PHYSICAL MATHEMATICS SEMINAR
TOPIC: SELF-ADAPTATION IN VIBRATING SYSTEMS:
FROM STRINGS TO SOAP FILMS
SPEAKER: AREZKI BOUDAOUD
Department of Mathematics
Massachusetts Institute of Technology
ABSTRACT:
Vibrating systems with additional degrees of freedom are studied
experimentally and theoretically. They exhibit specific dynamics
characterized by the existence of a self-adaptative behaviour: The
additional degrees of freedom adapt to the forcing and the resonance
spectrum is continuous instead of being discrete, as demonstrated through
two examples. First, a system where a mass is free to slide on a
vibrating string is investigated. In wide forcing frequency bands, the
mass adjusts its position so that the whole system becomes resonant. The
theoretical model accounts for all the observations. A continuous limit
of this system is exhibited. Then, the vibration of a soap film set into
motion by a sound wave is considered. The film has oscillations of large
amplitude for all frequencies. The interference fringes observed in
monochromatic light show the adaptation of the film mass distribution.
The theoretical model accounts for the thickness spatial variations and
the vibration amplitude and thus gives an interpretation of the
self-adaptative behaviour of the film.
DATE: TUESDAY, SEPTEMBER 18, 2001
TIME: 2:30 PM
LOCATION: Building 2, Room 338
Refreshments will be served at 3:30 PM in Room 2-349
Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 02139