Self-excitation

Fluid-Elastic Coupling Fluid flowing over tubes causes them to vibrate with a whirling motion. The mechanism of fluid-elastic coupling occurs when a critical velocity is exceeded and the vibration then becomes self-excited and grows in amplitude. This mechanism frequently occurs in process heat exchangers which suffer vibration damage. 

Forced or Resonant Vibration Self-Excited or Instability Vibration... 

Figure 5-22a. Hysteretic whirl. (Ehrich, F.F., Identification and Avoidance of Instabilities and Self-Excited Vibrations in Rotating Machinery, Adopted from ASME Paper 72-DE-21, General Electric Co., Aircraft Engine Group, Group Engineering Division, May 11, 1972.)...

Self-Excited Vibration Hyslerelic whirl N> Nt Nf A equipment misaligned Shrink fits and... 

This phenomenon is caused by self-excitation of the blade and is aero-elastic. It must be distinguished from classic flutter, since classic flutter is a coupled torsional-flexural vibration that occurs when the freestream velocity over a wing or airfoil section reaches a certain critical velocity. Stall flutter, on the other hand, is a phenomenon that occurs due to the stalling of the flow around a blade. 

One of the most serious forms of instability encountered in journal bearing operation is known as half-frequency whirl. It is caused by self-excited vibration and characterized by the shaft center orbiting around the bearing center at a frequency of approximately half of the shaft rotational speed as shown in Figure 13-15. 

Resonant responses must not coincide with excitation frequencies of rotational shaft speed, especially gear meshing frequency (the speed of a shaft times the number of teeth of the gear on that shaft), or other identi fied system frequencies otherwise, a self-excited system will exist. Lateral response criteria should conform to API 613. 

Wlieatstone s self-excited generator was an important step in the development of the electric generator. Although It proved to be the last of Wheatstone s inventions in that field, the remainder of his life was devoted to further improvements in the telegraph. 

The impedance of the transducer is important if it provides an output signal to an electronic device (an amplifier, for example) and the impedance of the two must be matched for accurate measurement. Some transducers (thermocouples, for example) generate their output by internal mechanisms (i.e. they are self-excited). Others such as resistance thermometers need an external source and an appropriate type must be available. Transducers used in the measurement of the more common physical quantities are discussed below. 

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... 

The deep philosophical significance of the new theory lies precisely at this point, and consists in replacing a somewhat metaphysical concept of the harmonic oscillator (which could never be produced experimentally) by the new concept of a physical oscillator of the limit cycle type, with which we are dealing in the form of electron tube circuits and similar self-excited systems. 

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. 

A difference between these two concepts can be illustrated in many ways. Consider, for example, a mathematical pendulum in this case the old concept of trajectories around a center holds. On the other hand, in the case of a wound clock at standstill, clearly it is immaterial whether the starting impulse is small or large (as long as it is sufficient for starting, the ultimate motion will be exactly the same). Electron tube circuits and other self-excited devices exhibit similar features their ultimate motion depends on the differential equation itself and not on the initial conditions. 

This analogy has been found to be very useful in investigating more complicated situations. For instance, in applications one often encounters the so-called phenomenon of a hard self-excitation. The... 

If, however, one communicates to such a system an impulse capable of transferring the representative point JR to a point A outside the unstable cycle (point A, Fig. 6-6), it is clear that from that point the self-excitation can start and JR will approach the outer stable cycle. 

Negative Criterion of Bendixson.—This criterion is useful when one wishes to know that no self-excited (parasitic) oscillations are possible. 

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... 

It was observed that with a linear circuit and in the absence of any source of energy (except probably the residual charges in condensers) the circuit becomes self-excited and builds up the voltage indefinitely until the insulation is punctured, which is in accordance with (6-138). In the second experiment these physicists inserted a nonlinear resistor in series with the circuit and obtained a stable oscillation with fixed amplitude and phase, as follows from the analysis of the differential equation (6-127). 

L. Mandelstam and N. Papalexi performed an interesting experiment of this kind with an electrical oscillatory circuit. If one of the parameters (C or L) is made to oscillate with frequency 2/, the system becomes self-excited with frequency/ this is due to the fact that there are always small residual charges in the condenser, which are sufficient to produce the cumulative phenomenon of self-excitation. It was found that in the case of a linear oscillatory circuit the voltage builds up beyond any limit until the insulation is ultimately punctured if, however, the system is nonlinear, the amplitude reaches a stable stationary value and oscillation acquires a periodic character. In Section 6.23 these two cases are represented by the differential equations (6-126) and (6-127) and the explanation is given in terms of their integration by the stroboscopic method. 

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... 

Action potentials are generated in single-unit smooth muscle. Simultaneous depolarization of 30 to 40 smooth muscle cells is required to generate a propagated action potential the presence of gap junctions allows this to occur readily. Because single-unit smooth muscle is self-excitable and capable of generating action potentials without input from the autonomic nervous system, it is referred to as myogenic. In this muscle, the function of the autonomic nervous system is to modify contractile activity only. Input is not needed to elicit contraction. 

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