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General relations are presented for the power flow at the frequencies of interest in a Josephson element. These general power flow relations depend upon whether the autonomous frequency is phase-locked, either harmonically or subharmonically, to a frequency in the system or is unlocked. The results presented generalize those given previously by Russer (1971) for the harmonically locked case.
The criteria for the stability of the subharmonic, harmonic, or superharmonic oscillations determine the relation between acoustic field parameters and particle parameters. The derived formulas underlie the destruction of the fragile Widmanstatten structure in weldings and therefore the designing of the generators that must be used for this welding process.
The insulation of nonlinear and random vibrations is considered for some ore preparing and sorting implements: rotary crushers, resonance screens, hammer mills, etc. The appearance of subharmonic vibrations is analyzed, and the conditions for their appearance are determined. A method is given for calculating the insulation of these vibrations by means of elastic elements made of rubber. The insulation of the random vibrations produced by Symons crushers is calculated by determining the transmissability and deformation of the insulation system for a narrow band random response.
An analysis is presented describing four-photon parametric amplification in an unbiased Josephson junction. Central to the theory is the model of the Josephson effect as a nonlinear inductance. Linear, small signal analysis is applied to the two-fluid model of the Josephson junction. The gain, gain-bandwidth product, high frequency limit, and effective noise temperature are calculated for a cavity reflection amplifier. The analysis is extended to multiple (series-connected) junctions and subharmonic pumping.
Very low frequency emissions with subharmonic cyclotron frequency from magnetospheric electrons were detected by the S(3)-A satellite (Explorer 45) whose orbit is close to the magnetic equatorial plane where the wave-particle interaction is most efficient. These emissions were observed during the main phase of a geomagnetic storm in the nightside of the magnetosphere outside of the plasmasphere. During the event of these side-band emissions, the pitch angle distributions of high energy electrons (greater than 50 keV) and of energetic protons (greater than 100 keV) showed remarkable changes with time, whereas those of low energy electrons and protons remained approximately isotropic. In this type of event, emissions consist essentially of two bands, the one below the equatorial electron gyrofrequency, and the other above. The emissions below are whistler mode, and the emissions above are electrostatic mode.
The mixing properties of a current-biased resistively-shunted Josephson junction irradiated at two frequencies are calculated by a perturbation technique, treating both signals as perturbations. The size of the mixing steps is obtained from second-order calculations. It is shown that subharmonic mixing steps are absent in the case of a single frequency. The amplitude of the voltage oscillations at the difference and sum frequencies is shown to be nonzero at all voltages. The microwave resistance is calculated for one frequency to third order in the perturbation.
An analysis is presented of the superharmonic, subharmonic, and combination resonances in a multi-degree-of-freedom system which has cubic nonlinearity and modal viscous damping and is subject to harmonic excitation. It is shown that, in the absence of internal resonances, the steady-state response contains only the modes which are directly excited. It is shown that, in the presence of internal resonances, modes other than those that are directly excited can appear in the response. The strong influence of internal resonances is exhibited in numerical examples involving hinged-clamped beams. It is shown that when a multimode solution exists the lowest mode can dominate the response, even when it is not directly excited.
A multi-rate digital command system is disclosed which uses the composite signal of a mu-type ranging system as a subcarrier to transmit range codes and data from a station to a receiver where the range codes are sequentially phase modulated on a subcarrier of frequency by one of its own subharmonics and data is phase modulated on a selected ranging component. A range cleanup loop in a spacecraft locks the phase of a locally generated reference component to a received ranging component and retransmits the component to a ground station. When the inverse phase of a ranging component is received and detected, the cleanup loop is modified to demodulate phase modulated command symbols while continuing tracking the same ranging component. The command symbol rate is coherently related to the ranging signal component bit rate.
The following technical developments are described: (1) a reliable 183 GHz subharmonic mixer, (2) a precision noise figure test setup, (3) the successful deposition of SiO2 on a noncontacting backshort, and (4) sturdier whisker points used for diode contacting.
The stability of a secondary Tollmien-Schlichting wave, whose wavenumber and frequency are nearly one half those of a fundamental Tollmien-Schlichting instability wave is analyzed using the method of multiple scales. Under these conditions, the fundamental wave acts as a parametric exciter for the secondary wave. The results show that the amplitude of the fundamental wave must exceed a critical value to trigger this parametric instability. This value is proportional to a detuning parameter which is the real part of k - 2K, where k and K are the wavenumbers of the fundamental and its subharmonic, respectively. For Blasius flow, the critical amplitude is approximately 29% of the mean flow, and hence many other secondary instabilities take place before this parametric instability becomes significant. For other flows where the detuning parameter is small, such as free-shear layer flows, the critical amplitude can be small, thus the parametric instability might play a greater role.
A type of active control for helicopters was designed and tested on a four foot diameter model rotor. A single blade was individually controlled in pitch in the rotating frame over a wide range of frequencies by electromechanical means. By utilizing a tip mounted accelerometer as a sensor in the feedback path, significant reductions in blade flapping response to gust were achieved at the gust excitation frequency as well as at super and subharmonics of rotor speed.
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.
A new, advanced type of active control for helicopters and its application to gust alleviation is described. Each blade is individually controlled in the rotating frame over a wide range of frequencies up to the sixth harmonic of rotor speed. Considerable system simplification is achieved by means of modal decomposition. It is shown both analytically and experimentally that by utilizing a tip-mounted accelerometer as a sensor in the feedback path, significant reductions in blade flapping response to a sinusoidal gust can be achieved at the gust excitation frequency as well as at super- and subharmonics of rotor speed.
This paper investigates a wavelength selection mechanism under ideal and nonideal flow conditions. The conditions of the total streamwise growth of Gortler vortices generated under ideal and nonideal flow conditions and its effect on the laminar-turbulent transition process is also examined. The stabilizing effects of suction on the total growth of these vortices are analyzed. It is demonstrated that the wavelength selection mechanism and the total growth of the vortices are affected by the departures from ideal flow conditions. It is shown that under ideal flow conditions, a wavelength selection mechanism can be based on the maximum amplification rate of the disturbances. However, this mechanism is easily affected by the departures from ideal flow. The case of streamwise vorticity in the basic flow is analyzed and is shown to affect disturbances through a subharmonic resonance.
Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.
A low noise, broadband, balanced mixer has been developed for use as a 225-GHz receiver. It utilizes a local oscillator (LO), whose frequency is nearly 1/4 the signal frequency, to mix the signal power to a low IF, which is then amplified. This same LO drives a similar mixer that is used to phase lock a 225-GHz transmitter. The use of a subharmonic mixer lowers LO cost, noise, and complexity, increases LO availability and reliability, and is compact and portable. Typical applications for this type of mixer include coherent receivers, passive imaging, multiple receiver systems, and broadband detection systems
The feasibility of an adaptive control system designed to alleviate helicopter gust induced vibration was analytically investigated for an articulated rotor system. This control system is based on discrete optimal control theory, and is composed of a set of measurements (oscillatory hub forces and moments), an identification system using a Kalman filter, a control system based on the minimization of the quadratic performance function, and a simulation system of the helicopter rotor. The gust models are step and sinusoidal vertical gusts. Control inputs are selected at the gust frequency, subharmonic frequency, and superharmonic frequency, and are superimposed on the basic collective and cyclic control inputs. The response to be reduced is selected to be that at the gust frequency because this is the dominant response compared with sub- and superharmonics. Numerical calculations show that the adaptive blade pitch control algorithm satisfactorily alleviates the hub gust response. Almost 100% reduction of the perturbation thrust response to a step gust and more than 50% reduction to a sinusoidal gust are achieved in the numerical simulations.
Work on the development of an improved 183 GHz subharmonic mixer was concentrated in two areas. First, there was an improved performance from current mixer body designs by testing different diodes and varying the whisker lengths. Second, there is the design of a new body structure. The whisker and diode pinsare in the same piece of the mixer that holds the substrate, reducing any motion of the parts that form the ohmic contacts of the diodes circuit. The broadband, low loss, quasi-optical diplexer, which is designed for use with a single ended mixer, has been developed. It uses a Gaussian beam waveguide as its transmission medium. The difference between the diplexer and other diplexers is the use of a Fabry Perot parallel plate filter. One is a multichannel radiometer system. Another approach is a quasi-optical RF polarization diplexer and another receiver. Some of the receivers developed were flown in aircraft and degraded considerably because of an LO failure. A technique for adding a 118 GHz channel to the existing Atmospheric Moisture Microwave Scanner radiometer system, using the RF diplexing scheme, is presented.