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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

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

ωn = ( 1 / ( a b ) [ ( 3 E I l3 ) / ( m a b ) ](1/2)

Where:

m = Mass of Load ( lbf-sec2 / 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 ( in4 )
E = Young's Modulus ( Lb / in2 ),
ωn = 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:

Reference Harris, Shock and Vibration Handbook

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