Acoustic Chaos Caused by the Sommerfeld Effect

Abstract

The vibrations of an infinite plate in contact with an acoustic where the plate is subjected to a point excitation by an electric motor 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 are determined: stationary, periodic and chaotic. The vibrations of the plate and the pressure in the acoustic fluid are described for each of these regimes of excitation. For the first class they are periodic functions of time, for the second they are modulated periodic functions, in general with an infinite number of carrying frequencies, the difference between which is constant. For the last class they correspond to chaotic functions. In another mathematical model where the exciter stands 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 shaft rotation. In this case the process of rotation can be approximately described as a solution of the fourth order nonlinear differential equation and may have the same three classes of steady-state regime as the first model; i.e., the electric motor may generate periodic acoustic waves, modulated waves with an infinite number of frequencies, or chaotic waves in the fluid.