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Vibration Absorber question

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data

    An air compressor of mass m1 = 150 kg is mounted on a spring of stiffness k1= 3000 N/m. The measured
    displacement amplitude X1 = 0.0002 m at the operating speed of N = 1800 r/min. If an undamped isolation
    system with mass m2=12 kg and a natural frequency w2 = 105 rad/s is fixed to the compressor, calculate the
    changed displacement amplitude X1 for the overall system


    2. Relevant equations

    As far as I understand this is the relevant equation: X1/delta_st=(1-(omega/omega2)^2)/((1+k2/k1-(omega/omega_1)^2)(1-(omega/omega_2)^2)-k2/k1)


    3. The attempt at a solution

    As far as I understand its a vibration absorber problem.

    omega=1800*(2π/60)=188,5rad/s
    omega1=(k1/m1)^.5=4.47
    k2=omega_2^2*m2=105^2*12=132300N/m

    X1/delta_st=(1-(omega/omega2)^2)/((1+k2/k1-(omega/omega_1)^2)(1-(omega/omega_2)^2)-k2/k1)

    X1/delta_st=-5,836x10^-4

    delta_st=-0,342m

    I dont think thats right :|
     
  2. jcsd
  3. Nov 18, 2011 #2
    It is a dynamic absorber problem. While I have not gone through your arithmetic, I see that delta_st is static deflection which is how much the weight of the compressor deflects the spring under static conditions.

    You should be solving for X1. Here is your equation: X1/delta_st=-5,836x10^-4
    Solve it for X1 by plugging in delta_st.
     
  4. Nov 18, 2011 #3
    That makes sense actually.

    So assuming that I go

    delta_st=F0/k=(150+12)*9.81/3000=0.52974

    X1=delta_st*-5,836x10^-4=-0.000309

    so then I'm assuming the changed displacement amplitude will be the difference between measured and X1 from calculations.

    so X1'=-0.000309+0.0002=-0.000109m


    Oh and thanks! <--- Sorry I forgot to add that :|
     
    Last edited: Nov 18, 2011
  5. Nov 18, 2011 #4
    That looks good to me. I went through your arithmetic.....
     
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