Interpreting Vibration Magnification Factor Overestimation

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In summary: It is important to further investigate and analyze the experimental setup to better understand the discrepancies between the theoretical and experimental values. In summary, the experimental results show that the damping effect of air resistance plays a significant role in the magnification factor, leading to higher values than expected at high frequencies. Further research and analysis is needed to fully understand the discrepancies between the theoretical and experimental values.
  • #1
hanson
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Hi all. (I've edited the question)
As far as my intuition tells me, an underestimation of the damping effect would results in an overestimation of the magnification factor, am I correct?
So I expect the experimental determined magnification factor for all frequency ratio to be smaller than the theoretical values given by the formula:
[tex]R=\frac{1}{\sqrt{(1 - r^2)^2+(2r\zeta)^2}}[/tex]
Because there would be extra damping due to the air resistance.

However, it turned out that the experimental magnification factors are greater than the theoretical values! How come?

Actually before exceeding the resonant frequency, the experimental values are greater than the theoretical values; after exceeding the resonant frequency a bit, the theoretical values are greater than the experimental values. How would you interpret this?
I can just think of one thing: For high frequency ratio (exceeding the resonant frequency), the air resistance effect would be more significatns ince air resistance is proportional to the square of the velocity of the system.

However, I have no idea on why the experimental values would be greater than the theoretical values, can anyone give some ideas?
 
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It is possible that the damping effect of the air resistance has been underestimated. This would lead to an overestimation of the magnification factor. The reason why the experimental values are higher than the theoretical values at high frequencies could be due to the fact that the air resistance increases with increasing velocity, which leads to a greater damping effect than expected. Also, other factors such as friction or losses in the system could be affecting the results.
 
  • #3



It is possible that there are other factors at play that are causing the experimental values to be greater than the theoretical values. One possibility could be measurement error or variability in the experimental setup. Another possibility could be that there are other sources of damping present in the system that are not accounted for in the theoretical formula, such as friction or material properties. It would be helpful to carefully examine the experimental setup and data to identify any potential sources of error or additional damping that could be contributing to the discrepancy between the theoretical and experimental values.

Additionally, it is important to consider the limitations of the theoretical formula and its assumptions. It may not accurately account for all the complexities and variations in a real-world system. It is always important to validate theoretical models with experimental data and make adjustments as needed.

In terms of the differences observed before and after exceeding the resonant frequency, it is possible that the effect of air resistance becomes more significant at higher frequencies, leading to a larger discrepancy between the theoretical and experimental values. It would be worth investigating the relationship between frequency and air resistance in the system to see if there is a correlation.

Overall, interpreting vibration magnification factor overestimation can be complex and there are many potential factors that could contribute to the discrepancies observed. It would be helpful to carefully analyze the experimental setup and data, consider the limitations of the theoretical model, and investigate any other sources of damping that could be affecting the results.
 

1. What is vibration magnification factor overestimation?

Vibration magnification factor overestimation is a phenomenon that occurs when the measured vibration levels of a structure are higher than the actual levels due to incorrect assumptions or calculations.

2. How does vibration magnification factor overestimation affect structural analysis?

Vibration magnification factor overestimation can lead to inaccurate predictions of structural response and potential overdesign or underperformance of a structure. This can result in unnecessary costs or safety concerns.

3. What are the common causes of vibration magnification factor overestimation?

The most common causes of vibration magnification factor overestimation are incorrect assumptions about the dynamic properties of the structure, improper measurement or instrumentation techniques, and inadequate understanding of the underlying physics.

4. How can vibration magnification factor overestimation be avoided?

Vibration magnification factor overestimation can be avoided by conducting thorough and accurate structural analysis, using appropriate measurement and instrumentation techniques, and considering the dynamic properties of the structure in the design process.

5. What are the potential consequences of not addressing vibration magnification factor overestimation?

If vibration magnification factor overestimation is not addressed, it can lead to costly repairs or retrofits, structural failures, or safety hazards. It can also result in unnecessary expenses or delays in construction projects.

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