- #1

spggodd

- 38

- 0

To start off, I have found a aluminium circular plate component 170mm dia and 10mm thick. It has 7 small thru holes on a 160mm pcd and a 20mm circular boss at the centre of the plate, protruding 30mm on one side.

I have held the component by the central boss and hit it.

I am reading what I think is a natural frequency of 1800 Hz.

To compare, I tried to compare this to simple theory of a circular plate and found the following equation:

w

_{n}=B √(Et

^{3}/ρa

^{4}(1-ν))

Where:

E = Youngs Mondulus

I = Area Moment of Interia

a = Diameter of the Plate

ν = Poisons Ratio

ρ = Mass Density

B = Constant based on the configuration (Clamped at edge = 11.84, Free at edge = 6.09, Clamped at center = 4.35 and Hinged at edge = 5.90)

I used some general values for the aluminium (ρ=2500kg/m^3, E = 75 GPa, ν=0.33)

I took B = 6.09

I ended up with 187.25 Hz which is way below what I was expecting.

Can anyone spot why I'm so far out or can you advise if my method is not correct?

Many Thanks

Steve