**Related Resources: vibration**

### Beam Fixed-Fixed Ends Angular Natural Frequency Equations and Calculator

**Machine Design and Engineering **

**Beam with Fixed-Fixed Ends Angular Natural Frequency Equations and Calculator **

= 1l |

ω_{n} = A [ ( E *I * ) / ( ( L *l *)^{4} µ ] ^{(1/2)}

Where:

Nodes are indiated in images as a proportion of length* l *measured from the the left,

*L = *Total Length of Beam (in),

*l *= Length Proportion at Node Location of Beam indicated in images (in),

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

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

µ = Mass per Unit Length of Beam ( lb-sec^{2}/in^{2} ),

A = Coefficient for given nodes from image table above,

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

Related and Useful Links:

Reference Harris, Shock and Vibration Handbook