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Cantilevered Beam Natural Frequency Formulas and Calculator

Natural Frequency of Cantilevered Beam Equation and Calculator

Eq. 1 Cantilevered Beam 1 Node

${\displaystyle {\mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby><!--\; \omega \; -->}}_1=\frac{36{\mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby><!--\; \pi \; -->}}^2}{L^2}\sqrt{\frac{EIg}{w}}}$

Eq. 2, 2 Nodes

${\displaystyle 6.27\cdot <!--\; \cdot \; -->{\mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby><!--\; \omega \; -->}}_1}$

Eq. 3, 3 Nodes

${\displaystyle 17.6\cdot <!--\; \cdot \; -->{\mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby><!--\; \omega \; -->}}_1}$

Eq. 4, 4 Nodes

${\displaystyle 34.4\cdot <!--\; \cdot \; -->{\mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby><!--\; \omega \; -->}}_1}$

Eq. 5, 5 Nodes

${\displaystyle 56.8\cdot <!--\; \cdot \; -->{\mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby><!--\; \omega \; -->}}_1}$

Where:

E = Modulus of elasticity lbs/in²

I = Area moment of inertia, in⁴

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

L = length, in

g = 386, in/sec²

Figure 1, Uniform Cantilever Beam

Source

Bell Helicopter Structural Design Manual, 1977

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