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Dunc26
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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??
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??
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