T.S.Krasnopolskaya Acoustical chaos in an infinite halfspace caused by the Sommerfeld-Kononenko effect |
Acoustic bulletin, Vol. 5 ¹ 3, (2002) |
| Vibration of an infinite plate contacting to an acoustic medium, where the plate is subjected to excitation by a motor of limited capacity, is considered. Considered system is divided into two subsystems: "motor-foundation" and "foundation-plate-medium". In the subsystem "motor-foundation" three classes of steady-state regimes are determined: the stationary, the periodical and the chaotic ones. For the first class of regimes the vibrations of the plate and the pressure in an acoustic fluid are periodic functions of time, and for the second they are modulated periodic functions (in general case, containing the countable set of harmonics having the frequencies at constant interval. The vibration and the waves corresponding to the third class are described by the chaotic functions having the continuous frequency spectra. For the system where the motor stands directly on an infinite plate (without foundation) it is shown that the chaos might occur in the system due to the feedback influence of waves, arising in the infinite hydro-elastic subsystem, onto the regimes of motor shaft rotation. In this case the process of rotation can be described as the solution of the fourth-order nonlinear differential equation. Here exists the same three classes, as for the model with elastic foundation. It is shown that the motor can generate three types of waves in the medium: periodic waves, modulated waves with an infinite number of harmonics, and the chaotic ones. |
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KEY WORDS: the effect of Sommerfeld-Kononenko, partial subsystem, stationary regime, the acoustic chaos |
| TEXT LANGUAGE: Russian |