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

In summary, the transmissibility ratio (T.R.) is a positive value that represents the ratio of force magnitudes. The negative root is taken when r>1, and r is the ratio between natural frequency and excitation frequency (ω/ωn). It indicates how close the driving frequency is to the resonant frequency and does not provide information on damping.
  • #1
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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  • #2
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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  • #4
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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  • #5
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
 

1. What is vibration transmissibility ratio?

Vibration transmissibility ratio is a measure of the amplification or attenuation of a vibration signal as it passes through a system. It is calculated as the ratio of the output vibration amplitude to the input vibration amplitude.

2. How does damping affect the transmissibility ratio?

Damping is a measure of the energy dissipation in a system. When damping is equal to zero, the transmissibility ratio sign changes from positive to negative, indicating that the system has reached resonance. This means that the output vibration amplitude is greater than the input vibration amplitude, leading to potential damage to the system.

3. Why does the transmissibility ratio sign change when damping is equal to zero?

When damping is equal to zero, the system is no longer able to dissipate energy, leading to a build-up of energy and ultimately reaching resonance. At resonance, the system amplifies the input vibration, resulting in a negative transmissibility ratio.

4. What is the significance of the transmissibility ratio sign change when damping is equal to zero?

The transmissibility ratio sign change when damping is equal to zero is significant because it indicates that the system has reached resonance, which can potentially cause damage to the system. It also serves as a warning sign for engineers to adjust the damping in the system to avoid resonance and potential damage.

5. How can the transmissibility ratio be used in engineering applications?

The transmissibility ratio is an important tool in engineering applications as it helps engineers to design and analyze systems to avoid resonance and potential damage. By understanding the transmissibility ratio, engineers can adjust damping and other parameters to optimize the performance and safety of the system.

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