ACOUSTIC CHAOS CAUSED BY THE SOMMERFELD EFFECT

The vibrations of an infinite plate in contact with an acoustic medium where the plate is subjected to a point excitation by an electric mot or of limited power-supply are considered. The whole system is divided into two: ''exciter-foundation'' and ''foundation-plate-medium''. In the system ''motor-foundation'' three classes of steady-state regime a re determined: stationary, periodic and chaotic. The vibrations of the plate and the pressure in the acoustic fluid are described for each o f these regimes of excitation. For the first class they are periodic f unctions of time, for the second they are modulated periodic functions , in general with an infinite number of carrying frequencies, the diff erence between which is constant. For the last class they correspond t o chaotic functions. In another mathematical model where the exciter s tands directly on an infinite plate (without foundation) it was shown that chaos might occur in the system due to the feedback influence of waves in the infinite hydroelastic subsystem in the regime of motor sh aft rotation. In this case the process of rotation can be approximatel y described as a solution of the fourth order nonlinear differential e quation and may have the same three classes of steady-state regime as the first model; i.e., the electric motor may generate periodic acoust ic waves, modulated waves with an infinite number of frequencies, or c haotic acoustic waves in the fluid.