# How to calculate natural frequency of a circular plate

1. Mar 12, 2015

### spggodd

I am trying to get used to using a Data Physics analyzer at work in order to measure the natural frequency of components of a larger project I am involved in, my method described is intentionally crude as I was trying to do this as a quick play around before diving into the real thing..

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:

wn =B √(Et3/ρa4(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

2. Mar 12, 2015

### spggodd

Also, the accelerometer I'm using is currently stuck down with duct tape on the outer edge of the component.

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3. Mar 12, 2015

### PizzaWizza

I'm by no means an expert here at all but the only thing that jumps out to me is the position & force of the strike. Does that not need to be considered?