Help w/ using Blevins formula for natural frequency of a cylinder
Help w/ using Blevins formula for natural frequency of a cylinder
(OP)
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.
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.





RE: Help w/ using Blevins formula for natural frequency of a cylinder
mass per unit length =CSA*density=pi*d*t*rho
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Help w/ using Blevins formula for natural frequency of a cylinder
Sorry for my ignorance but I have to ask, what does CSA refer to?
Thanks again Greg!
RE: Help w/ using Blevins formula for natural frequency of a cylinder
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Help w/ using Blevins formula for natural frequency of a cylinder
Cheers!
RE: Help w/ using Blevins formula for natural frequency of a cylinder
I = PI * (OD^4 - ID^4)/64
I = PI*d^3*t/8 (for a thin wall round tube)
RE: Help w/ using Blevins formula for natural frequency of a cylinder
Oh, I think I got it.... it should be I = pi/64*(OD^4-ID^4)
RE: Help w/ using Blevins formula for natural frequency of a cylinder
RE: Help w/ using Blevins formula for natural frequency of a cylinder
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Help w/ using Blevins formula for natural frequency of a cylinder
Fe (IronX32)
RE: Help w/ using Blevins formula for natural frequency of a cylinder
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