Related Resources: vibration

Beam one End Free Other Fixed Angular Natural Frequency Equations and Calculator

Machine Design and Engineering

Beam with one End Free and Other Hinged Angular Natural Frequency Equations and Calculator

l = 1

 

 

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 (in⁴)
E = Young's Modulus ( lb / in² ),
µ = Mass per Unit Length of Beam ( lb-sec²/in² ),
A = Coefficient for given nodes from image table above,
ω_n = Angular Natural Frequency ( rad / sec )

Related and Useful Links:

• AISC Steel Construction Shapes Properties Viewer
• Young's Modulus on Common Engineering Materials

Reference Harris, Shock and Vibration Handbook