Plate Deflection under Bending Loads

[Jieve]

Hello,

I am designing a machine to demonstrate machine vibration phenomena to students at our technical college. An assembly is bolted to a flat plate 10mm thick of 6082-T66 Aluminum, 370mm x 618mm reinforced with U-Channel (same material) welded on length-wise along the bottom, and the entire assembly is supported on spring isolators. I am interested in determining the maximum bending deflection of the plate due to the fluctuating loads acting on it. Will I get anywhere near an accurate solution using solid mechanics beam theory and treating the plate with U-Channel as a single beam, calculating the deflection and bending stresses in 2D (side view)? I think this beam would be too “wide” to fall under the criteria for achieving an accurate solution with this method, but I’m not sure.

I looked through roark’s, there are a number of equations for deflections in different plate loading cases but I was having difficulty finding one in which the plate is reinforced by some type of channel, etc. I’d be appreciative if anyone could provide me with some direction or point me to a method of solving these types of problems. Thanks

Jieve

 

[prex]

How many channels and what size?
If the channels run in only one direction, the deflections due to bending in the transverse direction could be much higher than beam like deflections.
Also: how is the assembly supported? At four corners or...?
A sketch would be helpful.

prex

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[Jieve]

Thanks for the response, Prex.

The assembly is supported at four corners by spring isolators similar to these:

http://www.kineticsnoise.com/hvac/floor.html

There are holes at each corner through which the height adjustment screws are attached.

There are 3 longitudinal U-channels - one down the center, 20x80x20x6mm, and two on each side of it, 20x30x20x3. They run about the entire length of the plate.

There ARE actually pieces of U-Channel welded transversely between these at a few locations, however I was neglecting them for the calculation. If there is an approximate way to incorporate these as well, that would be helpful.

I'm attaching a jpeg of the bottom of the plate. The back 4 pieces welded transversely are 20x80x20x6 and the 2 front transverse pieces are 20x30x20x3.

Thanks,
Jieve

 

[rb1957]

if you want an accurate number, i'd go with FEA.

if you want a simple number, i'd go with a handbook, using a rectangle bounded by the channels ... the length x 1/2 the width; as i see these surfaces vibrating individually, and the channel would provide a bunch of support.