Related Resources: vibration

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

Machine Design and Engineering

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

ω_n = ( 1 / a b ) [ ( 3 E I l ) / m ]^(1/2)

Where:

m = Mass of Load ( lbf-sec² / in )
l = Length of Beam ( in ),
a = Some Length from Hinged End ( in ),
b = Some Length from Hinged End ( in ),
I = Area Moment of Inertia of Beam Cross Section ( in⁴ )
E = Young's Modulus ( Lb / in² ),
ω_n = Angular Natural Frequency ( rad / sec )

Note: 1 ( lbf-sec² / Ft ) = 1 Slug

1 ( lbf-sec² / in ) = 12 ( lbf-sec² / Ft ) or 1 ( lbf-sec² / Ft ) = 0.08333 ( lbf-sec² / in )

Related and Useful:

• AISC Steel Construction Shapes Properties Viewer
• Young's Modulus

Reference Harris, Shock and Vibration Handbook