We considered the possibility of detecting a combined two-frequency effect of an alternating magnetic field in a ferrite plate. The main attention is paid to the properties of excited elastic oscillations when changing the magnitude of the alternating field and the plate thickness. The character and features of the magnetic and elastic oscillations excitation under resonance conditions at a difference frequency in linear and nonlinear cases are considered. It is noted that detection at the difference frequency has a pronounced nonlinear character, since it occurs only at a sufficiently high excitation level. The efficiency of elastic oscillations excitation at the difference frequency under various parameters of material and conditions has been evaluated.

The task about interaction of super-short light pulse on magnetoelastic system which has precession motion of magnetization is investigated. As a main mechanism it is investigated the decreasing of magnetization with power light action on spin system. It is investigated the development of magnetization precession by the action of light pulse. It is found that during the pulse action the amplitude vibrations is decreased and its frequency is increased. It is investigated the precession development in different meanings of light power. It is established the multi-regime character of magnetization vibrations by small pulse duration which is the same order as signal excitation period. It is established three regimes: regime №1 – stabile vibrations, regime №2 – the destroy of stabilization, regime №3 – shock excitation. It is established that the main distinguishing of regime №3 from first two regimes is the sharp jump increasing of amplitude as magnetic so the elastic vibrations which take pulse as a result of pulse action. It is found that as a result of high power long duration pulse it is arising the regime of in-flatness magnetic component stabilization. It is found that the main role in formation of this regime plays the magnetoelastic interaction.

The nonlinear magnetization precession in normal magnetized ferrite film which has magnetic, elastic and magnetoelastic properties is investigated. The excitation field is presented as a vibration on resonance frequency which is modulated by short pulses which frequency is more lower than resonance frequency. It is proposed the formation procedure of periodic succession of ultra-short pulses by the involution to even degree of modulation signal sine. It is found two different cases of excitation: first when modulate pulse duration is larger than initial signal period and second when modulate pulse duration is smaller than initial signal period. In the first case the modulated signal has the form of main frequency vibrations tandem and in the second case the modulated signal has the form of unit sign-variation pulse. It is investigated the time development of magnetic and elastic vibrations whish are firmed by excitation field. It is shown that in the first case the magnetization vibrations at first hat sharp jump to upward and after this decreases by exponent. In this case the elastic vibrations after the same jump at first increases and then decreases by exponent. The elastic vibrations behaviour is interpret as energy pump from magnetic system to elastic system. In the second case the initial jump both vibrations is absent. It is investigated the degree modulation index influence to excited vibrations. It is shown that by increasing of this index the amplitude of magnetic and elastic vibrations decreases. It is investigated the magnetization excited vibrations character by different degree of magnetoelastic connection. It is introduced the coefficient multiple of magnetoelastic constant which is equal to ratio of considered constant to value of magnetoelastic constant of yttrium iron garnet. It is shown that by increasing of multiple coefficient the magnetization vibrations period is increased. It is found the sharp increasing the period by determined value of multiple coefficient which has a threshold character. It is investigated the excitation of magnetization in large time interval when the multiple coefficient is above the threshold value. It is found the principle difference between two cases when pulse duration is large or smaller as alternating field period. It is shown that in the first case the magnetization vibrations has the character of equilibrium position precession in conditions of orientational transition. In the second case the magnetization vibrations has the form of periodic re-orientational jumps from one equilibrium position to another. It is mentioned some properties of observed phenomena and proposed some recommendations for further investigations.

The parametric excitation of non-stationary magnetoelastic vibrations in magnetostriction converter by action of light from femto-second laser is investigated. The scheme of sine modulation of saturation magnetization is investigated. It is found two regimes: sign-constant and sign-varied. It is shown that by sign-varied modulation it is organized sharp pronounced non-stationary delay splash of amplitude magnetic and elastic vibrations. It is shown that in mechanism of splash formation the mast role plays magnetoelastic interaction. It is investigated the splash amplitude dependences from magnetoelastic constant, parameters magnetic and elastic relaxation, constant field value and thickness of magnetoelastic plate. It is investigated the splash structure by variation of step in time. It is shown that the step variation causes to changing of splash position in time and its amplitude so as splash has fractal character. It is proposed some recommendations for work development.

The nonlinear dynamics of the magnetic and elastic subsystems of an yttrium iron garnet film excited by an alternating frequency-modulated magnetic field has been studied. The possibility of demodulating a frequency-modulated signal on a microwave magnetostrictive film transducer has been considered. The dependence of the excitation of oscillations of a magnetization vector and elastic displacements on the material and excitation parameters has been determined.

The authors demonstrate the possibility of using a magnetostrictive transducer to detect a frequency-modulated microwave signal. Elastic and magnetization oscillations of a ferrite film with crystallographic anisotropy are considered. The influence of the orientation of the crystallographic cell on the dynamics of the magnetoelastic system, the establishment of various oscillations modes, and the detection process are analyzed.

In this paper, we consider the problem of generation of hypersonic oscillations in the circuit of a magnetostrictive converter covered by a positive feedback circuit. A “coupling parameter” that reflects the amplification of the signal in the feedback loop was introduced. The development of magnetic and elastic oscillations in time is considered. As the coupling parameter increases, three main oscillation modes are revealed: initial relaxation, stationary self-oscillations, and chaotic self-oscillations. The effect of the coupling parameter and the damping parameter of the magnetization on the time of development and the amplitude of oscillations was studied. The characteristic values of both parameters corresponding to transitions between modes are revealed. Practical recommendations for choosing system parameters for the most efficient excitation of hypersonic oscillations are given.

A study is performed of oscillations of magnetization and elastic oscillations in a YIG film. Parametric portraits are presented for oscillations of the vector of magnetization, time sweeps of elastic oscillations, and their amplitude–frequency characteristics at different depths of modulation and strengths of an ac magnetic field. The dependences on the modulation depth and the amplitude of the alternating field are also given. The conditions for effective detection of external magnetic field oscillations are determined.

Oscillations of the magnetoelastic subsystem of a ferrite film excited by an amplitude-modulated alternating magnetic field are studied. The possibility of detecting oscillations at the modulation frequency due to the magnetostrictive properties of the magnetic film is considered. The dependence of the excitation of magnetic and elastic dynamics on the material and excitation parameters, including the type of polarization of an alternating magnetic field, is determined.

A study is performed of the second-order precession of the vector of magnetization in a two-layer magnetically coupled structure. Numerical solutions are obtained for the dynamics of the magnetic subsystem of a two-layer film. Parametric portraits of the vector of magnetization’s motions are constructed for the effect external asymmetric fields and internal fields of anisotropy have on the dynamics of magnetization. A correlation is established between interlayer coupling and the character of parametric magnetization portraits.

The detection of an amplitude-modulated magnetic linearly polarized alternating field on the elastic subsystem of a magnetic film is considered. The dynamics of oscillations of the magnetization vector and elastic displacement of an isotropic film and films with different orientations of the easy axes of cubic anisotropy with respect to the normal is studied. Parametric patterns of oscillations of magnetization vector components and frequency characteristics of excited oscillations of magnetization and elastic displacement are constructed. The dependence of the oscillation modes of the elastic displacement of the magnetic film on the amplitude of the alternating magnetic field strength and the modulation index is determined.

The task about nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies is investigated. The thickness of plate is chosen so as the frequency of its elastic resonance was equal to difference of two components of alternating field. The most attention is given to properties of excited elastic vibrations by changing the value of applied constant field. The system of nonlinear motion equations of magnetization and elastic displacement is described. For solving of this system, the numerical method Runge-Cutta is applied. The results of this calculation are the time-evolvent of vibrations, dependencies magnetic end elastic vibrations amplitudes and also the spectra of vibrations in permanent conditions after end of relaxation processes. The influence of constant field value on character of vibrations is investigated. The comparison of amplitude-frequency characteristics of magnetic and elastic vibrations in linear and nonlinear regimes by the thickness of plate correspond to resonance on central and different frequencies is carried out. It is shown that by thickness which correspond to resonance on different frequency the characteristic has large indented skirting. It is found the large variety of dependencies of elastic vibrations character from field. In condition of stabilization so as after the completion of relaxation establishment processes it is found five more character regimes of vibrations: regime №1 – small-amplitude chaos; regime №2 – regular vibrations; regime №3 – non-symmetrical doubling of period; regime №4 – symmetrical doubling of period; regime №5 – irregular beating. For each of regimes the evolution of vibrations along time are obtained and the corresponding frequency spectra are found. The localization of regimes along the value of constant field by difference excitation level is investigated. It is found that the region of large-amplitude regimes (№2–№5) is limited in both sides by regions of small-amplitude regime №1. It is found that inside of region where large-amplitude regimes take place the most extended regime is generalized regime with doubling of period which is the sum of regimes №3 and №4 which occupies about 79%. The next on prevalence it the regime №5 – irregular beating which occupies 13% of whole region. The most exceptional is the regime №2 – regular vibrations which occupies only 8% from whole interval. It is found the extremely large critical intending of dependence of elastic vibrations amplitude from constant field. It is found that the structure of amplitude-field characteristic is very sensual to excitation level and plate thickness and the degree of sensitivity reach part of percent. From the comparison of localization on field by magnetic and elastic characteristics it is found that elastic characteristics as a whole are displaced down along field relatively magnetic characteristics. In this case the low-field falling of elastic characteristics is localized on the same falling of magnetic characteristics but the high-field falling of elastic characteristics is localized slightly lower of the field value which correspond to ferromagnetic resonance on central frequency. It is found that the reason of this displacement in this case is elastic resonance of plate on difference frequency. The card of regimes on the plane "alternating field – constant field” along broad interval of varying of both fields is constructed. It is found that by the constant field the large-amplitude regimes on the card occupy the “curved-linear trapezium” which axis lies along the coordinate “alternating field” and transverse width along coordinate “constant field” by increasing of alternating field is increased. It is found that outside of both sides by constant field of this “trapezium” the low-amplitude regime №1 – “small-amplitude chaos” is exited. The middle of “trapezium” occupies the strip directed along coordinate “alternating field” which is filled by regime №5 – “irregular beating”. Along both sides from this strip also right until the boundaries of “trapezium” the regimes №3 and №4 – “doubling of period” are excided. The reasons and necessary conditions of chaotic character of elastic vibrations are investigated. It is found that the necessary condition of chaos is excitation simultaneous in two frequencies. It is found that the large indented jumping character of dependence elastic vibrations amplitude from constant field has as first-reason the chaotic character magnetic vibrations. The character of jumps in dependence elastic vibrations amplitude from constant field is investigated. It is shown that by two-frequencies excitation the increasing of step along field causes large increasing of indenting of characteristics. It is found that the same behavior of amplitude-field dependencies of vibrations reveals its fractal character. The some comments about nature of jumps are proposed. It is found that jumps are determined by non-permanent character exactly magnetic vibrations which are shown only by two-frequency excitation on enough large level and have fractal character. As an analogy is mentioned that the line (skirting) of elastic vibrations field dependence on the plane “amplitude-field” is similar to chaotic trajectory of time-evolvent of vibrations on the plane “amplitude-time” for different oscillators which show chaotic vibrations. It is mentioned that the same behavior of trajectories on the plane “coordinate-potential” take place in cases when potential has dynamic character. The supposition is proposed that in investigated here task about two-frequency excitation of magnetostriction transducer may by constructed the function which can play the role of dynamic potential.

The task about nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies is investigated. As a most important parameter which is varied it is proposed the relative thickness of plate which is determined as relation of real thickness to the thickness which correspond to elastic resonance on the difference of excitation frequencies. It is established the necessity of choosing of character value of constant field which is determined by enough effective excitation of elastic vibrations. The system of nonlinear equations of motion of magnetization and elastic displacement is described. For solving of this system, the numerical Rounge-Cutta method is applied. The results of this calculation are the time-evolvent of vibrations, dependencies magnetic end elastic vibrations amplitudes and the spectra of vibrations in permanent conditions after end of relaxation processes. It is found the multi-regime character of elastic vibrations which takes place by variation of plate thickness. In the character of development of elastic vibrations in time by the increasing of plate thickness it is found four regimes: regime №1 – regular beatings, regime №2 – established resonance, regime №3 – displacement of center of established vibrations, regime №4 – gigantic oscillations. The intervals of thickness values which are necessary, or realization of these regimes are determined. The properties of each regimes taken separately are investigated. It is found that the regime №1 is realized when the thickness of plate is more less then the thickness of resonance on differential frequency. In this case the elastic vibrations in generally repeats the vibrations of magnetization which are realized as beating between two frequencies of excitation. The regime №2 takes place when the plate thickness is near to resonance on differential frequency. When thickness is corresponds to resonance on differential frequency it is found large raising of resonance character. In the vibrations of elastic displacement, the constant component is discovered. The regime №3 takes place when the plate thickness is exceeded of resonance on several (from two to seven) times. The vibrations of magnetization in this regime are the same as in regimes №1 and №2. The elastic displacement has two components: oscillatory on differential frequency and constant which value by increasing of thickness smoothly is increased. The displacement of center of oscillatory component by thickness is increased has quadratic character. The regime №4 takes place by plate thickness exceeds resonance thickness on the order and more. The vibrations of magnetization maintain the character of beating which are the same as in regimes №1, №2 and №3. The vibrations of elastic displacement are characterized by extremely large amplitude which is more then the amplitude in regime №3 on order and more and has extremely large period which is more then period of differential frequency vibrations on two-three order and more. The amplitude of vibrations and its period by the thickness is increases also increase by linear meaning. The some quality opinions about the nature of observed phenomena are proposed. It is established the specific character of two-frequency excitation in comparison to single-frequency excitation. As the possible task it is proposed the plan of singing the part of solution as dependence of vibration amplitude from plate thickness has quadratic character with necessary appreciation of two-frequency excitation. The mechanical analogy for vibrations of hard rod which is compressed on both ends by approaching forces is proposed. This analogy allows to interpret the displacement of vibrations center and gigantic oscillations regime.

The task about nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies is investigated. As a preliminary task the investigation of only magnetic vibrations by two-frequency excitation is carried out. The possibility of description of forced linear vibrations on the basis of single nonuniform linear second order equation with arbitrary excitation is shown. It is found the analytical solution of task about excitation of oscillator by two signals which frequencies are distinguishes up and down from central frequency on the same frequency interval. It is shown the equivalency of representation of magnetic vibrations in linear regime and model vibrations on the basis of oscillator. It is found that in the general case the vibrations have view as beating which rounding frequency is equal to difference between excitation frequencies. The whole positing of task about excitation of nonlinear magnetoelastic vibrations in normal magnetized ferrite plate by two-frequency excitation is proposed. It is found that in conditions of large nonlinearity when the own elastic resonance of plate is equal to the difference frequency the powerful elastic vibrations are excited. It is found the nonlinear excitation of powerful non-resonance vibrations which take place also in the case of large elastic dissipation. It is shown that the non-resonance vibrations are determined precisely two-frequency character of excitation. It is found that the amplitude of non-resonance vibrations by increasing of plate thickness also is increased. By the small level of excitation, the low of increasing is linear, by middle – quadratic, by large – again approaches to linear with saturation and non-permanent sudden jumps. The character of excitation in conditions of resonance on difference frequency is investigated. It is shown that this resonance has powerful determined nonlinear character because it arises only by enough large excitation level. It is shown that the further increasing of resonance amplitude by the increasing the excitation level is realized by the low which is near to quadratic. But after this increasing when excitation level reaches determined value the resonance amplitude is saturated and remains constant. It is drawn attention to some discrepancy between the realization on nonlinearity by magnetic and elastic systems. For the de-scription of this discrepancy the empirical quadratic dependence is proposed. In brief is proposed some remarks about further development of work.

The paper analyses the issues of small and medium entrepreneurship development in the Arctic environment and proposes ways to solve them. The proposed mechanisms of organisational and economic stimulation of small and medium entrepreneurship in the Arctic refer to the theoretical and institutional foundations considering not only the elements of market relations but also - given the features of the Arctic - the principal role of the state. The methodology and capabilities of government stimulation of small and medium entrepreneurship in the Arctic are employed, as well as innovation-driven approaches, particularly the development of Arctic venture as a specific instrument. An analysis of the developmental factors of small and medium entrepreneurship in the Arctic environment highlights the governance aspects, particularly, the major role of efficient public, municipal and corporate governance, as well as the need to improve social and environmental responsibility standards. The possibility of establishment of special (free) economic zones is substantiated with a view to transforming the Arctic areas as a special tax and administrative zone and easing the conditions of doing business.