Help w/ using Blevins formula for natural frequency of a cylinder

In summary, the conversation is about a formula created by Blevins for calculating the natural frequency of a hollow cylinder. The formula includes variables for A, I, and m, where A is 9.87 for the first mode, I is the area moment of inertia, and m is the mass per unit length. The person asking the question is looking for clarification on how to determine the mass per unit length for a thin-walled cylinder and which formula to use for the area moment of inertia. They also question if the given formula for m is referring to the mass density of the beam or the mass per unit length. Finally, they ask for insight on the correct formula for I, mentioning two options they have found.
  • #1
GenSoft3d
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I came across this formula by Blevins for calculating the natural frequency of a hollow cylinder and was hoping that someone could answer a question I have for calculating the mass per unit length (m). Here's the formula:

f = A/(2*pi*L^2)*sqrt(E*I/m)

A= 9.87 for first mode
I = Area Moment of Inertia (m^4)
m= Mass per Unit Length (kg/m)


In this formula what equation should I use to determine the m (mass per unit length) for a thin-walled cylinder? Also, does I = pi/64*(d^4-di^4) in this case?
 
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  • #2
Does anyone have any insight on this? In the original data where I found this formula it states that "m = mass per unit length of beam (kg/m)". I take it that it's not referring to the mass density of the beam itself but rather the mass per unit length as described. If so then is this actually the area X the mass per unit volume (i.e., PI*d*t*density)?

As for the I (Area Moment of Inertia) I have found two formulas but can someone tell me which is the correct one to use for this application? Here's what I've found:

I = PI * (OD^4 - ID^4)/64

I = PI*d^3*t/8 (for a thin wall round tube)

Any help would be greatly appreciated.
 

What is Blevins formula for natural frequency of a cylinder?

The Blevins formula for natural frequency of a cylinder is an equation that calculates the natural frequency of a cylindrical structure based on its material properties and geometry.

How is Blevins formula used in engineering?

The Blevins formula is commonly used in engineering to predict the natural frequency of cylindrical structures such as pipes, columns, and vessels. This information is useful in designing and analyzing these structures to ensure they can withstand vibrations and other dynamic forces.

What are the inputs needed for the Blevins formula?

The Blevins formula requires the following inputs: the material properties of the cylinder (such as Young's modulus and density), the dimensions of the cylinder (diameter and length), and the boundary conditions (such as fixed or free ends).

Can the Blevins formula be used for all types of cylindrical structures?

Yes, the Blevins formula can be used for most cylindrical structures, as long as the material properties and dimensions are known. However, it may not be accurate for complex or non-uniform geometries.

Are there any limitations to using the Blevins formula?

Although the Blevins formula is a useful tool for predicting natural frequency, it has limitations. It assumes that the cylinder is homogeneous, isotropic, and has uniform cross-section. It also does not take into account any damping effects, which can affect the actual natural frequency of a structure.

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