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


Beam Simple Fixed-Fixed Ends Angular Natural Frequency Equations and Calculator 1
l
= 1
Beam Simple Fixed-Fixed Ends Angular Natural Frequency Equations and Calculator 2
Beam Simple Fixed-Fixed Ends Angular Natural Frequency Equations and Calculator 3

 

Beam Simple Fixed-Fixed Ends Angular Natural Frequency Equations and Calculator 4
Beam Simple Fixed-Fixed Ends Angular Natural Frequency Equations and Calculator 5

 

ωn = 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,
ωn = Angular Natural Frequency ( rad / sec )

Related and Useful Links:

Reference Harris, Shock and Vibration Handbook

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