Auto-oscillating Systems Research Articles

Class of Auto-Oscillating Systems

This article proposes a model that generalizes the well-known equations of the nonlinear theory of oscillations (Van der Pol and Rayleigh equations), the limit cycles of which are the curves of the phase plane, determined by the total energy of oscillations in the absence of dissipation/energy inflow into the system. By changing the parameters of the system and the type of force action, it is possible to set the oscillation characteristics that are resistant to disturbances. The phase portraits of the system are considered, including the case of multiply connected limit cycles.

Modeling of self-excited stress measurement system

In the paper two types of numerical models of the self-excited acoustical system are presented. This new type of auto-oscillating system is used for stress change measurement in constructions and rock masses. The essence of the self-excited acoustical system is to use a vibration emitter and vibration receiver placed at a distance, which are coupled with a proper power amplifier, and which are operating in a closed loop with a positive feedback. This causes the excitation of the system. The change of the velocity of wave propagation, which is associated with the change of the resonance frequency in the system is caused by the deformation of the examined material. Stress changes manifest themselves in small but detectable variations of frequency. The first of the presented models was created on the basis of estimating the model parameters by identification of the sensor–conditioner–amplifier–emitter system. The second mathematical model was delivered from the force–charge equation of the piezoelectric transducers: the sensor and the emitter. The model of the loaded beam, which determined the response of any beam point to the force applied to any other beam point is also presented.

Development of auto­oscillating system of vibration frequency sensors with mechanical resonator

At present, resonator sensors with an auto-oscillating system have a number of advantages in comparison with the known sensors with frequency output. In this case, developed auto-oscillating systems of resonator sensors are very specific; their elements are oriented toward a particular type of resonator and possess a certain degree of nonlinearity, which makes studying and modeling such systems impossible. In the present work, analytical expressions were obtained for the reduction of parameters of mechanical systems of resonators to the lumped ones. This allowed us to apply the methods of research into nonlinear systems of control to the analysis of AOS and to receive the expression of transfer function of nonlinear resonator with consideration to the nonisochronicity. A structure of auto-oscillating system with a nonlinear resonator is devised, which was not explored earlier. With the purpose of selecting the character of nonlinearity in the elements of feedback and mechanical resonator of the assigned type in AOS to warrant the assigned stability of frequency and amplitude of auto-oscillations, we performed imitation simulation in the Matlab Simulink programming environment. The simulation demonstrated that a nonlinear amplifier at work with a nonlinear mechanical resonator provide for the auto-oscillating system that is stable by frequency and amplitude. Thus, auto-oscillating system of the devised structure can be used in the design of vibration frequency sensors.

Nonlinear Auto-Oscillator Theory of Microwave Generation by Spin-Polarized Current

This paper formulates a general analytic approach to the theory of microwave generation in magnetic nano-structures driven by spin-polarized current and reviews analytic results obtained in this theory. The proposed approach is based on the universal model of an auto-oscillator with negative damping and nonlinear frequency shift. It is demonstrated that this universal model, when applied to the case of a spin-torque oscillator (STO) based on a current-driven magnetic nano-pillar or nano-contact, gives adequate description of most of the experimentally observed properties of STO. In particular, the model describes the power and frequency of the generated microwave signal as functions of the bias current and magnetic field, predicts the magnitude and properties of the generation linewidth, and explains the STO behavior under the influence of periodic and stochastic external signals: frequency modulation, phase-locking to external signals, mutual phase-locking in an array of STO, broadening of the generation linewidth near the generation threshold, etc. The proposed nonlinear auto-oscillator theory is rather general and can be used not only for the development of practical nano-sized STO, but, also, for the description of nonlinear auto-oscillating systems of any physical nature.

Determinate and random processes in cyclic and dynamic systems

A method for the description of fluctuations (variations) in the period of the motion of cyclic-dynamic systems elements is presented. The random change of the period of cyclic mechanisms, high-Q oscillators and auto-oscillating systems, as well as random changes of the time intervals between the moments of passing fixed linear co-ordinates by the moving mirror of a Fourier spectro-radiometer is studied. It is shown that the period of the fluctuations follows from a non-Markov random process.

Two modes of operation of a model combustion chamber as a thermoacoustic autooscillating system

It is shown that soft and hard modes of operation of a model combustion chamber as an autooscillating system are possible. In the case of oscillations with transverse acoustic waves we: a) determined the ranges of these modes experimentally; b) detected oscillatory hysteresis (“persistence”) effects and observed the abrupt appearance and disappearance of oscillations during gradual variation of the parameters. We also noted excitation of autooscillations when finite perturbations acted on the gas column in the combustion chamber in the case of the hard mode.