Vibration Design and Engineering

Vibration Resonant Frequency of a Flat Plate / Electronic Circuit Card Equation and Calculator.

Equations and calulator will determine resonant frequency of a rectangular plate or PCB that is subjected to a know G peak sinusoidal vibration. With a low input G level, the four edges of the circuit board will act as though they were simply supported. The plate board has a uniformly distributed weight.

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Preview: Resonant Frequency of a Flat Plate / Electronic Circuit Card Calculator

Natural frequency Vibration equation derived with the use of a trigonometric expression (Equation a),

f_n = Π / 2 ( D/ρ )^1/2 ( 1/a²+ 1/b² )

Natural frequency equation shown above is exact using the Rayleigh method, because the deflection curve used for the vibrating plate is exact for the boundary conditions.

D = E h³ / [ 12 (1 - µ²) ]

ρ = W / g a b

Where:

a = Plate length (in)
b = Plate Width (in)
h = Plate Thickness (in)
W= Plate Weight (lbs, N)
g = 386 in./s² (gravity)
E = Modulus of Elasticity ( lbs/in² )
µ = Poisson’s ratio (dimensionless)
ρ = Mass per Unit Area ( lb · s² / in³ )
D = Plate Bending Stiffness Factor (lb · in)
f_n = Natural Frequency (Hz)

Or, the natural frequency can also be determined from the equation derived with the use of a polynomial expression (Equation b):

f_n =5.31 / Π · { D / ρ [ 1/ (15 c⁴⁾ + 1/ (9 c² d² ) + 1/ ( 15 d⁴) ] } ^(1/2)

Where:

c = a / 2 (in)
d = b / 2 (in)