Quick Natural Frequency Estimates 2

[fionac]

I am looking for some quick assessment methods for getting quick estimates of the natural frequencies of building elements from their dead load deflections

Any ideas?
Otherwise possible sources might be useful!

Fiona

 

[coco1953]

Deflections and fequencies are closely related. At Roark's Formulas for Stress and Strain you can find a table with formulas for the frequencies of beams and bars, and also of course for deflections, and you can derive the relations yourself, that in some cases are quite simple. For example since the first mode for a simply supported beam uniformly loaded is 3.55/sqrt(5WL³/384 EI) and its deflecton is 5WL³/384 EI the ratio of frequency to deflection would be 3.55/(5WL³/384 EI)^1.5.

 

[coco1953]

But, I have to add, calculating the freqs takes exactly the same effort, so you can also do it directly once you know the load and inertia. I guess tha trying to estimate the freq just from the deflections without taking load and inertia into account coul lead you to gross deviations from the exact solution that you have at hand. For more complex situations, it is advisable that you use some software like SAP2000. that can very fast find the modes for any load, material and geometry case. If you dont have that at hand you can always ask a friend like me.

 

[corus]

There is a method by which the natural frequency can be obtained from the deflections under load. I think it's the Rayleigh-Ritz or Galerkin method, I'm not sure. It only gives the first mode though and is an approximation.

 

[imr]

hi
u can use softwares like ANSYS which contains Verification manuals, where certain tutorials or help is given to calculate the natural frequency of structures like simply supported beam etc.

 

[imr]

just now i have solved a problem in ANSYS
William Thomson Book on "Vibration Theory and Applications"
prob # 33 of chapter 1
by using block lancoz method. Third mode is the accurate answer. if u want the method u can contact me

 

[antolara]

Check CEB - Vibration Problems in Structures, Bulletin D'Information No. 209, August 1991
Antonio Laranjeiras,
Salvador, Brazil

 

[DonTh]

In the UK an approximation we often use for beams is 18/sqrt deflection(in mm) which converts to 3.6/sqrt (in inches).
Regards
Don

 

[Imagineer]

While doing a google search for some frequency information, I was sent to this thread. Should have known to check the Tips first.

A quick estimation of building natural frequency is 0.1sec per story. Note that this is not the resonance of the building just it's natural frequency to outside input.

Imagineer