Natural Frequency of Cantilevered Coil

[Sami Lakka]

I would like to calculate the natural frequency of a cantilevered spiral coil. So instead of having a standard beam which is straight, I have a beam which has one end fixed to an axle and the beam is spiralled several times around the axle. The end of the beam comes out of the spiral and runs straight for some length.

I know that I can compute the frequency of the standard beam using:

f=1/(2*pi) * sqrt( (3 * E * I)/(l^3*0.23m))

where E = elastic modulus, I=Inertia, l=length of the beam and m=mass of the beam.

Can I use the same formula by just noting the increased length?

 

[Navin A S]

Or are there any special considerations that I have to take into account?The formula you provided applies to straight beams and is not suitable for calculating the frequency of a cantilevered spiral coil. The formula assumes a uniform cross-section, which is not applicable in this case. In addition, the spiral shape will affect the stiffness and mass distribution of the beam, which will need to be taken into account when calculating the frequency of the cantilevered spiral coil. If possible, it would be best to use a finite element analysis (FEA) to calculate the frequency of the cantilevered spiral coil. FEA is a computer simulation technique that can accurately simulate the behavior of complex structures. This would allow you to account for all the factors that might influence the frequency of the cantilevered spiral coil, including its shape, mass distribution, and stiffness.