Finding natural frequency of a steel flat

In summary, there is no single formula for finding the natural frequency of a steel flat with specific dimensions and end conditions. However, an engineering approach using Dunkerley's method can provide an estimate of the fundamental frequency. This method involves calculating the frequency under just the weight of the beam and the deflection due to each point load, and then using Dunkerley's formula to find the overall frequency. While this formula may underestimate the actual value, it can provide a close approximation.
  • #1
lonthia
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is there a straight formula for finding one of the natural (preferably fundamental) frequency of a steel flat with dimension say, L=1000 mm, B=100 mm and Thickness T=10 mm ? The flat is fixed at both ends by bolts and two weights of equal magnitude are suspended at 1/4 and 3/4 (i.e. 250 mm and 750 mm) of the flat.

I am yet to find understandable solution to the above problem on the net; so I had to post it to this forum. Please help, I am lost.
 
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  • #2
lonthia said:
is there a straight formula for finding one of the natural (preferably fundamental) frequency of a steel flat with dimension say, L=1000 mm, B=100 mm and Thickness T=10 mm ? The flat is fixed at both ends by bolts and two weights of equal magnitude are suspended at 1/4 and 3/4 (i.e. 250 mm and 750 mm) of the flat.

I am yet to find understandable solution to the above problem on the net; so I had to post it to this forum. Please help, I am lost.

This article gives an engineering approach to estimating the fundamental frequency of a shaft under various end conditions and loadings:

http://www.impactap.com/joe/Chapter%207.pdf

Dunkerley's method is outlined in this article:

http://www.freestudy.co.uk/dynamics/free vibrations.pdf

Basically, you can calculate the natural frequency of the beam under just its own weight, and under the deflection due to each point load, separately, and then find the overall frequency by using Dunkerley's formula. This formula tends to underestimate the actual value of the frequency. There are more complicated approaches to finding the natural frequency, but this should give a close approximation.
 
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What is the natural frequency of a steel flat?

The natural frequency of a steel flat is the frequency at which the flat will vibrate when it is disturbed. It is a characteristic property of the material and shape of the flat.

What factors affect the natural frequency of a steel flat?

The natural frequency of a steel flat is affected by several factors including the material properties (such as density, elasticity, and stiffness), the dimensions and shape of the flat, and any external forces acting on the flat.

How do you calculate the natural frequency of a steel flat?

The natural frequency of a steel flat can be calculated using the equation f = (1/2π) * √(k/m), where f is the natural frequency, k is the stiffness of the flat, and m is the mass of the flat.

Why is it important to find the natural frequency of a steel flat?

Knowing the natural frequency of a steel flat is important for structural engineers and designers as it helps them to ensure that the flat is not susceptible to resonance, which can cause structural damage and failure.

How can the natural frequency of a steel flat be determined experimentally?

The natural frequency of a steel flat can be determined experimentally by conducting a modal analysis, where the flat is subjected to different frequencies and the corresponding vibrations are measured. The frequency at which the flat vibrates the most is the natural frequency.

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