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Frequency response mode of vibration

  1. Mar 19, 2012 #1
    I'm working on an analysis problem using Abaqus. I would like to compare my results with an exact equation. My problem is modeled as a simply supported beam with a lumped mass at the end. The equation that I'm using for the exact solution is as follows:

    k=3EI/L3
    ωn=[itex]\sqrt{k/(M + 0.23m)}[/itex]

    How do I incorporate the mode number to find what the exact solution is at say mode 2 or 3?
     
  2. jcsd
  3. Mar 19, 2012 #2

    OldEngr63

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    That "exact" solution is probably only an analytic approximation for the first mode. Run the numbers and see which mode it compares with most favorably. I would bet it will be the first mode.
     
  4. Mar 19, 2012 #3
    The exact solution does compare most favorably with the first mode results from Abaqus.
     
  5. Mar 19, 2012 #4

    OldEngr63

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    Gold Member

    Don't hold your breath on that being an exact solution. It is most likely obtained from a Rayleigh approximation.
     
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