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.
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
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