Natural Frequency hand calc
Natural Frequency hand calc
(OP)
To all hotshots out there,
Can anyone tell me a formula for approximating the natural frequency of a simply supported beam, given the length, moment of inertia, material, mass, and first order deflection?
I know of a neat approach for building design called the Rayleigh approximation, using the masses and first order deflections.
Is there a comparable method for beams?
What about for a beam overhanging 2 supports (like a railcar, for example)?
Thank you in advance.
tg
Can anyone tell me a formula for approximating the natural frequency of a simply supported beam, given the length, moment of inertia, material, mass, and first order deflection?
I know of a neat approach for building design called the Rayleigh approximation, using the masses and first order deflections.
Is there a comparable method for beams?
What about for a beam overhanging 2 supports (like a railcar, for example)?
Thank you in advance.
tg





RE: Natural Frequency hand calc
fn = [1/(2*pi)]*sqrt[g/dst]
g = gravity
dst = static deflection under it's own weight
RE: Natural Frequency hand calc
...or just look it up in Marks' or Roark's :)
Garland
RE: Natural Frequency hand calc
(If you apply the formula to a beam that is built-in at each end, the underestimate in the case of uniform mass distribution is about 12%. For a cantilever it is about 19%.)
Once you have some parts of the structure that move upwards when the main part of the structure moves downwards under static gravity loading, then the formula should not be used. In such cases, there is indeed a method known as Raleigh's Method. It involves assuming a deflected shape, then (based on that assumed shape) calculating and equating the strain energy at full deflection and the kinetic energy at zero deflection. The more accurate your assumed deflected shape the more accurate your estimate of the natural frequency. However you usually get adequate estimates with even a crude assumed shape.