Normal Modes of a Stadium

These are pictures of normal modes of a Bunimovitch stadium. It consists of an aluminum plate 194 mm long by 100 mm wide by about 3 mm thick. The plate is attached via a screw through a hole in the middle to a resonator. The whole system is driven by an HP function generator putting out a 10 volt RMS sine wave at the frequencies indicated next to the pictures. All frequencies in Hertz. The modes are visualized by sand. When you hit a resonant frequency the thing is amazingly loud. Hearing protection definitely required.

Obviously the plate is not perfectly symmetric; although it was cut on a computer controlled milling machine and polished. Driving at the center was purely for convenience. Still, it's interesting that one of the modes has a node line straight through the center. Perhaps the most interesting modes are 1026 and 10011. These are the only modes I saw with particle motion transverse to the node lines. This sets up beautiful steady-state circulation patterns. For all the other modes shown, the sand moves normal to the node lines during the transient phase during which the sand settles into the nodes. The thickness of the lines is entirely a function of how much sand I dropped onto the plate. For each visualization I started with a clean plate.

For other nice Chaos pages see: The Quantum Chaos Group Darmstadt A very useful list of chaos pages is maintained by this group.

320 920 1007 1026 1754 2116 3990 4011 5915 7264 8764 10011