Infinite Modes Research Articles

General Field Theory Treatment of E-Plane Waveguide Junction Circulators---Part I: Full-Height Ferrite Configuration

In this paper an exact field theory treatment for the N-port E-plane full-height ferrite rod junction circulators is presented. Field expressions are written in each region of the junction in the form of infinite modes. Matching of the fields at the common boundaries is used to get a set of infinite nonhomogeneous equations in these mode amplitudes. The point matching technique is used to obtain an approximate solution for the field amplitudes by taking a finite number of modes in each region. Three types of junctions have been analyzed by this technique. These junctions are the symmetrical Y junction and two types of T junctions. Experimental measurements have been carried out to verify the obtained numerical results.

Generation of sound by rotor-stator interaction

Sound generation by rotor-stator interaction, which is the main cause of discrete frequency noise from subsonic compressor, is studied theoretically, taking into account the effect of compressibility of fluid. The combination of a single stator row and a single rotor row in a two-dimensional subsonic flow field is chosen as the interaction model, and two types of interaction, that is, potential interaction and wake interaction, are treated separately. By determining the unsteady lift distributions of the rotor and stator simultaneously in proper phase and amplitude, the sound pressures upstream and downstream are calculated in a form which includes the contributions from sound sources of both rows. In addition to the compressibility effect on source terms, the effect of the non-compact source distribution over the blades is also included. The array of acoustic doublets in the cascade direction is shown to involve infinite modes of pressure waves both propagating and decaying. Consideration of the phase relation between the stator source and the rotor source reveals the mode correspondence in both rotor and stator co-ordinate systems. Numerical examples derived from the theory are presented to show the effects of flow Mach number, rotor-stator axial separation, blade spacing ratio of both rows, and drag coefficient of upstream airfoils which defines the profile of wakes on the generated sound pressure. The ratio of the blade spacing of a rotor to that of a stator (in other words, the relation between the number of blades of both rows) is found to have a great influence upon the sound pressure through the effect of change in the angle of propagation of the generated sound wave.

Generation of sound by rotor-stator interaction

Sound generation by rotor-stator interaction, which is the main cause of discrete frequency noise from subsonic compressor, is studied theoretically, taking into account the effect of compressibility of fluid. The combination of a single stator row and a single rotor row in a two-dimensional subsonic flow field is chosen as the interaction model, and two types of interaction, that is, potential interaction and wake interaction, are treated separately. By determining the unsteady lift distributions of the rotor and stator simultaneously in proper phase and amplitude, the sound pressures upstream and downstream are calculated in a form which includes the contributions from sound sources of both rows. In addition to the compressibility effect on source terms, the effect of the non-compact source distribution over the blades is also included. The array of acoustic doublets in the cascade direction is shown to involve infinite modes of pressure waves both propagating and decaying. Consideration of the phase relation between the stator source and the rotor source reveals the mode correspondence in both rotor and stator co-ordinate systems. Numerical examples derived from the theory are presented to show the effects of flow Mach number, rotor-stator axial separation, blade spacing ratio of both rows, and drag coefficient of upstream airfoils which defines the profile of wakes on the generated sound pressure. The ratio of the blade spacing of a rotor to that of a stator (in other words, the relation between the number of blades of both rows) is found to have a great influence upon the sound pressure through the effect of change in the angle of propagation of the generated sound wave.

On infinite modes

article Free Access Share on On infinite modes Author: C. H. A. Koster Amsterdam AmsterdamView Profile Authors Info & Claims ACM SIGPLAN NoticesVolume 4Issue 3March 1969 pp 86–89https://doi.org/10.1145/1316865.1316868Online:01 March 1969Publication History 2citation46DownloadsMetricsTotal Citations2Total Downloads46Last 12 Months3Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

On the generation of ALGOL 68 programs involving infinite modes

article Free Access Share on On the generation of ALGOL 68 programs involving infinite modes Author: L. Meertens Mathemetical Centre, Amsterdam, The Netherlands Mathemetical Centre, Amsterdam, The NetherlandsView Profile Authors Info & Claims ACM SIGPLAN NoticesVolume 4Issue 3March 1969 pp 90–92https://doi.org/10.1145/1316865.1316869Published:01 March 1969Publication History 3citation44DownloadsMetricsTotal Citations3Total Downloads44Last 12 Months4Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Localized modes at extended defects in crystals

Abstract Perturbations in the homogeneity of a crystal can give rise to localized modes of vibration. We have discussed the simplest cases of extended defects, namely planes of impurity atoms with special directions (001, 011, etc.) in a simple cubic crystal with nearest neighbour interaction. Extended defects, such as planes of impurity atoms, will have localized modes with exponentially decreasing amplitudes in the direction perpendicular to the planes and wave-like character in directions parallel to them. The different modes of localized vibrations have been analyzed group-theoretically. It comes out that there will be in general an acoustical and an optical branch of localized modes for a plane defect, the occurrence of which and the frequencies relative to the band of the ideal lattice frequencies depend on the defect-parameters (changes in mass and force constants). In the limit of vanishing coupling between defect plane and “host” lattice we get a free surface, which has been considered by Wallis et al. This limiting case has only an acoustical branch, which is identical with the Rayleigh-surface modes for long waves (provided the force-constants fulfill the conditions allowing localized states at all). Also lines of defects can have two branches of modes. The details depend as in other cases on the defect-parameters. If the homogeneity of a crystal lattice is disturbed by a defect, some of the eigenvibrations can be localized modes, i.e. modes the vibration amplitudes of which decrease exponentially with increasing distance from the defect. The occurrence of such localized modes at point defects has been investigated in a large number of cases.(1–5) A free surface can be considered as a perturbation of the infinite lattice and localized modes can occur; this has been discussed in some cases too.(6–8) But in lattices there might be other sorts of defects (e.g. stacking faults, dislocations, etc.) of one and two dimensions. As an attempt to study the localized modes at such defects we have investigated the simplest cases, namely a plane and a line of impurity atoms in a simple cubic lattice; we will explain here only the results concerning the plane defects, the calculation of which is very simple. Line defects are somewhat more involved, but show in general the same features.(9)