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Cantilever Beam with Mass at End Natural Frequency Calculator

Natural Frequency of Cantilever Beam with Mass at End Equation and Calculator

Eq. 1 Cantilever Beam with Mass at End Natural Frequency

${\displaystyle {\mathrm{\omega <!--\; \omega \; -->}}_1=0.56\mathrm{\pi <!--\; \pi \; -->}\sqrt{\frac{EI}{(m+\frac{33}{140}\frac{g}{w})L^3}}}$

Where:

E = Modulus of elasticity lbs/in²

I = Area moment of inertia, in⁴

w = weight per unit area of plate, lbs/in²

m = mass at end, lbs

L = length, in

g = 386, in/sec²

Figure 1, Cantilever Beam with Mass at End Natural Frequency

Source

Bell Helicopter Structural Design Manual, 1977

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