Нестационарные колебания в системе из двух связанных осцилляторов в условиях кубической нелинейности и кубической связи. Часть 2. Вариация параметров системы

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. The dynamics of transducer is investigated on the basis of equations system for nonlinear vibrations of two connected oscillators – magnetic and elastic. The equation for magnetic oscillator is nonlinear and for elastic oscillator – linear. The nonlinearity and connections between oscillators have cubic character. In connection with excitation level there are five basal regimes: synchronize, three-multiplication of frequency, chaos, gigantic oscillations and delayed stabilization. The first two regimes are stable, without-threshold and completely determined. The remaining three regimes are non-stable and separated form stable regimes by sharp threshold by the excitation level. It is shown that by the increasing excitation level the vibrations amplitude approach to saturation experiences in value jumps about one and half or two times. The dependence of vibrations threshold of non-stable vibrations from excitation frequency is investigated. It is shown that by increasing the excitation frequency the threshold on non-stable vibrations in very high precision increases by power low of third ore fourth order. The character of vibrations by variation of oscillator dissipation is investigated. It is found that the primary influence on the character first oscillator vibrations exercise the dissipation not first but second oscillator. The variation of own oscillators frequencies is investigated. It is shown that the increasing of own oscillator frequencies leads the system to chaos and further to regularization of vibrations. The decreasing of own oscillator frequencies leads to compressed sine with centre displaced regime and leaving of system to infinity. The variation of cubic nonlinearity of first oscillator is investigated. The large nonsymmetry of variation of vibration character by nonlinearity parameter to both sides is established. The decreasing of nonlinearity parameter leads to compressed sine with displaced centre and further leaving of system to infinity. The increasing of nonlinearity parameter leads to chaos and regularization. The variation of connection between oscillators is investigated. It is found that the variation of connection parameters any of oscillators leads to the same order of regime replacement – from regularization to chaos, gigantic oscillations, delayed stabilization, compressed sine and leaving to infinity. On the plane in coordinates first and second connection parameters the regions of existence different regimes of vibrations is constructed. For the interpretation of described phenomena the model of dynamic potential is proposed. It is shown that the potential of first oscillator has minimum the place of which is determined by value of displacement of second oscillator. The course of chaotic vibrations in non-stable regimes is the difference of phase between vibrations of oscillator and jumps of potential in which these vibrations take place. The ring character of vibrations excitation in system as a whole is considered. The analogy with autovibrations in radioengineering system with positive opposite connection is proposed. The recommendations for further development of investigation are proposed.