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# Fundamental Natural Frequency

## Fundamental Natural Frequency

(OP)
Hello,
I am using National Building Code (Canada) 1995 detailed procedure to determine the wind load on an antenna.  However, I need to find the fundamental natural frequency of the antenna and have no clue.  The antenna is a circular aluminum antenna 17ft long.

### RE: Fundamental Natural Frequency

I got the following from Chopra (1995) *Dynamics of Structures*, pp. 589-592.

For a member of length L, constant bending stiffness EI, and uniform distribution of mass per unit length M, the natural frequencies w of "beam" (moment = curvature*EI) response are given by:

wi = Ai²*sqrt(EI/M)

where wi is the natural frequency of the ith mode of vibration,
and Ai is the ith term in a series of constants determined by the boundary conditions.

For cantilever beam boundary conditions, the constants Ai are from the solution of the freqency equation:

1 + cos(Ai*L)cosh(Ai*L) = 0

and are found to be A1² = 3.516/L², A2² = 22.03/L², A3² = 61.70/L², ....

So for first mode of vibration,

w1 = (3.516/L²)*sqrt(EI/M) radians/sec (assuming units of M/E = sec²)

### RE: Fundamental Natural Frequency

To get the natural frequency in cycles/sec, divide the above result by 2pi.

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