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

[anatman]

I came across this formula by Blevins for calculating the natural frequency of a hollow cylinder and was hoping that someone could answer a couple of questions I have. First, 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 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.

 

[GregLocock]

I suggest you substitute t=(OD-ID)/2 into the I formula to see if it makes any odds.

mass per unit length =CSA*density=pi*d*t*rho

Cheers

Greg Locock


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[anatman]

Excellent! Thanks for the help... I really appreciate that. I will definitely try subbing the thickness as you recommended and see how that works out.

Sorry for my ignorance but I have to ask, what does CSA refer to?

Thanks again Greg!

 

[GregLocock]

cross sectional area

Cheers

Greg Locock


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[anatman]

Thanks so much Greg... you've been a great help! Posted this on the "physics forums" and got no reply after 3 days so thought I'd try here. Glad I did!

Cheers!

 

[anatman]

oh, I forgot to ask... any advice on the I ? Which one would you recommend for this equation?

I = PI * (OD^4 - ID^4)/64
I = PI*d^3*t/8 (for a thin wall round tube)

 

[anatman]

Oh, I think I got it.... it should be I = pi/64*(OD^4-ID^4)

 

[anatman]

Would you happen to know if this formula gives the frequency in radians/sec or cps? Wondering if I need to /2*pi to convert it to Hz.

 

[GregLocock]

Blevins tells you, but I'd guess hz, the 2pi is probably the conversion from sensible units

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[FeX32]

Sometimes I really think EngTips should implement LaTeX script so that all the formulas can be typed easily and can appear very clearly. Sorry for the off topic comment.


Fe (IronX32)

 

[saplanti]

Natural frequencies can be looked for several reasons and they have different formulae.

In case you are looking for the beam natural frequency you are probably on the right path.

In case you are engaged with pulsating flow inside the cyclinder you need to look for the shell (wall) frquencies in addition to the frequencies for beam between nominated supports.

Ibrahim Demir