Two-Dimensional Problems in Elasticity (in Polar Coordinate System)

2021 ◽  
pp. 163-222
Author(s):  
T. G. Sitharam ◽  
L. Govindaraju
Keyword(s):  
Coordinate System ◽  
Polar Coordinate System ◽  
Two Dimensional ◽  
Polar Coordinate

Investigating the Polar Qualification System

1998 ◽  
Vol 6 (A) ◽  
pp. A191-A200 ◽  
Author(s):  
Károly J. Kaffka ◽  
László S. Gyarmati
Keyword(s):  
Infrared Spectroscopy ◽  
Coordinate System ◽  
Near Infrared Spectroscopy ◽  
Near Infrared ◽  
Polar Coordinate System ◽  
Base Line ◽  
Two Dimensional ◽  
International Conference ◽  
Polar Coordinate ◽  
Characteristic Features

A new, rapid qualification method was introduced at the 3rd International Conference on Near Infrared Spectroscopy according to which a “quality point” was defined on a two-dimensional “quality plane”. The quality point of the investigated material was given by the center of its spectrum represented in a polar coordinate system. The method was further developed, three interpretations were given for the “center” of the polar spectrum, resulting in three different formulas for determining the x and y coordinates of the quality point. The effect of the change in the amplitude of the absorption peaks, the effect of the noise of the spectrum, the effect of the shifting and tilting the base-line of the spectrum on the location of the quality point were investigated using the three formulas. The results of the investigation and the characteristic features of the three formulas are introduced.

Rapid and precise method to convert a two dimensional image from Cartesian to polar coordinate system

1997 ◽  
Vol 68 (9) ◽  
pp. 3490-3493 ◽  
Author(s):  
Weimin Wu ◽  
Yoshihiro Kato ◽  
K. Yamazaki ◽  
M. Yoshino ◽  
A. Danjo ◽  
...  
Keyword(s):  
Coordinate System ◽  
Polar Coordinate System ◽  
Two Dimensional ◽  
Precise Method ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
Polar Coordinate

Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions

1991 ◽  
Author(s):  
C. Rajalingham ◽  
R. B. Bhat ◽  
G. D. Xistris
Keyword(s):  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Polar Coordinate System ◽  
Free Boundaries ◽  
Natural Modes ◽  
Polar Coordinate ◽  
Boundary Characteristic

Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

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