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I am confused about the cantilever beam

  1. Jan 11, 2013 #1
    Hi

    For a cantilever beam with a load at its end,

    flexural rigidity is:

    EI = m*g*L3 / 3Y

    Where m=mass, g=gravity, L=length of beam and Y=deflection

    the natural frequency is

    f = 1/(2∏) * √ ( 3EI/mL3)

    Plugging in EI to the formula for f reveals that f depends only on the deflection, Y.

    If I wanted to predict the frequency, would I therefore only need to measure Y? I am stuck in a circular logic loop because Y depends on m, L and EI but m and L cancel out in f =
     
  2. jcsd
  3. Jan 11, 2013 #2
    So why is that surprising?

    The deflection depends upon the end load m.

    The frequency is the √(ratio of elastic forces to inertial ones) ω = √(k/m)

    and k, the spring constant = Load/Deflection.

    The equation of motion is (for vubrations in the y direction)


    [tex]m\frac{{{d^2}y}}{{d{t^2}}} + ky = 0[/tex]
     
    Last edited: Jan 11, 2013
  4. Jan 11, 2013 #3
    I have measurements of m, L, Y and f

    there is no relationship between Y and m, Y and L , F and m, F and L
    there is correlation between Y and f

    Could the lack of correlation in Y vs m and Y vs L indicate that in my system, EI is the most important predictor of Y and by extension f ?

    I guess the real problem is that I do not have enough degrees of freedom to determine the effect of EI.
     
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