Frequency response mode of vibration

In summary, the conversation discusses using Abaqus to solve an analysis problem and comparing the results with an exact equation. The problem is modeled as a simply supported beam with a lumped mass at the end. The equation for the exact solution is provided, but there is uncertainty about its accuracy and how to incorporate the mode number in the solution. The conversation concludes with the suggestion to run the numbers and compare with the first mode results from Abaqus, but with the caveat that the exact solution may not be completely accurate.
  • #1
roldy
237
2
I'm working on an analysis problem using Abaqus. I would like to compare my results with an exact equation. My problem is modeled as a simply supported beam with a lumped mass at the end. The equation that I'm using for the exact solution is as follows:

k=3EI/L3
ωn=[itex]\sqrt{k/(M + 0.23m)}[/itex]

How do I incorporate the mode number to find what the exact solution is at say mode 2 or 3?
 
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  • #2
That "exact" solution is probably only an analytic approximation for the first mode. Run the numbers and see which mode it compares with most favorably. I would bet it will be the first mode.
 
  • #3
The exact solution does compare most favorably with the first mode results from Abaqus.
 
  • #4
Don't hold your breath on that being an exact solution. It is most likely obtained from a Rayleigh approximation.
 

FAQ: Frequency response mode of vibration

1. What is frequency response mode of vibration?

Frequency response mode of vibration is a phenomenon in which a system or structure vibrates at a specific frequency when subjected to a periodic input. This frequency is known as the natural frequency of the system and is determined by its physical characteristics such as mass, stiffness, and damping.

2. How is frequency response mode of vibration different from other modes of vibration?

Frequency response mode of vibration is different from other modes of vibration, such as forced or free vibration, because it is a specific response to a periodic input. In forced vibration, the system is forced to vibrate at a specific frequency, while in free vibration, the system vibrates at its natural frequency without any external input.

3. What factors affect the frequency response mode of vibration?

The frequency response mode of vibration is affected by various factors, including the physical properties of the system, such as mass, stiffness, and damping, as well as the type and magnitude of the input force. Other external factors, such as temperature and environmental conditions, can also influence the frequency response of a system.

4. How is frequency response mode of vibration measured?

The frequency response mode of vibration can be measured using various techniques, such as modal analysis, which involves exciting the system at different frequencies and measuring its response. Other methods include impact testing, where a force is applied to the system and the resulting vibrations are measured, and laser Doppler vibrometry, which uses a laser beam to measure the displacement of the system.

5. Why is understanding frequency response mode of vibration important?

Understanding frequency response mode of vibration is important for engineers and scientists in various fields, such as structural and mechanical engineering, as it allows them to predict the behavior of a system and make necessary adjustments to ensure its stability and durability. It is also crucial in designing and testing structures and machines to ensure they can withstand specific frequencies of vibrations without failure.

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