How to calculate natural frequency of a circular plate

AI Thread Summary
The discussion focuses on measuring the natural frequency of a 170mm diameter aluminum circular plate using a Data Physics analyzer. The user reports an experimental frequency reading of 1800 Hz, which contrasts sharply with a theoretical calculation yielding only 187.25 Hz based on standard equations and material properties. Concerns are raised regarding the accuracy of the measurement method, particularly the placement of the accelerometer and the force applied during the strike. The user seeks advice on potential errors in their approach or calculations. Overall, the discrepancy between experimental and theoretical results highlights the importance of precise measurement techniques in frequency analysis.
spggodd
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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
 
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Also, the accelerometer I'm using is currently stuck down with duct tape on the outer edge of the component.

|----|
|...| <------- here
|...|
|...|
|...|
|...|
|...|--------|
|.....|
|----- - -----| - ----- - -----
|.....|
|...|--------|
|...|
|...|
|...|
|...|
|...|
|----|
 
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?
 
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