of motion for modal analysis

  6. Equations of motion for modal analysis

  7. Equations of motion for modal analysis

  8. 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

  9. 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

  10. Selection of cable radius Forbidden Range of Frequencies

  11. 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

  12. 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

  13. Hab Rocking Modes: Rotation about x axis z Cables r1-3(a, b) y L  Cables r1-5(a, b)

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