Self-excited oscillations

A little later (1929) the Russian physicist Andronov pointed out3 that the stationary state of self-excited oscillations discovered by van der Pol is expressible analytically in terms of the limit cycle concept of the theory of PoincarA... 

As a closed trajectory in the phase plane means obviously a periodic phenomenon, the discovery of limit cycles was fundamental for the new theory of self-excited oscillations. 

The use of this theory in studies of nonlinear oscillations was suggested in 1929 (by Andronov). At a later date (1937) Krylov and Bogoliubov (K.B.) simplified somewhat the method of attack by a device resembling Lagrange s method of the variation of parameters, and in this form the method became useful for solving practical problems. Most of these early applications were to autonomous systems (mainly the self-excited oscillations), but later the method was extended to... 

Nonanalytic Nonlinearities.—A somewhat different kind of nonlinearity has been recognized in recent years, as the result of observations on the behavior of control systems. It was observed long ago that control systems that appear to be reasonably linear, if considered from the point of view of their differential equations, often exhibit self-excited oscillations, a fact that is at variance with the classical theory asserting that in linear systems self-excited oscillations are impossible. Thus, for instance, in the van der Pol equation... 

Both transducers are self-excited oscillating systems (usually piezoelectric crystals— see Section 6.3.1) which act alternately as transmitters and receivers, the receiving pulses being used to trigger the transmitted pulses in a feedback arrangement. A pulse from transmitter Tt is directed downstream over a path length Lp to transducer T2 (Fig. 6.3). The downstream elapsed time is ... 

IIIN) Nazarenko, V. G., Sel kov, E. E. Self-excited Oscillations in an Open Biochemical... 

An instability effect of a closed passive resonance system in a self-exciting oscillating amplitude because of a small perturbation of frequency, co, in the potential state given by... 

Very recently, EW has been employed to trigger self-excited oscillations of millimetersized sessile droplets of water-glycerol mixtures [13]. During these oscillations, contact angles of the droplets have been found to vary periodically between 130° and 80°, with a frequency between 10 and 125 s. The resultant mixing of fluids within the droplets has been found to be two orders of magnitudes faster than the conventional chaotic micromixing processes. 

This phenomenon is often called "hard self-excitation" because there exists a self-excited (i.e. orbitally asymptotically stable) limit cycle, but to reach the self-excited oscillation requires a "hard" (i.e. finite) perturbation from the steady state. (In contrast, a "soft self-excitation" is illustrated in Fig. I.l.) There is some experimental indication of hard self-excitation in the Belousov-Zhabotinskii reaction. Notice in Fig. II. 1 that after a short induction period the oscillations appear suddenly with large amplitude. This is to be expected for hard self-excitation during the induction period the system is trapped in a locally stable steady state until the kinetic parameters change such that the steady state loses its stability and the system jumps to large amplitude stable oscillations. In the case of soft self-excitation it is expected that as the steady state loses stability, small amplitude stable oscillations first appear and then grow in size. 

Self-excited oscillations have been reported to occur in L-B films of dioleyl lecithin (Y-fihns and Z-films). The films separated equimolar solutions of KCl and NaCl solutions, and also in polytetrafluoroethylene membrane doped with triolein and monolein [3, 4], No satisfactory theory has been proposed so far to explain self-excited oscillations in such systems. However, it has been postulated that such a situation can occur on account of any one of the following factors [5]... 

Self-excited oscillations are quite relevant in the context of biological oscillator. Typical self-excited oscillations observed in the case of (i) density oscillator, (ii) liquid-liquid interface oscillator and (iii) liquid-vapour interface oscillator, the mechanism of... 

The vapor-liquid oscillator described above provided an example of self-excited oscillator, which has relevance to biology. Since in living systems self-excited oscillations are quite common, it is tempting to examine its co-relation with sensing mechanism of smell. 

Self-excited oscillations are extremely important from the viewpoint of Electrophysiology and nerve transmission. As an example, sense of taste, smell and injury are related to such self-excited oscillations [36]. Some of the examples of self-excitation which we have come across in previous chapters are... 

The above defects are due to different reasons. In the article (41), the stick-slip effect is related to self-excited oscillations initiated by the dependence of static friction-stress between the billet and the die at the time when they are in contact. The latter is connected with the viscoelastic properties of the rough billet surface and by lubricant squeezing out from the region of contact. Ward and co-workers (1) explain the stick-slip effect by the heating of billet dining the deformation. The pulsatory flow is assumed to be due to a competition between the viscosity and high elasticity of polymers (42). 

Toda, A., Tomita, C., Hikosaka, M., Hibino, Y., Miyaji, H., Nonomura, C., Suzuki, T., and Ishihara, H. (2002) Thermo-mechanical coupling and self-excited oscillation in the neck propagation of PET films. Polymer,... 

Dielectric systems usually employ negative grid triode tubes, although some systems operating in the 50 to 100-MHz range use beamed power types. RF circuits are usually simple, self-excited oscillators of the Hartley, Colpitts, or tuned plate-tuned grid type. These circuits usually consist of coils and capacitors or coaxial lines. The load to be heated may actually form part of the tank circuit capacitance, it may be separately tuned or inductively or capacitively coupled to the oscillator, or it may be a combination of these, which is directly connected to the oscillator and also... 

Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16 263-277 Caughey TK, Payne HJ (1967) On the response of a class of self-excited oscillators to stochastic excitation, hit J Non Linear Mech 2 125-151... 

Friction-induced vibration, in the most general sense, is the deviation from uniform sliding due to the interaction of friction and system dynamics. This can occur due to surface topography. However, the problem which is of the most concern is self-excited oscillations that occur due to a functional dependence of friction with velocity or... 

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