Vibration: Transmissibility ratio sign change when damping is equal to zero

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Discussion Overview

The discussion revolves around the transmissibility ratio in the context of vibration analysis, specifically addressing the conditions under which different roots of the equation are taken when damping is zero. The scope includes mathematical reasoning and conceptual clarification related to the transmissibility ratio and its dependence on the frequency ratio.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes confusion regarding when to take the positive or negative root of the transmissibility ratio equation when damping is zero.
  • Another participant suggests that the transmissibility ratio is generally considered a positive value, indicating that the negative root is applicable when the frequency ratio (r) is greater than one.
  • A question is raised about the meaning of the variable r in the equation, prompting a reference to external material for clarification.
  • A subsequent reply defines r as the ratio between natural frequency and excitation frequency (ω/ωn), explaining its significance in relation to the resonant frequency without addressing damping explicitly.
  • A participant expresses a lack of interest in the subject matter, indicating a disengagement from the discussion.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the general interpretation of the transmissibility ratio as a positive value, but there is uncertainty regarding the conditions for taking different roots. The discussion remains unresolved regarding the specific circumstances under which each root should be applied.

Contextual Notes

Participants reference the ratio r and its relationship to frequency without fully resolving the implications of damping on the transmissibility ratio. There is a lack of consensus on the mathematical steps involved in determining the appropriate root to use.

Pipsqueakalchemist
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So for the transmissibility ratio equation, after doing a lot of questions when damping is zero and I have to take the square root of the denominator. Some questions take the positive root (1-r^2) while for other questions the solution takes the negative root (r^2-1). Can someone explain when we take the positive or negative root please and thank you
 

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The T.R. is a ratio of force magnitudes and is generally taken as a positive value. So the negative root is taken when r>1.
 
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It looks like Pipsqueak is no longer with us... Nevertheless, r in the above equation is the ratio between natural frequency and excitation frequency (ω/ωn). It's a measure of how close the driving frequency is to the resonant frequency, and doesn't provide any explicit information on the damping.
 
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onatirec said:
It looks like Pipsqueak is no longer with us... Nevertheless, r in the above equation is the ratio between natural frequency and excitation frequency (ω/ωn). It's a measure of how close the driving frequency is to the resonant frequency, and doesn't provide any explicit information on the damping.
Yea I stopped caring about that class so it’s whatever
 

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