Deflection of uniform plates during vibration

[tikina33]

Which rectangular plate would have higher delection for a G force: a plate free on four sides and a plate simply supported on four sides? I know the resonant frequency is higher in case of simply supported plate. So the deflection would be smaller in simply supported plate because deflection=(9.8*G)/(f^(3/2)) where f is the resonant frequency. If this is the answer, then why do people always try to keep the plates free instead of supporting or fixing in their design?

Thank you.

 

[badbunny]

Hi, what is the loading for the plate free on all sides to give a uniform body acceleration? Pete.

 

[badbunny]

Actually you talk about resonance, so it is a dynamic G load. Where is the dynamic loading coming from? A fluctuating pressure? A component mounted to the plate? It would be useful if you could provide a bit more info about the problem you're thinking about, specifically the boundary conditions of the real structure, and the loading. Pete.

 

[tikina33]

Yes resonance happens when there is dynamic loading. Right now I am only talking fundamentals: That if a plate is held on all sides in an edge guide which resembles a simply supported condition, then the deflection is less than if the plate is floating i.e., if the plate is loosley held in the edge guide. Floating here means that the plate is held in the edge guide where the gap is very large so it just sits on the support but it can move freely. And such free floating condition would give more deflection in dynamic loading. So my question is why people go for such free floating design when the deflection is more which is more damaging?

 

[badbunny]

Hi Tikina, I think it becomes more complex for the situation you are describing because it has a non-linear boundary condition, ie stiffness for one direction, zero stiffness for the other. If it has a net load such that the edge is always sat down in compression, then this is effectively a simply supported boundary. If it is responding such that it can lift off then it becomes a whole lot more complex (think bouncing) and I don't think you can directly compare it to an unrestrained hand calc for natural frequency. Interested to hear your thoughts on this. The reason I'm thinking bouncing is a while back we looked at a road access hole cover plate which was bouncing up from its frame and slamming down again following certain types of road vehicle wheel loads. Pete.

 

[tikina33]

I agree with you on the simply supported boundary condition and the bouncing. Then floating boundary condition I can think of is a plate floating in air. Then there can never be a physical case where a plate can have a floating boundary condition because it has to be held by some object or sit on something and then other boundary conditions apply.

 

[badbunny]

I'm not sure if you can talk about it on here, but I'd be interested to know what application you were thinking about with this. Pete.