An autostochastic system with parametric excitation

The parametric excitation of chaotic motions in a dynamic system with a resonator in a delayed feedback chain is numerically analyzed. It is shown that the structure of oscillations can be effectively controlled for a resonator parametrically pumped with both regular and chaotic signals.     

Transients in an autostochastic oscillator with delayed feedback

A numerical analysis of the turn-on transients in an autostochastic oscillator with delayed feedback is reported. Dependence of the transients on the intensity of chaotic initial conditions is studied. It is demonstrated that the chaotic oscillations may switch from one basin of attraction to another.     

Controlled stochastization of oscillations in a chaotic delayed-feedback system

A mathematical model of the ring autooscillatory system, which possesses chaotic dynamics and comprises a nonlinear amplifier with a differentiating element in the feedback chain, a nonlinear oscillatory circuit, and a delay line, is considered. Numerical analysis has been performed for irregularly varying initial conditions. These conditions were set by the solutions of equations describing chaos that simulated intrinsic noises of a real autooscillatory system. It is shown that the irregularly varying conditions of excitation can lead to stochastization of the chaotic oscillations, in which case the oscillatory process becomes irreproducible.     

Surface- and interface oscillations in an immiscible spherical visco-elastic system

Summary The transcendental frequency equation is presented for various visco-elastic immiscible spherical liquid arrangements exhibiting free surface- and interfacial tension. The system is in a zero-gravity environment. The natural damped frequencies depend on the viscosity, surface tension, density and the Maxwell relaxation time. For a freely floating sphere the numerical results of the frequency equation are presented and exhibit with larger surface tension higher natural frequencies, for small relaxation times stronger and for larger relaxation times weaker decay of the oscillations. The increase of viscosity renders stronger decay of the oscillations. For smaller surface tension the oscillation ceases to exist and yields for small relaxation parameter /a ² an aperiodic motion of the drop, while for higher surface tension the oscillation of the visco-elastic sphere exhibit higher frequencies and larger decay. Increase of visco-elasticity (relaxation time) renders the begin of aperiodic motion of a liquid sphere a larger diameter. For further increased relaxation time, however, the sphere always oscillates.List of Symbols a radius of undisturbed outer free liquid surface of sphere - b radius of undisturbed interfacial surface - c radius of undisturbed inner free liquid surface - I _n ,K _n modified Besselfunctions of ordern and first and second kind resp - p _j pressure in regionj=1, 2 - P _n ⁰ Legendre polynomials - P _n ^m associated Legendre functions - r, , spherical coordinates - complex, frequency, - t time - T ₀₁ outer surface tension atr=a - T ₁₂ interfacial surface tension atr=b - T ₀₂ inner surface tension atr=c - u _j velocity distribution in radial direction - v _j velocity distribution in -direction - x=cos or abbreviation for - _j density of liquids - _j dynamic viscosities of liquids (Newtonian limit viscosity) - v _j = _j / _j kinematic viscosities of liquids - _r normal stress - _r tangential stress - _j streamfunctionsj=1, 2 - _j relaxation time - D rate-of-strain tensor - T stress tensor - W antisymmetric part of the rate-of-strain tensor - circular frequency - free liquid surface elevation - meridial stress - angular stress - e _r unit vector in radial direction - e unit vector in meridial direction - decay magnitude - circular oscillation frequency With 7 Figures     

Damped oscillations modeled by an n-th order time dependent quasi-linear differential system

Summary. A general formula based on the extended (by Popov [4]) Krylov-Bogoliubov-Mitropolskii method [1], [2] is presented for obtaining asymptotic solution of an n-th order time dependent quasi-linear differential equation with damping. The method of determination of the solution is simple and easier than the classical formulae developed by several authors as well as the technique initiated by the original contributors [1], [2]. The general solution can be used arbitrarily for different values of n = 2, 3. The method can be used not only for periodic forcing terms, but also for some non-periodic (bounded) forces. All the solutions can be determined from a single trial solution. On the contrary, at least two trial solutions are needed to investigate time-dependent differential equations; one is for the resonance case and the other for the non-resonance case. The later solution is sometimes used in the case of non-periodic external forces. However, the resonance cases (including damped forced vibrations [7]) are mainly considered in this paper, since these are important in vibration problems.     

Controlled oscillations in chain of unidirectionally coupled bistable oscillators with chaotic dynamics

Equations of a chain of n (n = 1, 2, ...) unidirectionally coupled bistable oscillators possessing chaotic dynamics are presented. Numerical analysis has been performed for a system of three identical autooscillatory systems with nonlinear elements admitting cubic approximation. It is shown that, as the degree of coupling between units in the chain increases, their motions in the phase space become more complicated and even chaotization of oscillations may take place at the parameters with which separate oscillators exhibit regular motions in the autonomous regimes. The features of the influence of a driving oscillator on the motions of a driven bistable subsystem are related to filtration of the driving signal in the circuit of the driven subsystem.     

Self-excited oscillations in a fiber-optic laser-collimator-microresonator system

This paper proposes and studies experimentally a design for a fiber-optic self-excited oscillator, characterized by high stability of the operating point. The design appears promising for developing fiber-optic transducers of physical quantities with a frequency output. Pis’ma Zh. Tekh. Fiz. 23, 33–39 (March 26, 1997)     

Excitation of oscillations in a gas-blower-fluidized-bed system

It is shown that hydraulic characteristics in a fluidized bed oscillate in a spectrum that is discrete due to the reciprocal effect of the fluidization regime on gas-blower operation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 3, pp. 453–458, September, 1985.     

Forced oscillations in an exothermic chemical reaction

We study non-linear behaviour in a model chemical reaction scheme (proposed by Sal?nikov), in which a single chemical species undergoes a two-stage, first-order decay process. The second stage is exothermic and has a temperature-dependent rate, and as a result, spontaneous oscillations in the temperature and the concentration of an intermediate chemical are known to be possible. An additional oscillation is imposed on the system by varying the ambient temperature in a sinusoidal manner. Primary resonance occurs when the forcing frequency coincides with the frequency of the natural oscillations in this scheme and an infinite sequence of super-and subharmonic resonances is also present. Chaos is possible for appropriate parameter values and may result either from the Feigenbaum period-doubling cascade, or else as a result of the Ruelle-Takens approach through quasi-periodicity.     

Effect of TCPS on oscillations in tie-power and area frequencies in an interconnected hydrothermal power system

The analysis of automatic generation control of a two-area interconnected hydrothermal power system considering a thyristor-controlled phase shifter (TCPS) in series with the tie-line is presented. It is possible to damp the system frequency and tie-power oscillations by controlling the phase angle of TCPS. A control strategy using TCPS is proposed to provide active control of system frequency. Gain settings of the integral controllers with and without considering TCPS are optimised using integral squared error technique following a step load disturbance in each of the areas by minimising a quadratic performance index. Analysis reveals that a TCPS is quite capable of suppressing the frequency and tie-power oscillations effectively under the occurrence of sudden load changes in any of the areas when compared with that obtained without TCPS.     

Chaotic oscillations in a system of coupled triggers

A circuit consisting of two triggers coupled by a capacitance is studied. The equations of motion are presented with a cubic approximation for the nonlinear terms. It is shown by numerical analysis that chaotic oscillations can be excited. A mechanism for the transition of the oscillations to chaos is described. Pis’ma Zh. Tekh. Fiz. 25, 1–6 (March 26, 1999)     

Controlled chaotic autooscillatory system

A mathematical model of the chaotic system based on a three-dimensional modification of the van der Pol-Duffing equation is considered. Solutions possible in the presence of a chaotizing feedback algorithm are analyzed by numerical methods. It is shown that the chaotization of oscillations can be controlled by an autocommutator, and the behavior of a modified system for various parameters of the additional feedback is analyzed.     

Fluid oscillations in an open,flexible container

In this paper we study normal oscillation modes of an incompressible fluid in an open container, part of the wall of which may be flexible. The flexible part of the container wall is modelled by a membrane. We first investigate the eigenfrequencies of an inviscid fluid in a flexible container. We are able to show, by analytical means, that the eigenfrequencies of an inviscid fluid decrease when part of the rigid container wall is replaced by a membrane. The problem of viscous fluid oscillations in a flexible container is then studied numerically using the finite-element technique. Two different types of eigenmodes are observed: free-surface oscillation modes and structural vibration modes. The dependence of the two modes on the Bond number (measure of the ratio of gravitational and tension forces) and the Reynolds number is investigated.     

Torsional oscillations of an elastic stratum

Summary This paper is concerned with straightforward solution of the problem of torsional oscillations set up in an elastic stratum, one face of which is rigidly secured, by a rigid circular disk which is attached to the free surface of the material and which performs simple harmonic oscillations about its axis. The problem has been solved after reducing it to the solution of a Fredholm Integral Equation of the second kind.

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Torsionsschwingungen einer elastischen Schicht

Zusammenfassung Die Arbeit beschäftigt sich mit der Lösung des Problems der Torsionsschwingungen in einer elastischen Schicht. Diese werden durch eine starre kreisscheibe erzeugt, die mit der freien Oberfläche der Schicht verbunden ist und einfache harmonische Schwingungen um die Rotationsachse ausführt, während die andere Grenzfläche der Schicht festgehalten wird. Das Problem wurde durch Rückführung auf eine Fredholmsche Integralgleichung zweiter Art gelöst.

     

Transient chaotic oscillations of a tethered satellite system

Summary For the simulation of large amplitude motions of thin, visco-elastic tethers connecting two satellites several numerical algorithms were developed recently. However, since we are dealing with highly nonlinear, nearly Hamiltonian multiple degree of freedom systems we typically will have to expect transient chaotic motions if the motion starts in the neighborhood of a saddle point. For tethered satellite systems we have two stable radial and two unstable tangent-to-orbit equilibria. By simulation with a specially adapted finite-element program we show that the asymptotic behaviour of the system strongly depends on the choice of the initial conditions. Thus, starting in the vicinity of an unstable equilibrium, we cannot predict in which of the attractors it settles down finally. A simple tether model by V. Beletsky and D. Pankova is used to demonstrate the fractal nature of the basin boundary of the two attractors.     

Spectra of microwave oscillations in an SPD-ATON stationary plasma thruster

The spectra of microwave oscillations and electromagnetic radiation in an SPD-ATON stationary plasma thruster have been measured. Using the results of determination of the spectral characteristics and the spatial distribution of microwave intensity, features of the plasma jet instability manifestations related to the trapping of electrons in a magnetic field of the acceleration channel are analyzed. A method for the evaluation of the spectral and energy parameters of microwave oscillations and electromagnetic radiation generated by the operating plasma thruster is proposed.     

Thermal oscillations in rat kidneys: an infrared imaging study

A high-resolution infrared (IR) camera was used to assess rhythmicity in localized renal blood flow, including the extent of regions containing nephrons with spontaneous oscillations in their individual blood flow. The IR imaging was able to follow changes in rat renal perfusion during baseline conditions, during occlusion of the main renal artery and during the administration of either saline or papaverine. Concurrent recordings were made of tubular pressure in superficial nephrons. Spontaneous vascular oscillations centred around 0.02-0.05Hz and approximately 0.01Hz could be detected reproducibly by IR imaging. Their spectral characteristics and their response to papaverine were in line with tubular pressure measurements. The intensity of and synchrony between thermal signals from different local areas of the kidney may allow, after surgical exposure, non-invasive imaging of functional clusters involved in renal cortical blood flow. Through visualization of the spatial extent of thermal oscillations, IR imaging holds promise in assessing kidney autoregulatory mechanisms.