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Homework Help: Frequency Response Function - Random Vibration

  1. Apr 30, 2010 #1
    Hi looking for some help on the below I'm a little bit stuck.

    The effect of an earthquake on an elevated water tank is to be investigated. The water tank has mass m=2x10^6 kg and natural frequency wn=10.6 rad/s and a damping coefficient of 12% critical damping.
    Ground acceleration can be approximated by constant spectrum So=0.0075m2/s3
    Obtain:
    i) The frequency response function for the displacement of tank mass relative to the ground
    ii) Mean square response of displacement
    iii) Standard deviation of displacement

    Frequency Response = Output / Input

    mz"+cz'+kz=-my" ........................................Eq 1

    Where z is the relative displacement
    and y is input

    I've done some work on something similar in the past where I have used the Force input to the system to get the frequency response function and obtain the equation:

    H(w) = 1 / (k-(mw^2)+icw

    This gives the frequency response function of the elevated mass displacement relative to the input force?

    Using the equation: mz"+cz'+kz=-my"

    If I take the input displacement
    y = Ae^iwt (where A is a constant then)
    y' = iwtAe^iwt
    y"= -w^2.Ae^iwt

    The output would then be
    z = Be^iwt
    z' = iwtBe^iwt
    z" = -w^2.Be^iwt

    subtituting into Eq 1

    (k+iwc-mw^2)B.e^iwt = (mw^2)A.e^iwt

    Therefore response is equal to B/A
    = (mw^2) / (k+iwc-mw^2)

    Is this along the correct lines??
     
    Last edited: Apr 30, 2010
  2. jcsd
  3. Apr 25, 2012 #2
    could anyone shed some light on this question? i have the same problem (saves me writing a new thread etc.)
     
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