Resonant Frequency Flat Plate Electronic Circuit Equations and Calculator

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.

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

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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),

fn = 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)
fn = Natural Frequency (Hz)

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

fn =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)

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