Нестационарные колебания в системе из двух связанных осцилляторов в условиях кубической нелинейности и кубической связи. Часть 1. Мультирежимный характер колебаний

Abstract

The task about the excitation of magnetoelastic vibrations in geometry of magnetostriction transducer which contains normal magnetized ferrite plate excited by alternating magnetic field is investigated. It is proposed the model presentation of transducer in the view of two connected oscillators first of its corresponds to magnetic part of structure and the second correspond to elastic its part. The first oscillator is linear and the second is nonlinear. The nonlinearity and connection have cubic character. In dependence from the excitation level it is found five basal regimes of vibrations: №1 – synchronize, №2 – three-multiplication of frequency, №3 – chaos, №4 – gigantic oscillations, №5 – delayed stabilization. In these regimes the time-evolvent of vibrations and its parametric portraits in coordinates displacement – derivative from displacement and also frequency spectra of forced vibrations are investigated. The regimes №1б №2 are stable. The vibrations in this regimes are harmonic and complete determined. The regimes №3-№5 are non-stable. The vibrations in this regimes has chaotic or near to chaotic character. On the level of excitation the stable regimes are separated from non-stable by sharp threshold. By the overcoming of which the vibration amplitude increases by sharp jump over two-three orders. By the excitation on non-stable regimes it is established the application on the main vibrations the attendant vibrations. The frequency of attendant vibrations is higher than excitation frequency on two-three orders. The amplitude of attendant vibrations is smaller than the main vibrations amplitude more then two orders. It is proposed the model of attendant vibrations excitations. On the basis of this model the quantity appreciation of vibrations character in non-stable regimes. The recommendations for future development of investigations are proposed.