I found this equation for predicting the bending natural frequency of a tube but am having trouble working it out. I was hoping that someone might be willing to steer me in the right direction. First the equation and the info provided on the website:(adsbygoogle = window.adsbygoogle || []).push({});

w = (B*l)2 * SQRT (E*I/(rho*l4))

w - frequency radian per second

E - modulus of elasticity

I - area moment of inertia = PI*d3*t/8 for a thin wall round tube

d - mean diameter

t - wall thickness

rho - mass per unit length = Area * mass per unit volume = PI*d*t*density

l - length of tube

(B*l)2 - Constants based on the boundary conditions.

For a wind chime (Free-Free Beam):

(B*l)2= 22.373 for the first natural frequency.

To get the units correct you must multiply the values inside the square root by gravity (g).

g = 386.4 in/sec2 for the units I'm using.

for frequency in cycles per second (Hz) f = w/(2*PI)

Now, the problem that I'm having is that when following the above format that uses non SI units I end up with a different result than when I swap them out for SI units. So, for example; when usinglbmass/in^3for the density andpsifor Young's Modulus (*gravity) along with imperial units for size inputs (inch) the results are different than the results from usingkg/m3andpascalsalong with metric sizes (meters). When using SI units I'm dropping the*gravity.

Here are the values that I am working with:

E = 16969415.3 psi (1.17e+11 Pa)

density = 0.323 lbmass/in^3 ( 8940 kg/m3)

mean dia = .428 in (0.0108712 m)

thickness = .048 in (0.0012192 m)

length = .3885 in (0.0098679 m)

When using the above format I'm getting 2 MHz but when switching to SI units I'm getting 66.7 MHz.

So, where am I going wrong here? Any ideas? Any advice would be greatly appreciated.

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# Question regarding Euler's equation for predicting the bending natural freq of a tube

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