**Related Resources: vibration**

### Beam Fixed Ends Off-Center Load Applied Angular Natural Frequency Equations and Calculator

**Machine Design and Engineering **

**Beam Fixed Ends Off-Center Load Applied Angular Natural Frequency Equations and Calculator **

ω_{n} = ( 1 / ( a b ) [ ( 3 E I *l*^{3} ) / ( m a b ) ]^{(1/2)}

Where:

m = Mass of Load ( lbf-sec^{2} / in )

*l* = Length of Beam ( in ),

a = Distance as Shown ( in ),

b = Distance as Shown ( in ),

I = Area Moment of Inertia of Beam Cross Section ( in^{4} )

E = Young's Modulus ( Lb / in^{2} ),

ω_{n} = Angular Natural Frequency ( rad / sec )

Note: 1 ( lbf-sec^{2} / Ft ) = 1 Slug

1 ( lbf-sec^{2} / in ) = 12 ( lbf-sec^{2} / Ft ) or 1 ( lbf-sec^{2} / Ft ) = 0.08333 ( lbf-sec^{2} / in )

Related and Useful:

Reference Harris, Shock and Vibration Handbook