how to calculate the natural frequency of poles

Pretend the mass of the flagpole is acting laterally instead of vertically, and calc what the deflection is at the tip. The natural frequency is (approximately) 0.18*((g/deflection)^0.5), where g is 386 inches/second squared.

For finding frequency of pole you can use any FEM software and use eigen value solution.

If you want to do this by hand procedure is as follow :-
Here I have considered that there is mass lumped at the tip of the pole.
1) Calculate the deflection of pole with horizontal unit force at the tip of the pole.
2) Inverse the value which you have got, this is stiffness of the pole K.
3) You have mass lumped at the tip of the pole. Let's call it as M.
4) Circular frquency of vibration is given by
OMEGA = sqrt(k/m)
5) Frequency in Hz is given by
N = OMEGA / [2*pi()]

If there is no mass attached at the tip of the pole, and pole is self standing then frequency of pole is given by

OMEGA = [3.66/L^2] x sqrt[E x I / M]

L = Height of pole
E = Modulus of elasticity
I = Moment of inertia
M = Mass per unit length

Note - In above equation it is assumed that pole is considered as of uniform shape

Hope this will answer your querry

OMEGA = [3.66/L^2] x sqrt[E x I / M]

3.66/in^2 * sqrt(lb/in^2 * in^4 / (lb/in))

=3.66/in^2 * sqrt (in^3) ?

M is the mass. sorry about that

It is also assuming a fixed base - not entirely true. You need to add to the length above ground the depth to the point of fixity below ground to give a correct "L" value.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

SEIT- no, that is wrong.

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

Greg-

Why is that wrong?

That's the procedure/equations used in DG #11 for vibrations.

What's wrong with it?

SEIT-

Formula 3-3 of DG#11 is for beams supported at both ends. For a cantilevered beam, the attached example solves for the first natural frequency for a cantilever with a uniform weight and a concentrated load at the end.

DG #11 says (on page 13) That the natural frequency of a cantilever can be approximated using Eq 3-3 to Eq 3-5, by substituting a different delta (namely delta for a cantilever beam). It doesn't matter if the pole is horizontal, vertical, or somewhere in between. The natural frequency is the natural frequency.

Is DG #11 wrong or I am reading something wrong?

SEIT

You're right. DG #11 says the natural frequency can be approximated using Eq 3-3 to 3-5. The difference between the formula I posted vs. DG #11 is 12%, so it's a good approximation. See the attached example.

The equation is based on a simple spring and a lumped mass. A cantilever will give the same result as that equation if you load it at its end with a lumped mass, if the beam's mass is negligible. That is not the case here. Admittedly a 12% error in this case probably won't kill anyone, but wrong is wrong. The reason the error is small is quite neat, see the usual beam example for Rayleigh's method.



Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

The ASCE 7-05 commentary has equations for estimating the natural frequency of poles. See page 294.

from page 294 of ASCE-7
n = [0.56/L^2] x sqrt[E x I / M]