Related Resources: vibration

Thin Flat Plates Uniform Thickness Natural Frequency Equations and Calculator

Machine Design and Engineering

Thin Flat Plates of Uniform Thickness Natural Frequency Equations and Calculator

ωn = B [ ( E t2 ) / ( ρ a4 ( 1 - v2 )] (1/2)

Shape
Edge Conditions
B Value for Mode
1
2
3
4
5
6
7
8
Clamped at
Clamped at
Edge
11.84
24.61
40.41
46.14
103.12
-
-
-
Free
Free
6.09
10.53
14.19
23.80
40.68
44.68
61.38
69.44
Clamped at Center
4.35
24.26
70.39
138.85
-
-
-
-
Simply Supported
Simply Supported
at Edge
5.90
-
-
-
-
-
-
-
One Edge Clamped
One Edge Clamped
Three Edges Free
1.01
2.47
6.20
7.94
9.01
-
-
-
All Edges
All Edges
Clamped
10.40
21.21
31.29
38.04
38.22
47.73
-
-
Two Edge Clamped
Two Edge Clamped
Two Edges Free
2.01
6.96
7.74
13.89
18.25
-
-
-
All Edges Free
All Edges Free
4.07
5.94
6.91
10.39
17.80
18.28
-
-
One Edge Clamped
One Edge Clamped
Three Edges Simply
Supported
6.83
14.94
16.95
24.89
28.99
32.71
-
-
Two Edges Clamped
Two Edges Clamped
Two Edges Simply
Supported
8.37
15.82
20.03
27.34
29.54
37.31
-
-
All Edges
All Edges
Simply Supported
5.70
14.26
22.82
28.82
37.08
48.49
-
-

Where:

E = Young's Modulus ( lb / in2 ),
t = Thickness of Plate (in),
ρ = Mass Density (lb-sec2 / in4)
a = Diameter of Circular Plate or Side of Square Plate (in),
v = Poisson's Ratio
B = 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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