Undamped vibrations (only spring present)

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The discussion focuses on calculating the transmitted force and static deflection of an exhaust fan supported by an undamped vibration isolator. The user successfully determined the transmission ratio (Tr) as 0.2258 by calculating the frequency ratio (r) using the excitation and natural frequencies. There is clarification that the magnitude of the harmonic force (F0) is indeed 12 kN, which is essential for further calculations. The user seeks confirmation on whether the harmonic force is equivalent to the applied force and amplitude. Overall, the conversation revolves around understanding the relationship between the harmonic force and the transmitted force in the context of vibration isolation.
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Homework Statement



An exhaust fan mass 90 kg operates at 1100 rpm and is supported by an UNDAMPED vibration isolator i.e a spring that has a stiffness of 220 kN. If the harmonic force produced by the fan has a magnitude of 12 kN determine:
a) The transmitted force through the isolator to the foundations(TR)
b) The static deflection of the exhaust fan (δst)




Homework Equations



how do we work out the trasmitted force?

The Attempt at a Solution



I'm able to find trasmission ratio (Tr) as it becomes Tr=1/(1-r^2) with r being the frequency ratio. that is Tr= 0.2258 ( i first found out the frequency of excitation and natural frequency and devided the first by the second to find r and from there i found Tr). however i know Tr=Ft/Fo (Ft transmitted force and Fo applied) but i don't know how to get Ft as the value of Fo is still unknown and i don't think its 12000 mentioned in the question (because that's magnitude of harmonic force). or maybe it is i don't know. can anyone help?
 
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kaminho said:

The Attempt at a Solution



I'm able to find trasmission ratio (Tr) as it becomes Tr=1/(1-r^2) with r being the frequency ratio. that is Tr= 0.2258 ( i first found out the frequency of excitation and natural frequency and devided the first by the second to find r and from there i found Tr). however i know Tr=Ft/Fo (Ft transmitted force and Fo applied) but i don't know how to get Ft as the value of Fo is still unknown and i don't think its 12000 mentioned in the question (because that's magnitude of harmonic force). or maybe it is i don't know. can anyone help?

Yes, F0 is the magnitude of the harmonic force, F0=12kN.
 
rock.freak667 said:
Yes, F0 is the magnitude of the harmonic force, F0=12kN.

so after i found r (frequency ratio) and subsequently Tr which is 0.2258 then the rest is pretty straight forward ?
am i right in saying the magnitude of the harmonic force is always the applied force (Fo) and also the amplitude ?
and thanks loads for the help too.
 
kaminho said:
so after i found r (frequency ratio) and subsequently Tr which is 0.2258 then the rest is pretty straight forward ?
am i right in saying the magnitude of the harmonic force is always the applied force (Fo) and also the amplitude ?
and thanks loads for the help too.

I think that would be correct.
 

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