natural frequency of sign structure
 

natural frequency of sign structure
i have been asked to calculate the natural frequency of a rectangular sign structure, 20' long x 12' high, cantilevered from it's base. i have not been able to source a formula for this particular shape. can anyone point me in the right direction for a source of this type of information for various shapes.

model it as a fixed end beam (cantilever), with it's self weight as a distributed load and the load of the sign at the tip. when you get the deflection at the tip, use that deflection in the traditional formula, fn=0.18(g/delta)^.5.
yes. you could also just replace the distributed load by a known force at the tip. say 1 newton.
or, you know that the stiffness of the "beam" is given by k=3*e*i/l^3, and so...wn=sqrt(k/m). m can be approximated by 1/3*mass_of_beam.
also, you know this is only the first fundamental natural frequency. the weighted nat. frequencies are of the form (2n-1)*pi/2.
and the 'real' pde describing the motion of the structure has the form:
d^2w/dt^2+c^2*d^4w/dx^4=0
where c=sqrt(e*i/rho*a)

fe
i think you are talking two different frequencies here - one torsional due to vortex shedding, and the other just a natural pendulum freqency.
you might provide both and impress your boss.
mike mccann
mmc engineering
mike has a point. you could also provide a range of velocities that the frequency of vortex shedding may coincide with a nat. freq.
fe
use asce 7-05 chapter 15. there is an equation in there that can be used for non-building structures. i don't have my copy on me, but i can get the equation number tomorrow.
it basically comes down to a similar equation to that by fex32, but it makes it easier to discretize the column if there are any splices and changes in stiffness
it is section 15.4.4, equation 15.4-6.
t = 2*pi* sqrt((sum i=1 to n)(w_i*delta_i^2)/(g*(sum i=1 to n)(f_i*delta_i))
where f_i represents any lateral force distribution in accordance with the principles of structural mechanics
delta_i is the elastic deflection calculated at each level, i, using the lateral forces f_i
w_i is the weight tributary (assigned) to each level i.
the equation looks much simpler in the standard itself.