Cantilever beam natural frequency depends only on deflection?

[rarara]

Hi

For a cantilever beam with a load at its end,

flexural rigidity is:

EI = m*g*L³ / 3Y

Where m=mass, g=gravity, L=length of beam and Y=deflection

the natural frequency is

f = 1/(2∏) * √ ( 3EI/mL³)

Plugging in EI to the formula for f reveals that f depends only on the deflection, Y.

If I wanted to predict the frequency, would I therefore only need to measure Y? I am stuck in a circular logic loop because Y depends on m, L and EI but m and L cancel out in f =

 

[Studiot]

rarara
Plugging in EI to the formula for f reveals that f depends only on the deflection, Y.

So why is that surprising?

The deflection depends upon the end load m.

The frequency is the √(ratio of elastic forces to inertial ones) ω = √(k/m)

and k, the spring constant = Load/Deflection.

The equation of motion is (for vubrations in the y direction)


$$m\frac{{{d^2}y}}{{d{t^2}}} + ky = 0$$

 

[rarara]

I have measurements of m, L, Y and f

there is no relationship between Y and m, Y and L , F and m, F and L
there is correlation between Y and f

Could the lack of correlation in Y vs m and Y vs L indicate that in my system, EI is the most important predictor of Y and by extension f ?

I guess the real problem is that I do not have enough degrees of freedom to determine the effect of EI.