Backward Components Research Articles

On the application of directional time-frequency distributions to the identification of simultaneous forward and backward whirling in flexible rotors

One of the greatest advantages of using complex coordinates on the study of rotating machinery is the gain on the physical insight into the forward and backward precessional modes. Together with the complex modal analysis formulation, other interesting tools were developed to characterize the shape and directivity of the whirl modes. These tools are helpful in understanding the bizarre phenomenon of mixed operational modes in rotors where some stations describe their precessional movement in the forward direction while others move in the backward direction. This paper enhances the discussion on the existence of these modes in flexible rotors when the rotating system is subjected to multiple unbalance forces applied on some stations of the rotor. It is worth noting that the concepts of the complex modal analysis are valid only for rotors operating at constant rotational speed. Consequently, if it is necessary to investigate the whirling motion of each station of the rotor when it is operating under non-stationary conditions, other procedures must be used. In this work, it is used the directional Wigner distribution, which is able to split the total response of any station of the rotor into its forward and backward components. The considered rotor is supported on anisotropic bearings and operates at varying rotational speed. The experimental results are presented, showing the usefulness of time-frequency distributions as an alternative tool to identify mixed modes.

Age-dependent emergence of oscillatory signal flow between the primary and secondary visual cortices in rat brain slices

Developmental changes in dynamics of signal propagation between the primary (Oc1) and secondary visual cortex (Oc2) were investigated by using optical recording methods with voltage-sensitive dyes. Propagating oscillatory optical responses were evoked by our previously reported procedure, and were recorded on stimulation to white matter of Oc1 in rat visual cortex slices. In immature slices, evoked signals spread out from the stimulation site by way of deep layers, but were restricted largely to Oc1. In mature slices, however, evoked signals spread upward from the stimulation site at first, and then spread out along layer II/III, finally to penetrate Oc2. More remarkably, after this initial signal was attenuated, oscillatory responses emerged and spread back from Oc2 to Oc1 by way of layer II/III, suggesting that the origin of backpropagating oscillation is located in Oc2. The initial forward component was dependent on both N-methyl- d-aspartate (NMDA) and non-NMDA receptors, and the subsequent backward components were dependent only on NMDA receptors. These results suggest that the extent of corticocoritcal signal propagation within the visual cortex grows wider horizontally during maturation, so that information interchange may become easier between the Oc1 and Oc2.

2.5-Dimensional Multi-Signal Large-Signal Analysis of Helix TWTs

A computer model (SUNRAY-3D) for the 2.5-dimensional multi-signal large-signal analysis of helix TWTs has been developed based on the approach developed earlier by the author for the one-dimensional large-signal modelling of helix and coupled-cavity TWTs. Some of the features of O'Malley's work for three-dimensional modelling of coupled-cavity TWTs were incorporated successfully for the modelling of helix TWTs. The present model is capable for the analysis of multiple input signals together with their higher order harmonics and inter-modulation products. The expressions for the circuit field and the induced current at a plane were derived from the electric field in a helical slow-wave structure instead of using the conventional equivalent circuit approach. The program analyses TWTs with arbitrary variations in the helix pitch and rf loss (including sever and tip loss) along the slow-wave structure. Induced backward voltage components and reflected voltage components due to mismatches at the terminations of the helix were included. The program has been shown to be accurate and self-consistent for drive powers from 60dB below saturation to well above saturation. The energy balance factor is satisfied to better than ±0.1% even at and above saturation. The CPU time to compute the performance of a typical TWT for a single drive power with 96 rings and 16 steps per wavelength is less than one minute on a DEC-ALPHA computer and is much less than 20 seconds on an IBM-P-IV.

Gaussian beam mode analysis of partial reflections in simple quasi-optical systems fed by horn antennas

Low-level reflections are particularly troublesome in sensitive high-resolution spectral line receivers in the submillimetre and terahertz wavebands, giving rise to baseline ripple on spectra which is hard to distinguish from wide lines. In typical systems for submillimetre-wave astronomy, for example, a lens or flat dielectric plate is often used as a cryostat window placed close to a feed horn. Partial reflection from such interfaces can give rise to return loss at the horn throat, which is considerably higher than for the horn radiating into free space. A full scattering matrix approach based on a combination of standard waveguide modes and quasi-optical Gaussian beam modes can be used to analyse standing waves due to partial reflections, in which track is kept of both the backward and forward going components of the propagating fields. In this paper, we consider how such an analytical tool can be set up and we present typical examples of interest in which horn antennas feed simple components including windows, lenses and reflecting central blockages.

Energy exchange properties during second-harmonic generation in finite one-dimensional photonic band-gap structures with deep gratings

We study second-harmonic generation in finite, one-dimensional, photonic band-gap structures with large index contrast in the regime of pump depletion and global phase-matching conditions. We report a number of surprising results: above a certain input intensity, field dynamics resemble a multiwave mixing process, where backward and forward components compete for the available energy; the pump field is mostly reflected, revealing a type of optical limiting behavior; and second-harmonic generation becomes balanced in both directions, showing unusual saturation effects with increasing pump intensity. This dynamics was unexpected, and it is bound to influence the way one goes about thinking and designing nonlinear frequency conversion devices in a practical way.

Forward-backward method for scattering from dielectric rough surfaces

The iterative forward-backward (FB) method is a recently proposed efficient technique for numerical evaluation of scattering from perfectly conducting rough surfaces. Extension of the method to include scattering from imperfect conducting surfaces, with a high imaginary part of the complex dielectric constant, has also been proposed. The FB method is further generalized to analyze scattering from dielectric rough surfaces with arbitrary complex dielectric constant. Electric and magnetic equivalent surface currents are split into forward and backward components and equations governing these current components are obtained. As a solution, an iterative scheme is proposed and its convergence rate is analyzed. Finally, the effectiveness of the method is assessed by comparing the obtained scattering results with "exact" ones, computed by employing the usual method of moments (MoM).

Experimental Study of a Rotor Supported by Deep Groove Ball Bearing

An experimental analysis has been done to analyze the effect of ball bearing support for a rigid, horizontal rotor. The effect of radial internal clearance of a ball bearing on its stiffness is studied by setting up a rigid, horizontal Jeffcott rotor supported by same type of ball bearings with known radial internal clearance. The nonlinear dynamic characteristics of the ball bearing are also studied by an experimental setup. The signal is acquired by displacement and acceleration transducers. Analysis of the acquired data with the help of Bode plots, cascade plots, time response plots, phase plane plots and frequency spectra brings out the non-linear nature of the ball bearing support. The effect of clearance on the varying compliance frequency, rotational frequency and the resultant sum-difference frequencies can be inferred from the various plots. The anisotropic nature of the ball bearing support shows up as the backward whirl components in full vibration spectra cascade plot. These experimental results validate theoretical results reported in literature.

Determination of wave speed and wave separation in the arteries

Considering waves in the arteries as infinitesimal wave fronts rather than sinusoidal wavetrains, the change in pressure across the wave front, d P, is related to the change in velocity, d U, that it induces by the ‘water hammer’ equation, dP=±ρc dU , where ρ is the density of blood and c is the local wave speed. When only unidirectional waves are present, this relationship corresponds to a straight line when P is plotted against U with slope ρc. When both forward and backward waves are present, the PU-loop is no longer linear. Measurements in latex tubes and systemic and pulmonary arteries exhibit a linear range during early systole and this provides a way of determining the local wave speed from the slope of the linear portion of the loop. Once the wave speed is known, it is also possible to separate the measured P and U into their forward and backward components. In cases where reflected waves are prominent, this separation of waves can help clarify the pattern of waves in the arteries throughout the cardiac cycle.

THE DIRECTIONAL CHOI–WILLIAMS DISTRIBUTION FOR THE ANALYSIS OF ROTOR-VIBRATION SIGNALS

The accurate analysis of time-varying signals is an essential pre-request for the fault diagnosis and hence safe operation of rotating machines. The Wigner distribution (WD) is probably most widely used among the Cohen's class in order to describe how the spectral content of a signal changes over time. However, the basic nature of such signals causes significant interfering cross-terms, which do not permit a straightforward interpretation of the energy distribution. A new signal processing technique, the directional Choi–Williams distribution (dCWD), is proposed to account for complex-valued time-varying signals, which represent the planar motion of rotating machinery at each instant of time. Using the dCWD, not only are the cross-terms minimised but also the interference terms between the forward and backward harmonic components are avoided by transforming complex signals into the forward and backward pass analytic signals. Therefore, the dCWD produces a much lower level of the interference terms than the WD and hence leads to a much clear understanding of the dynamic behaviour of rotors under rotating conditions. The effectiveness of the dCWD is demonstrated by comparing it with the WD and Choi–Williams distribution through some numerical examples and an application to experimental signals.

Correction of carotid augmentation index for heart rate in elderly essential hypertensives

Carotid augmentation index (AI) is used as a surrogate measure of arterial stiffness. Although arterial stiffness has been shown to either remain unchanged or increase with an increase in heart rate, AI decreases as heart rate increases. This study aimed to quantify this confounding effect of heart rate on AI. We investigated 873 hypertensives, mean age 72 ± 5 years, 44% men, mean brachial blood pressure 161 ± 21/82 ± 11 mm Hg. Carotid artery tonometry with simultaneous continuous wave Doppler measurement of ascending aortic blood flow was performed. AI was calculated from the carotid pressure waveform. Waveforms were decomposed into their forward and backward components and the time to reflection between the maxima of the forward and backward pressure waves was measured. AI showed a stronger ( P < .001) association with ejection time (r = 0.48, P < .001) than with heart rate (r = −0.28, P < .001). Although AI is strongly related to the time to reflection (r = −0.51, P < .001), only a weak association was seen between time to reflection and heart rate (r = 0.16, P < .001) or ejection time (r = −0.12, P < .001). Our analysis in an elderly cohort of patients with essential hypertension demonstrates that AI is related to the time to reflection. It also reiterates that AI is confounded by heart rate without any underlying heart rate-dependent change in wave reflection. In population-based studies the confounding effect of heart rate can potentially be corrected. AI remains strongly (r = −0.52) related to time to reflection after correction for the effects of ejection time on AI.

Nonlinear Propagation of Light in One-Dimensional Periodic Structures

We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is assumed to have an index of refraction which varies periodically along its length. The wavelength of light is selected to be in resonance with the periodic structure (Bragg resonance). The AMLE system considered incorporates the effects non-instantaneous response of the medium to the electromagnetic field (chromatic or material dispersion), the periodic structure (photonic band dispersion) and nonlinearity. We present a detailed discussion of the role of these effects individually and in concert. We derive the nonlinear coupled mode equations (NLCME) which govern the envelope of the coupled backward and forward components of the electromagnetic field. We prove the validity of the NLCME description and give explicit estimates for the deviation of the approximation given by NLCME from the {\it exact} dynamics, governed by AMLE. NLCME is known to have gap soliton states. A consequence of our results is the existence of very long-lived {\it gap soliton} states of AMLE. We present numerical simulations which validate as well as illustrate the limits of the theory. Finally, we verify that the assumptions of our model apply to the parameter regimes explored in recent physical experiments in which gap solitons were observed.

Spatial periodicity enhanced superradiance from an optically dense two-level medium

We show that, in an optically dense medium having an inverted active atom number density periodically distributed in space, it is possible, in a slab configuration, to enhance the forward–backward symmetric superradiance emission efficiency if the periodicity reciprocal lattice vector obeys a Bragg’s-like condition for coupling the forward and backward components of the active atoms polarization. We also show that the burst of superradiant light is emitted, in this case, at an earlier time than that for a homogeneously distributed medium having the same average atomic number density. Furthermore, this burst’s temporal duration is shown to be substantially shorter than that for the homogeneous active atoms distribution.

A new model-based method of reconstructing central aortic pressure from peripheral arterial pressure.

We have shown in our previous study that the transfer function between central aortic pressure and tonometric radial arterial pressure can be modeled as a pure elastic lossless tube terminated with a modified Windkessel. We hypothesized, using the model-derived radial arterial flow, that central pressure could be reconstructed by adding the time-shifted forward and backward pressure components (Stergiopulos et al.: Am J Physiol 274: H1386---H1392, 1998). In eight patients (age 16--75), central micromanometric and radial arterial tonometric pressure were measured simultaneously. We imposed measured tonometric pressure to the terminal modified Windkessel to estimate radial arterial flow, with which tonometric pressure was separated into forward and backward components. These components were then appropriately time shifted, and summed to central pressure. We used average parameter values for the terminal impedance, but individualized the transmission delay. The poor correlation (r(2)) between tonometric and central pressure (0.264--0.765) was improved by both central pressure reconstruction methods (generalized transfer function: 0.887--0.974, model-based method: 0.849--0.979). The sensitivity analysis indicated that the key model parameter in reconstructing central pressure was the transmission delay. We conclude that our model-based method was capable of reconstructing central pressure as precisely as the generalized transfer function method, and also capable of individualizing the transfer function by changing the transmission delay.

Sublingual Nitroglycerin Delays Arterial Wave Reflections Despite Increased Aortic “Stiffness” in Patients with Hypertension: A Doppler Echocardiography Study

Venodilatation with consequent reduction in left ventricular filling and end-diastolic wall stress is an important mechanism for the beneficial effects of nitroglycerin in ischemic heart disease and in left ventricular failure. The effects of sublingual nitroglycerin on arterial pulsatile hemodynamics are less well defined. Doppler echocardiography and the calibrated subclavian artery pulse tracing were used to assess hemodynamics in subjects with sustained arterial hypertension (n = 25) before and 5 to 10 minutes after sublingual deposition of 0.5 mg glyceryl trinitrate. Aortic characteristic impedance was calculated by averaging the modulus of the input impedance (ratio of pressure to flow) at high frequencies and by calculating the ratio of pressure and flow increments during upstroke. The pressure wave was split into forward and backward components, and the reflection coefficient (the ratio of backward to forward pressures) was calculated. Parameters of the arterial bed were estimated by using 2- and 3-element Windkessel models. Nitroglycerin delayed the return of arterial wave reflections by 17% (P =.02) and increased aortic characteristic impedance by 20% (P =.01), but it did not influence total arterial compliance. Mean arterial pressure decreased 7% (P =.0001), but pulse pressure did not change. Stroke volume and the acceleration time of aortic root flow decreased by 13% (P =.0001) and 8% (P =.01), respectively. Cardiac output decreased 7% (P =.01), despite an increase in heart rate of 10% (P =.0001). Peripheral resistance tended to decrease (4%, P =.06). Thus, in subjects with sustained hypertension, sublingual nitroglycerin dilates peripheral, predominantly muscular arteries with a subsequent delayed return of reflected pressure waves. Reflex activation of the sympathetic nervous system with consequent increased acceleration of left ventricular ejection seems to counteract the effect of reduced mean arterial pressure (distending pressure) with respect to the “stiffness” of the aorta. (J Am Soc Echocardiogr 2000;13:1100-8.)

On large-angle Bhabha scattering at LEP

The theoretical accuracy of the program TOPAZ0 in the large-angle Bhabha channel is estimated. The physical error associated with the full Bhabha cross section and its forward and backward components separately is given for some event selections and several energy points of interest for LEP1 physics, both for the s and non- s contributions to the cross section.

Physical basis of pressure transfer from periphery to aorta: a model-based study.

We propose a new method to derive aortic pressure from peripheral pressure and velocity by using a time domain approach. Peripheral pressure is separated into its forward and backward components, and these components are then shifted with a delay time, which is the ratio of wave speed and distance, and added again to reconstruct aortic pressure. We tested the method on a distributed model of the human systemic arterial tree. From carotid and brachial artery pressure and velocity, aortic systolic and diastolic pressure could be predicted within 0.3 and 0.1 mmHg and 0.4 and 1.0 mmHg, respectively. The central aortic pressure wave shape was also predicted accurately from carotid and brachial pressure and velocity (root mean square error: 1.07 and 1.56 mmHg, respectively). The pressure transfer function depends on the reflection coefficient at the site of peripheral measurement and the delay time. A 50% decrease in arterial compliance had a considerable effect on reconstructed pressure when the control transfer function was used. A 70% decrease in arm resistance did not affect the reconstructed pressure. The transfer function thus depends on wave speed but has little dependence on vasoactive state. We conclude that central aortic pressure and the transfer function can be derived from peripheral pressure and velocity.

Effects of friction and nonlinearities on the separation of arterial waves into their forward and backward components

In this paper we examine the importance of fluid friction and nonlinearities due to the area-pressure relationship and to the convective acceleration on the separation of arterial pressure and flow waves into their forward and backward components. Experiments were run in straight uniform nonlinearly elastic tubes. Different degrees of fluid friction and nonlinearities, covering the physiological range, have been tested. We predicted the forward and backward running pressure components using two wave separation methods: the classical linear method (Westerhof et al., Cardiovasc. Res. 6, 648–656, 1972) and the first order correction (FOC) method (Pythoud et al., Trans ASME J. Biomech. Engng, in press) which takes nonlinearities and fluid friction into account. We found that the two methods yield somewhat different predictions. The differences tend to increase with the degree of fluid friction and nonlinearities and are typically of the order of 4–8%. We further compared the transmission ratio of forward and backward waves predicted by both methods. The transmission ratio was found to be overestimated by 10% by the classical linear method. The nonlinear method gave more accurate estimates, consistent with theory. We conclude that, for in vivo applications, the classical linear method should be the method of choice because it is simpler to use and the errors involved (4–8%) are comparable to measurement errors.

Method for determining distribution of reflection sites in the arterial system.

We developed a new method to determine the location and importance of reflection sites in the arterial system. The method is based on the decomposition of the aortic pressure wave into its forward and backward components, and it provides the reflection profile of the arterial system as a wave reflection site amplitude versus distance from the heart. The reflection profile can be seen as the response of the arterial system to a pressure delta pulse where reflections upstream from the measurement location have been eliminated. The method was successfully tested on a simple model loaded with a pure resistor, a two-element windkessel, and a bifurcating tube system. It was then applied to the aortic pressure and flow signals measured in six mongrel dogs whose aorta was occluded at different levels. The profiles obtained from measurements at control showed two main reflection regions, one located in the vicinity (0.1-0.2 m) of the heart and the other located in the region of the iliac bifurcation. All occlusions, even the most distant one at the iliac bifurcation, could be identified in both amplitude (amount of reflections) and distance from the heart. The spatial resolution of the profiles was approximately 0.1 m as a result of the limited power spectrum contained in the arterial pulse, and the identification of reflection sites decreased rapidly with the distance.

Separation of arterial pressure waves into their forward and backward running components.

A new separation technique has been developed to determine the forward and backward running arterial pressure wave components. It takes into account friction as well as nonlinear effects due to convective acceleration and to the pressure dependence of the arterial compliance. The new method is a combination of two methods treating friction and nonlinearities separately. The method requires the measurements of pressure and flow at one location as well as the knowledge of the area-pressure relationship. The validity of the method was tested by a simulation experiment in which the forward and backward waves were known a priori. It was shown that the new method is significantly more accurate in the predictions of the forward and backward waves when compared to the classical method assuming linearity and no dissipation. The new wave separation method was also applied to simulated aortic waves for (a) a healthy subject and (b) a subject with decreased compliance. Comparison with the classical linear method showed that neglecting nonlinearities leads to an overestimation of the forward and backward pressure wave amplitudes. The errors, however, were in the order of 5 to 10 percent. We concluded that, for most clinical purposes, the improvement using the nonlinear method is of the same magnitude as experimental errors, and thus the linear method would suffice.

Dynamics of Anisotropically Supported Rotors

The paper discusses dynamic effects occurring in machinery rotors supported in bearings and pedestals with laterally different characteristics. In the considered rotor model the anisotropy of radial stiffness and tangential (“cross”) stiffness components are included. Within certain ranges of the rotative speed the support anisotropy leads to the specific, excited‐by‐unbalance rotor lateral synchronous vibrations in a form of backward (reverse) precession. In addition, one section of the rotor may precess backward, while the other section simultaneously precesses forward. Experimental results illustrate this phenomenon. The analytical model of the system is based on multimode modal approach. It is also shown in this paper that greatly enhanced information for machine malfunction diagnostics can be obtained by simulated rotation of the XY transducer system observing rotor lateral vibration. This simulated rotation can be accomplished by the machine diagnostic data acquistion and processing system. The data processing also includes extraction of forward and backward components of elliptical orbits filtered to one frequency, and the filtered orbit major axis magnitude and its angular orientation.Numerical examples, field data, and experimental results performed on a rotor rig illustrate applications.