Can anyone vouch for the validity of the following equation to calculate panel resonance frequencies?

f = (pi/ 2) * SQRT{D/ p[(1/a^2) + (1/ b^2)]}

where:

f = natural frequency

D = plate stiffness factor = [E(h^3)] / [12(1-u^2)]

E = modulus of elasticity in lb/ in^2

Note 3/4" no-void ply has an MOE of 1.8 mill psi,

while typical MDF is 0.53 mill psi.

h = plate thickness, inches

u = Poisson ratio, MDF = .33

p = mass per unit area = v * h / g

v = material density in lb/in^3, MDF =~ 50lb/ft^3 = 0.028935 lb/in^3

h = plate thickness, inches

g = acceleration of gravity, 386 inch/sec^2

a = length of the plate, in inches

b = width of the plate, in inches.

Source was here.

I found E needed to be in kilo psi (so, 530 for MDF and 1800 for ply) to give what look like appropriate results (I think):

For MDF:

40" x 12" x .75" = 83.3Hz (153.5Hz ply)

20" x 12" x .75" = 93.1Hz

20" x 6" x .75" = 166.6Hz

10" x 6" x .75" = 186.1Hz

6" x 6" x .75" = 225.7Hz

4" x 4" x .75" = 338.5Hz

The values seem perhaps to be a little low and, counter to common wisdom, doubling up the panel thickness had a more significant effect that dividing the panel in 2.

40" x 12" x 1.5" = 166.6Hz (307Hz ply)

20" x 12" x 1.5" = 186.1Hz

20" x 6" x 1.5" = 333.2Hz

10" x 6" x 1.5" = 372.2Hz

6" x 6" x 1.5" = 451.4Hz

4" x 4" x 1.5" = 677Hz

Seems like it could be a useful tool for designing cabinets and bracing even if the results are only ballpark figures. Can anyone comment?

f = (pi/ 2) * SQRT{D/ p[(1/a^2) + (1/ b^2)]}

where:

f = natural frequency

D = plate stiffness factor = [E(h^3)] / [12(1-u^2)]

E = modulus of elasticity in lb/ in^2

Note 3/4" no-void ply has an MOE of 1.8 mill psi,

while typical MDF is 0.53 mill psi.

h = plate thickness, inches

u = Poisson ratio, MDF = .33

p = mass per unit area = v * h / g

v = material density in lb/in^3, MDF =~ 50lb/ft^3 = 0.028935 lb/in^3

h = plate thickness, inches

g = acceleration of gravity, 386 inch/sec^2

a = length of the plate, in inches

b = width of the plate, in inches.

Source was here.

I found E needed to be in kilo psi (so, 530 for MDF and 1800 for ply) to give what look like appropriate results (I think):

For MDF:

40" x 12" x .75" = 83.3Hz (153.5Hz ply)

20" x 12" x .75" = 93.1Hz

20" x 6" x .75" = 166.6Hz

10" x 6" x .75" = 186.1Hz

6" x 6" x .75" = 225.7Hz

4" x 4" x .75" = 338.5Hz

The values seem perhaps to be a little low and, counter to common wisdom, doubling up the panel thickness had a more significant effect that dividing the panel in 2.

40" x 12" x 1.5" = 166.6Hz (307Hz ply)

20" x 12" x 1.5" = 186.1Hz

20" x 6" x 1.5" = 333.2Hz

10" x 6" x 1.5" = 372.2Hz

6" x 6" x 1.5" = 451.4Hz

4" x 4" x 1.5" = 677Hz

Seems like it could be a useful tool for designing cabinets and bracing even if the results are only ballpark figures. Can anyone comment?

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