Laboratory Practicum on Computer Graphics

To master such important section of computer graphics as “Geometric Transformations of Coordinates” have been proposed laboratory works on discipline “Engineering and Computer Graphics” for MSUN students of specialties 27.03.04 “Management in Engineering Systems” and 09.03.01 “Informatics and Computer Engineering”. In contrast to existing laboratory works on computer graphics, demanding the knowledge of algorithmic languages and programming essentials, the presented tasks are performed in a MathCAD package, which allows represent results in the form of geometrical drawings without writing complicated computer programs. In this paper are considered elementary geometrical transformations and their compositions. Matrixes of object coordinates transformations at transfer, rotation and scaling on the plane and in space have been described. Constructions of orthogonal, axonometric and central projections on screen plane have been considered. Distinctions in algorithms for objects’ geometrical transformations above reference zero and arbitrary point have been noted. It has been showed that the end result of complex transformations depends on sequence of elementary transformations. A large number of examples covering the laboratory practicum’s content have been provided. Results have been presented in the form of numbers and drawings using MathCAD. In the first laboratory work have been considered the objects geometrical transformations (transfer, rotation and scaling) on the plane and in space; in the second one – construction of central, orthogonal and axonometric projections for three-dimensional objects on a computer screen (plane). Have been developed methodological instructive regulations for performance of laboratory and independent works which are used for students training on the MSUN’s descriptive geometry and graphics chair.

Experimental and numerical studies on the flow-induced vibration of propeller blades under nonuniform inflow

This article presents the experimental and numerical studies on the flow-induced vibration of propeller blades under periodic inflows. A total of two 7-bladed highly skewed model propellers of identical geometries but different elastic characteristics were operated in four-cycle and six-cycle inflows to study the blade vibratory strain response. A total of two kinds of wire mesh wake screens located 400 mm upstream of the propeller plane were used to generate four-cycle and six-cycle inflows. A laser Doppler velocimetry system located 100 mm downstream of the wake screen plane was used to measure the axial velocity distributions produced by the wake screens. Strain gauges were bonded onto the propeller blades in different positions. Data from strain gauges quantified vibratory strain amplitudes and excitation frequencies induced by the wake screens. The propellers were accelerated through the flexible propeller’s fundamental frequency to investigate the effect of resonance on vibratory strain response. The numerical work was conducted using large eddy simulation and moving mesh technique to predict the unsteady forces acting on the propeller blade when operating in a nonuniform inflow.

The diffraction of light by metallic screens

Gouy discovered that when a metallic screen with a sharp and highly-polished edge is held in the path of a pencil of light, its boundary appears as a luminous line diffracting light through large angles, both into the region of shadow (interior diffraction) and into the region of light (exterior diffraction). He noticed further that this diffracted light is strongly polarised, but in perpendicular planes in the two regions mentioned; the colour of the diffracted light and its state of polarisation depend in a remarkable manner on the material of the screen and on the extent to which its edge is rounded off in the process of polishing. When the edge is viewed through a double-image-prism from within the shadow, only that image appears coloured which is more intense and is polarised with the magnetic vector parallel to the edge. The second image which is fainter and is polarised with the electric vector parallel to the edge, appears perfectly white. When the incident light is polarised in any arbitrary azimuth, the diffracted light is found to exhibit elliptic polarisation. These and other results have been confirmed by later observers. Gouy’s experimental results were discussed by Poincaré on the basis of the electromagnetic theory of light in two memoirs published in the “Acta Mathematica.” The special case of an ideal screen (plane or wedge-shaped), supposed perfectly-reflecting and having a sharp edge, is amenable to complete theoretical treatment, and was dealt with by Poincaré himself, and later in a rigorous manner by Sommerfeld, and following him by numerous other mathematicians. The behaviour of actual metallic screens, however, differs considerably from that found theoretically for this ideal case. Though attempts have been made by Poincaré himself in the memoirs quoted, and later also by Epstein, to take the nature of the screen and the rounding of its edge into account, it cannot be said that Gouy’s observations have so far received a complete or satisfactory explanation. We propose in this paper to discuss more particularly the influence of the material of the screen on the diffraction by a sharp edge, and to show how it may be explained in a very simple manner. The case of rounded edges is reserved for discussion in a separate paper.