Related Resources: vibration

Beam Fixed End and Cantilevered Angular Natural Frequency Equations and Calculator

Machine Design and Engineering

Beam Fixed End and Cantilevered Angular Natural Frequency Equations and Calculator

Beam Spring Fixed End and Cantilevered 3.52
l = 1
Beam Spring Fixed End and Cantilevered 22.0
Beam Spring Fixed End and Cantilevered 61.7

 

Beam Spring Fixed End and Cantilevered  A 121.0
Beam Spring Fixed End and Cantilevered  A 200.0

 

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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