Natural Frequency of Sign Structure
Natural Frequency of Sign Structure
(OP)
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.






RE: Natural Frequency of Sign Structure
RE: Natural Frequency of Sign Structure
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
RE: Natural Frequency of Sign Structure
You might provide both and impress your boss.
Mike McCann
MMC Engineering
RE: Natural Frequency of Sign Structure
Fe
RE: Natural Frequency of Sign Structure
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
RE: Natural Frequency of Sign Structure
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.