Related Resources: vibration

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

ω_n = 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)
ω_n = Angular Natural Frequency ( rad / sec )

Related and Useful Links:

• AISC Steel Construction Shapes Properties Viewer
• Young's Modulus on Common Engineering Materials

Reference Harris, Shock and Vibration Handbook