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Massless Circular Plate With Concentrated Center Mass Simply Supported Edges Natural Frequency Equations and Calculator

Machine Design and Engineering

Massless Circular Plate With Concentrated Center Mass Simply Supported Edges Natural Frequency Equations and Calculator

Massless Circular Plate With Concentrated Center Mass Simply Supported Edges Natural Frequency Equations and Calculator

ωn = 4.09 [ ( E h3 ) / ( m a2 ( 1 - v2 ) ( 3 + v ) ] (1/2)

Where:

Nodes are indiated in images as a proportion of length l measured from the the left,
E = Young's Modulus of Plate( lb / in2 ),
v = Poisson's Ratio
m = Mass of Load ( lb-sec2 / in ),
a = Diameter of Plate (in),
h = Thickness of plate (in)
ωn = Angular Natural Frequency ( rad / sec )

Related and Useful Links:

Reference Harris, Shock and Vibration Handbook

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