Equal Frequency Spacing Research Articles

Frequency comb generation by cascade cavity-enhanced four-wave mixing in a semiconductor optical amplifier

The generation of a frequency comb of optical signals with equal frequency spacing has been demonstrated in a semiconductor-fiber ring laser. A simplified theoretical approach based on cascade cavity-enhanced four-wave mixing in a semiconductor optical amplifier is given, and potential applications are described. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 134–137, 1999.

Fletcher and pitch

Preparing remarks on Fletcher’s work on pitch changed drastically. My view of the development of our present understanding. In 1940 Jan Schouten showed that canceling out of the fundamental of a pitched tone did not change pitch. Schouten called the surviving pitch residue pitch. This inspired a spate of papers by people ignorant of earlier work. I had known Fletcher [Phys. Rev. 23(3), 427–437 (1924)] had shown that filtering out the fundamental and lower harmonics of a variety of musical sounds did not change the pitch, and, through synthetic sounds, that mere equal frequency spacing of tones did not give a pitch equal to the spacing. Thus, the pitch heard was evoked by harmonic partials. Unhappily, Fletcher proposed an unsound explanation in terms of production of the fundamental in the ear by nonlinearities. In a latter report, Fletcher [ 311–343 (1930)] gave an incomplete analysis of the functioning of the cochlea. Among his valid conclusions he said ‘‘the pitch of a tone is determined both by the position of its maximum stimulation on the basilar membrane and also by the time pattern sent to the brain. The former is probably more important for high tones and the latter for low tones.’’ That is our present understanding. Fletcher [ 637–645 (1951)] subsequently gave a ‘‘correct’’ analysis of the functions of the cochlea, agreeing with the experimental work of von Bekesy, and going a little beyond papers a year earlier by Peterson and Bogert and by Zwislocki.

The Effects of Surface Irregularities on Roller Bearing Vibrations

A mathematical model is proposed to illustrate the frequency characteristics of roller bearing vibrations due to surface irregularities which come from manufacturing errors. The bearing vibration is modeled as the system output when it is subjected to the excitations from surface waviness and surface roughness through the lubricating film. It is shown that the vibration spectrum of a normal bearing under a preloaded condition has a pattern of equal frequency spacing distribution (EFSD) which is similar to that of a defective bearing. Consequently, the application of frequency analysis, such as the high frequency resonance tecnique, on bearing monitoring should be undertaken with great care.

On initial fault detection of a tapered roller bearing: Frequency domain analysis

The frequency characteristics of vibration for a defective bearing subjected to various loadings are investigated. The vibration model developed by McFadden and Smith [2] is extended to describe the bearing vibration induced by a single defect, or by multiple defects located at arbitrary positions, of a bearing under diverse loadings. On the basis of the model, the vibration spectrum is a discrete one with a pattern of “equal frequency spacing distribution”. In the demodulated spectrum, there are peaks at the defect frequency and its harmonics. Around each peak, there are side bands associated with the periodic properties of the loadings and the transmission path. The validity of the analytical study is confirmed by an extensive evaluation of experiments.

Signature Analysis of Roller Bearing Vibrations: Lubrication Effects

This study investigates the vibration signature of roller bearings, induced by the surface irregularities of components, under various lubricating conditions. The bearing vibration is modelled as the output of the bearing assembly which is subjected to the excitations of surface irregularities through the oil-film. The oil-film acts as a spring between the roller and race. The stiffness of oil-film under different lubricating conditions is studied from the empirical equation of minimum oil-film thickness. It is shown that the vibration spectra of a normal roller bearing may have a pattern of equal frequency spacing distribution (EFSD) whose frequency information is similar to that of a damaged bearing. Under large loading and low running speed, the vibration energy is low if the lubricant viscosity is high. On the other hand, at high running speed, the vibration energy is high with high lubricant viscosity.

Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets

High-resolution interferometric spectra of the stimulated Raman scattering (SRS) spectra from flowing ethanol droplets are presented. The linewidths of the SRS peaks are less than 0.005 cm(-1), and the equal frequency spacings of the SRS peaks are an order of magnitude smaller than the spacings for morphology-dependent resonances of a perfect sphere. The observed results from droplets that are deformed by inertial effects are consistent with T-matrix and perturbation predictions of frequency splitting into the various azimuthal modes of a (2n + 1)-degenerate morphology-dependent resonance with angular momentum n in a perfect sphere.

Transfer Functions with Elliptic Distribution of Poles at Equal Frequency Spacings

This paper presents the amplitude and phase-delay responses for a class of transfer functions with all zeros at infinity and poles located on an ellipse in the complex frequency plane, with equal spacings along the imaginary axis. The class is generated by varying the eccentricity of the ellipse, and it is found that when the ratio of the axis in the real direction to that in the imaginary direction lies in the range 0.4-0.8, good delay responses result, together with wide amplitude bandwidths. By varying the eccentricity in the range mentioned, a choice of amplitude and delay response can be made to facilitate any particular application.

Synthesis of Reactive Mechanical Circuits for Impact Loading

High-speed operation of modern machines has emphasized the effects of high loading rates and impacts. With wide-frequency-band excitation, it becomes necessary to consider an extended range of structural resonances to determine dynamic response and to improve the effectiveness of structural damping. In this paper, synthesis techniques are applied to the design of simple undamped (i.e., reactive) structural elements. Synthesis of mechanical circuits is complicated by the characteristically large numbers of degrees of freedom, and by difficulties of response measurement over a wide frequency range. However, Cauer's method of ladder network synthesis is readily applied for more than 20 alternating zeros and poles arrayed in a wide variety of frequency patterns. Of particular interest for dissipative purposes is the equal frequency spacing of zeros and poles for the reactive structure. Examples are given of circuit synthesis for this zero-pole spacing in the derivation of dimensions for simple circuits, including 15 degree-of-freedom ladders, cantilever beams, and circular disks. Computed circuit characteristics are then verified by mechanical driving-point impedance measurements over a frequency range extending to 50 kc/sec.