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Finding the natural frequency of a steel beam

  1. Nov 4, 2011 #1
    1. The problem statement, all variables and given/known data
    I am trying to calculate the natural frequency of a steel beam.


    2. Relevant equations
    I=1/12*W*T^3
    Volume= T*W*L
    M0=V*ρ
    K=(3EI/L^3)
    Meff=(33/140)*M0+Mend
    ωn=√(k/Meff)

    3. The attempt at a solution
    This should be a simple plug and chug problem but I can't see what I'm doing wrong.

    L=0.4572m
    W=0.026035m
    T=0.006223m
    E= 3*10^6
    ρ=7850kg/m^3

    Mend=.025kg


    I=5.22848E-10

    V=7.41E-05 m^3

    M0=5.81E-01

    K=0.049237907

    Meff=2.43E-01

    ωn=0.450088787 Hz

    But this is way off from my experimental value of around 20Hz. Everything is in kg and m.
     
  2. jcsd
  3. Nov 4, 2011 #2
    Re: Finding the natural frequency if a steel beam

    Sorry to ask this , what is K and what is E? and their units
     
  4. Nov 4, 2011 #3
    Re: Finding the natural frequency if a steel beam

    Your modulus of elasticity appears to have units of psi. Change it to N/m^2 & you'll fix your problem.
     
  5. Jan 29, 2013 #4
    Re: Finding the natural frequency if a steel beam

    natural frequency = (square root)k/m
     
  6. Jan 29, 2013 #5

    SteamKing

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    Re: Finding the natural frequency if a steel beam

    E for steel is 3*10^7 psi (30,000,000 psi) not 3,000,000 psi
     
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