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Simply Supported Beam Mass at Center Natural Frequency Calculator

Natural Frequency of Simply Supported Beam with Mass at Center Equation and Calculator

Eq. 1 Simply Supported Beam with Mass at Center

${\displaystyle {\mathrm{\omega <!--\; \omega \; -->}}_1=2.2\mathrm{\pi <!--\; \pi \; -->}\sqrt{\frac{EI}{(m+\frac{17}{35}\frac{g}{w})L^3}}}$

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 center, lbs

L = length, in

g = 386, in/sec²

Figure 1, Simply Supported Beam with Mass at Center Natural Frequency

Source

Bell Helicopter Structural Design Manual, 1977

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