Natural Frequency of Sign Structure

[SkiisAndBikes]

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.

 

[Lion06]

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.

 

[FeX32]

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

 

[msquared48]

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

 

[FeX32]

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

 

[enginerding]

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

 

[enginerding]

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.