Lecture16-Prof.Ju

Lecture16-Prof.Ju - CEE M237A / MAE M269A Lecture 16:...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
CEE M237A / MAE M269A Lecture 16: Hamilton’s Principle on Dynamic Structural Systems IV: Equation of Motion via Hamilton’s Principle Professor J. Woody Ju
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 5–Forced Vibration of a Beam –Column Supporting a Mass 2 () 2 This column is in the presence of a gravity field whose acceleration of gravity is units: / . This structural system is driven by a forcing function with a displacement history of (such as an earth M gL T Wt 1 quake) applied to mass . Determine the EOM and the appropriate BCs. M
Background image of page 2
Example 5–Forced Vibration of a Beam – Column Supporting a Mass (Cont’d) y The Lagrangian L is: ( w r is the relative displ.) y The first variation of the time integral of L gives 3 ( ) ( ) Note: 0 M Wt δ =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 5–Forced Vibration of a Beam – Column Supporting a Mass (Cont’d) y Integration by parts of the variations w.r.t. the velocities shows that: 4
Background image of page 4
Example 5–Forced Vibration of a Beam – Column Supporting a Mass (Cont’d) y Integration by parts of the variations of the potential energy gives: 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 5–Forced Vibration of a Beam – Column Supporting a Mass (Cont’d) y Recomposing the total variation renders: 6
Background image of page 6
Example 5–Forced Vibration of a Beam – Column Supporting a Mass (Cont’d) y Therefore, the Euler Equation becomes: y The Natural and Kinematic Boundary Conditions are: 7 222 2 22 2 0 rr rM ww Aw M g EI AW xx x ρρ ⎛⎞ ∂∂∂ ++ + = ⎜⎟ ∂∂ ⎝⎠ ±±
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/18/2011 for the course MAE 269A taught by Professor Ju during the Spring '11 term at UCLA.

Page1 / 26

Lecture16-Prof.Ju - CEE M237A / MAE M269A Lecture 16:...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online