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Uniform Beam with Clamped Ends Equation and Calculator

Natural Frequency of Uniform Beam with Clamped Ends Equation and Calculator

Eq. 1 Uniform Beam 2 Nodes

${\displaystyle {\mathrm{\omega <!--\; \omega \; -->}}_1=\frac{22.4}{L^2}\sqrt{\frac{EIg}{w}}}$

Eq. 2, 3 Nodes

${\displaystyle 2.77\cdot <!--\; \cdot \; -->{\mathrm{\omega <!--\; \omega \; -->}}_1}$

Eq. 3, 4 Nodes

${\displaystyle 5.44\cdot <!--\; \cdot \; -->{\mathrm{\omega <!--\; \omega \; -->}}_1}$

Eq. 4, 5 Nodes

${\displaystyle 9.00\cdot <!--\; \cdot \; -->{\mathrm{\omega <!--\; \omega \; -->}}_1}$

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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