Undamped vibrations (only spring present)

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Discussion Overview

The discussion revolves around the analysis of undamped vibrations in a system involving an exhaust fan supported by a spring isolator. Participants are focused on determining the transmitted force through the isolator and the static deflection of the exhaust fan, with specific attention to the calculations involving harmonic forces and frequency ratios.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant calculates the transmission ratio (Tr) as Tr=1/(1-r^2), where r is the frequency ratio, and finds Tr to be 0.2258.
  • There is uncertainty regarding the value of the applied force (Fo), with one participant questioning if it is the same as the magnitude of the harmonic force (12 kN).
  • Another participant confirms that Fo is indeed the magnitude of the harmonic force, stating F0=12 kN.
  • Participants discuss whether the magnitude of the harmonic force is always the applied force and also the amplitude.

Areas of Agreement / Disagreement

There is some agreement on the value of the harmonic force being the applied force, but uncertainty remains about the implications of this in the context of the calculations. The discussion does not reach a consensus on the interpretation of the applied force and its relationship to the amplitude.

Contextual Notes

Participants express uncertainty about the relationship between the harmonic force and the applied force, indicating potential limitations in their understanding of the definitions involved.

kaminho
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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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