SUSTAINED OSCILLATION OF SYSTEMS WITH DRY FRICTION AND RAMP INPUT
Sustained oscillation of systems with dry friction and ramp input
OSCILLATION↗
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A temporary threshold shift for self-motion detection following sustained, oscillating linear acceleration
Thresholds for detecting linear motion (self-motion) increased following exposure of human observers to sustained linear oscillation (fatiguing stimulus) at 0.26 Hz and approximately 0.5 G peak-to-peak for durations up to 30 min. Recovery to preexposure levels took place over a period of 10 to 15 min following the sustained oscillation termination. Differences in threshold shift magnitudes following sustained oscillation in various orientations support the interpretation that the observed threshold shifts resulted from fatigue of the utricular otolith receptors. Threshold shifts were not obtained following exposure of the human observers to sustained, unidirectional linear acceleration (2G) for durations up to 10 min with a centrifuge. The results of this study suggest a previously unobserved response property of the otolith organs, namely, that these organs can be fatigued in a manner analogous to other receptor systems.
Parker, D. E.↗
Self-sustained oscillations of a shock wave interacting with a boundary layer on a supercritical airfoil
A theory is proposed of the self-sustaining oscillations of a weak shock on an airfoil in steady, transonic flow. The interaction of the shock with the boundary layer on the airfoil produces displacement thickness fluctuations which convect downstream and generate sound by interaction with the trailing edge. A feedback loop is established when this sound impinges on the shock wave, resulting in the production of further fluctuations in the displacement thickness. The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic "tone bursts' by a supercritical airfoil section.
Ventres, C. S.↗
Self-sustained oscillations of a shock wave interacting with a boundary layer on a supercritical airfoil
A theory is proposed of the self-sustaining oscillations of a weak shock on an airfoi in steady, transonic flow. The interaction of the shock with the boundary layer on the airfoil produces displacement thickness fluctuations which convect downstream and generate sound by interaction with the trailing edge. A feedback loop is established when this sound impinges on the shock wave, resulting in the production of further fluctuations in the displacement thickness. The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic 'tone bursts' by a supercritical airfoil section.
Ventres, C. S.↗
Numerical simulations of unsteady transonic flow in diffusers
Forced and naturally occurring, self-sustaining oscillations of transonic flows in two-dimensional diffusers were computed using MacCormack's hybrid method. Depending upon the shock strengths and the area ratios, the flow was fully attached or separated by either the shock or the adverse pressure gradient associated with the enlarging diffuser area. In the case of forced oscillations, a sinusoidal plane pressure wave at frequency 300 Hz was prescribed at the exit. A sufficiently large amount of data were acquired and Fourier analyzed. The distrbutions of time-mean pressures, the power spectral density, and the amplitude with phase angle along the top wall and in the core region were determined. Comparison with experimental results for the forced oscillation generally gave very good agreement; some success was achieved for the case of self-sustaining oscillation despite substantial three-dimensionality in the test. An observation of the sequence of self-sustaining oscillations was given.
Liou, M.-S.↗
Self-sustained hydrodynamic oscillations in a natural-circulation two-phase-flow boiling loop
Results of an experimental and theoretical study of factors affecting self-sustaining hydrodynamic oscillations in boiling-water loops are reported. Data on flow variables, and the effects of geometry, subcooling and pressure on the development of oscillatory behavior in a natural-circulation two-phase-flow boiling loop are included.
Jain, K. C.↗
The acoustic characteristics of turbomachinery cavities
Internal fluid flows are subject not only to self-sustained oscillations of the purely hydrodynamic type but also to the coupling of the instability with the acoustic mode of the surrounding cavity. This situation is common to turbomachinery, since flow instabilities are confined within a flow path where the acoustic wavelength is typically smaller than the dimensions of the cavity and flow speeds are low enough to allow resonances. When acoustic coupling occurs, the fluctuations can become so severe in amplitude that it may induce structural failure of engine components. The potential for catastrophic failure makes identifying flow-induced noise and vibration sources a priority. In view of the complexity of these types of flows, this report was written with the purpose of presenting many of the methods used to compute frequencies for self-sustained oscillations. The report also presents the engineering formulae needed to calculate the acoustic resonant modes for ducts and cavities. Although the report is not a replacement for more complex numerical or experimental modeling techniques, it is intended to be used on general types of flow configurations that are known to produce self-sustained oscillations. This report provides a complete collection of these models under one cover.
Lucas, M. J.↗
Numerical simulation of unsteady viscous flows
Most unsteady viscous flows may be grouped into two categories, i.e., forced and self-sustained oscillations. Examples of forced oscillations occur in turbomachinery and in internal combustion engines while self-sustained oscillations prevail in vortex shedding, inlet buzz, and wing flutter. Numerical simulation of these phenomena was achieved due to the advancement of vector processor computers. Recent progress in the simulation of unsteady viscous flows is addressed.
Hankey, Wilbur L.↗
Limit cycle analysis of large space telescope with CMG nonlinearity
The existence and characteristics of self-sustained oscillations were studied in the Large Space Telescope (LST) system due to the presence of nonlinear gimbal friction in the control moment gyroscopes (CMG's). A continuous data single-axis model of the LST is considered. A solid friction model is used to represent CMG gimbal friction. A rigorous mathematical model is derived for use in a continuous describing function analysis. Conditions for self-sustained oscillations are then determined.
Seltzer, S. M.↗
Stability study of the Large Space Telescope /LST/ system with nonlinear CMG gimbal friction
The purpose of the investigation reported upon is to study the existence and characteristics of self-sustained oscillations in the dynamic behavior of the Large Space Telescope (LST) system due to the presence of nonlinear gimbal friction in the control moment gyroscopes (CMGs). A continuous-data single-axis model of the LST is considered. A solid friction model is used to represent CMG gimbal friction. A rigorous mathematical model is derived for use in a continuous describing function analysis. Conditions for self-sustained oscillations are then determined.
Kuo, B. C.↗
Research study on stabilization and control: Modern sampled-data control theory. Design of the large space telescope system
Conditions of self-sustained oscillations in a two-axis model of the nonlinear LST system are studied. The describing function of the CMG frictional nonlinearity of the LST system is used for the analysis, as well as continuous-data and discrete-data models of the simplified LST control system. A numerical-iterative method is described for the analysis of the two-axis system. Approximation methods and the direct plotting of the stability equation are implemented in the study. It is shown that although the dynamics of the two axes are identical, the amplitudes of self-sustained oscillations in the two axes may in principle be different. Analysis shows that the LST systems are of equal amplitudes but with 180-degree phase shift.
Kuo, B. C.↗
Sustained small oscillations in nonlinear control systems
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
George, J. H.↗
Effects of low frequency vibration of a limb
Low frequency oscillations were applied on the ankle joint in plantarflexion/dorsiflexion rotation using a torque motor. The torque, the angular rotation and the evoked electromyogram from the gastronemius soleus and the anterior tibial muscles were recorded. Significant nonlinearities were observed in the angular rotation from 8 to 12 Hz. The following methods are used for data analysis: (1) Two cycle averaged response; (2) Fourier transform; and (3) Fourier analysis at the driving frequency. Important observations are: (1) resonance near 6 to 8 Hz; (2) slowly increasing amplitudes of oscillation near resonance; (3) self sustaining oscillations after the motor is turned off, particularly in the fatigued limb; and (4) distortion of angular rotation during which there are spontaneous recurrences of oscillation at the driving frequency.
Agarwal, G. C.↗
Part 1: Classical laser. Part 2: The effect of velocity changing collisions on the output of a gas laser
A classical model for laser action is discussed, in which an active medium consisting of anharmonic oscillators interacts with an electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. A theoretical model is presented for the pressure dependence of the intensity of a gas laser, in which only velocity-changing collisions with foreign gas atoms are included. A collision model for hard sphere, repulsive interactions was derived. Collision theory was applied to a third-order expansion of the polarization in powers of the cavity electric field (weak signal theory).
Borenstein, M.↗
Classical laser.
In this paper a completely classical model for laser action is discussed. An active medium consisting of classical anharmonic oscillators interacts with a classical electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. The results for the classical model are found to be similar to those for a semiclassical model of the ammonia-beam maser. The conclusion is that laser action is not intrinsically a quantum-mechanical effect. The classical-laser theory as given in this paper can also be applied to the case of the electron-cyclotron maser.
Borenstein, M.↗
Some observations on the oscillatory behavior of carbon monoxide oxidation
The oscillatory behavior of the oxidation of carbon monoxide was experimentally studied in an attempt to further elucidate the reaction at low pressure. The phenomenon is observed as multiple explosions and involves successive flashes of light accompanying the slow reaction in a static system, including over 450 flashes in one case. Electronically excited hydroxyl radicals (water impurity) and carbon dioxide have been identified as components of the emission. The phase difference between the two was seen to be negligible. The nature of the temperature and pressure changes during a cycle indicates that the oscillation is purely kinetic rather than thermokinetic. A procedure is presented whereby sustained oscillations can be obtained for particular regions in the pressure-temperature plane, vessel surface pretreatments, and H2O-containing reactants.
Mccaffrey, B. J.↗
Circuit for Driving Piezoelectric Transducers
The figure schematically depicts an oscillator circuit for driving a piezoelectric transducer to excite vibrations in a mechanical structure. The circuit was designed and built to satisfy application-specific requirements to drive a selected one of 16 such transducers at a regulated amplitude and frequency chosen to optimize the amount of work performed by the transducer and to compensate for both (1) temporal variations of the resonance frequency and damping time of each transducer and (2) initially unknown differences among the resonance frequencies and damping times of different transducers. In other words, the circuit is designed to adjust itself to optimize the performance of whichever transducer is selected at any given time. The basic design concept may be adaptable to other applications that involve the use of piezoelectric transducers in ultrasonic cleaners and other apparatuses in which high-frequency mechanical drives are utilized. This circuit includes three resistor-capacitor networks that, together with the selected piezoelectric transducer, constitute a band-pass filter having a peak response at a frequency of about 2 kHz, which is approximately the resonance frequency of the piezoelectric transducers. Gain for generating oscillations is provided by a power hybrid operational amplifier (U1). A junction field-effect transistor (Q1) in combination with a resistor (R4) is used as a voltage-variable resistor to control the magnitude of the oscillation. The voltage-variable resistor is part of a feedback control loop: Part of the output of the oscillator is rectified and filtered for use as a slow negative feedback to the gate of Q1 to keep the output amplitude constant. The response of this control loop is much slower than 2 kHz and, therefore, does not introduce significant distortion of the oscillator output, which is a fairly clean sine wave. The positive AC feedback needed to sustain oscillations is derived from sampling the current through the piezoelectric transducer. This positive AC feedback, in combination with the slow feedback to the voltage-variable resistors, causes the overall loop gain to be just large enough to keep the oscillator running. The positive feedback loop includes two 16-channel multiplexers, which are not shown in the figure. One multiplexer is used to select the desired piezoelectric transducer. The other multiplexer, which is provided for use in the event that there are significant differences among the damping times of the 16 piezoelectric transducers, facilitates changing the value of one of the resistors in the positive-feedback loop to accommodate the damping time of the selected transducer.
Randall, David P.↗
80-GHz MMIC HEMT Voltage-Controlled Oscillator
A voltage-controlled oscillator (VCO) that operates in the frequency range from 77.5 to 83.5 GHz has been constructed in the form of a monolithic microwave integrated circuit (MMIC) that includes high-electron-mobility transistors (HEMTs). This circuit is a prototype of electronically tunable signal sources in the 75-to-110-GHz range, needed for communication, imaging, and automotive radar applications, among others. This oscillator (see Figure 1) includes two AlInAs/GaInAs/InP HEMTs. One HEMT serves mainly as an oscillator gain element. The other HEMT serves mainly as a varactor for controlling the frequency: the frequency-control element is its gate-to-source capacitance, which is varied by changing its gate supply voltage. The gain HEMT is biased for class-A operation (meaning that current is conducted throughout the oscillation cycle). Grounded coplanar waveguides are used as impedance-matching transmission lines, the input and output matching being chosen to sustain oscillation and maximize output power. Air bridges are placed at discontinuities to suppress undesired slot electromagnetic modes. A high density of vias is necessary for suppressing a parallel-plate electromagnetic mode that is undesired because it can propagate energy into the MMIC substrate. Previous attempts at constructing HEMT-based oscillators yielded circuits with relatively low levels of output power and narrow tuning ranges. For example, one HEMT VCO reported in the literature had an output power of 7 dBm (.5 mW) and a tuning range 2-GHz wide centered approximately at a nominal frequency of 77 GHz. In contrast, as shown in Figure 2, the present MMIC HEMT VCO puts out a power of 12.5 dBm (.18 mW) or more over the 6-GHz-wide frequency range from 77.5 to 83.5 GHz
Samoska, Lorene↗