Wednesday, February 27, 2008

Wave Prop 3

Today I simulate a shake table. These horrible things are in every seismic lab in the country, because they look sooo cute! And you can get a lot of pork money if you build the 'world's biggest' shake table.

In terms of Shrekian Analysis, we have to do terrible things to emulate a shake table. First, it is a massive steel thing, driven by huge hydraulic actuators. So you glue down your building to something that has a seismic reflection coefficient of 1.0. That is, everything is reflected back. They sometimes try to approach reality by putting in internal damping, or soil springs, but this has the irony that only crummy buildings get to absorb energy, and crummy foundations have some damping. It is better to build a crummy steel building on soft soup, than a decent stiff building on rock!

For my Shrekian shake table, I put on a big block of aluminum, and glue it down to solid steel. In proper terms, it means that I constrain the lower nodes to only roll in the x direction. I specify the x velocity as a sinusoid, at about the fundamental frequency of the block. This way I will get lots of resonance! You can see the lead propagation will be reflecting off the top and bottom boundary, and really starts shaking!

The fallacy here is that whatever you put on the shake table has 100% energy storage in resonance. In reality, a stiff structure such as a nuclear power plant, on a stiff foundation, has a high seismic transmission coefficient. That means the seismic energy goes in and goes out. There is no resonance. This assumption is costing Darlington about 1 billion dollars.

Next time, I try and show reality, as soon as I find absorbing boundary conditions.


Anonymous said...

And the dimensions of said "aluminum Block" are??!!

It appears to be a block of warm jello!

Harold Asmis said...

I've amplified the displacements by thousands of times. Normally, you wouldn't see anything.