Vibrations in a multiply connected plate with variously shaped perforations

1986 ◽  
Vol 22 (5) ◽  
pp. 447-451
Author(s):  
R. P. Mania ◽  
I. N. Preobrazhenskii
Keyword(s):  
Multiply Connected ◽  
Connected Plate ◽  
Multiply Connected Plate

Stress Systems in a Circular Disk Under Radial Forces

1937 ◽  
Vol 4 (3) ◽  
pp. A115-A118
Author(s):  
Raymond D. Mindlin
Keyword(s):  
Plane Stress ◽  
Infinite Plate ◽  
Circular Disk ◽  
The Other ◽  
Straightforward Calculation ◽  
Multiply Connected ◽  
Radial Forces ◽  
Particular Solution ◽  
The Many ◽  
Multiply Connected Plate

Abstract The transformation of inversion is employed in this paper to generalize a particular solution obtained by Michell (1), for plane stress in a circular disk. In Michell’s solution the disk is loaded in its plane with a pair of equal and opposite forces; one at the center of the disk and the other on the periphery as shown in Fig. 1. In the transformed state, the force in the interior of the disk is no longer at the center, as shown in Fig. 3 and represented by Equation [9]. By simple superposition, the transformed solution is extended to include any self-equilibrating system of radial forces applied in the plane of the disk as shown in Fig. 6b. The transformation would involve only straightforward calculation were it not for the fact that the disk is multiply connected. This condition is caused by the presence of a singularity in the interior of the disk at the point of application of the force. In the inversion of plane stress in a multiply connected plate, the displacement functions for the transformed state are not necessarily single-valued even though they may have arisen from single-valued displacements in the original plate. This difficulty is overcome by the introduction of suitable functions which remove the many valued terms in the displacements, but do not disturb the stress conditions on the boundaries of the transformed disk. The solution is shown to include, as particular cases two well-known problems: (a) A disk loaded on its periphery by forces acting along a diameter as shown in Fig. 4; and (b) a semi-infinite plate loaded near its edge by a force normal to the boundary as shown in Fig. 5.

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

Conformal and Quasiconformal Mappings of Close Multiply-Connected Domains

2002 ◽  
Vol 9 (2) ◽  
pp. 367-382
Author(s):  
Z. Samsonia ◽  
L. Zivzivadze
Keyword(s):  
Integral Equations ◽  
Quasiconformal Mappings ◽  
Multiply Connected Domains ◽  
Multiply Connected

Abstract Doubly-connected and triply-connected domains close to each other in a certain sense are considered. Some questions connected with conformal and quasiconformal mappings of such domains are studied using integral equations.

TOPOLOGICAL QUANTIZATION OF THE MAGNETIC FLUX

2000 ◽  
Vol 15 (24) ◽  
pp. 1491-1495 ◽  
Author(s):  
DANIEL WISNIVESKY
Keyword(s):  
Quantum Theory ◽  
Charged Particle ◽  
Magnetic Flux ◽  
Linear Group ◽  
Connected Region ◽  
Magnetic Tube ◽  
Dirac Monopole ◽  
Multiply Connected ◽  
Quantum Problem ◽  
Multiply Connected Region

We discuss the quantum problem of a charged particle in a multiply connected region encircling a magnetic tube, using a theory in which space and internal coordinates are derived from the parameters of a linear group of transformations (group space quantum theory). Based only on symmetry considerations, we show that, the magnetic flux in the tube must be quantized in multiples of the Dirac monopole charge.

scholarly journals A characterization of internal functions on multiply connected regions

1984 ◽  
Vol 96 ◽  
pp. 23-28
Author(s):  
Lee A. Rubel
Keyword(s):  
Hardy Spaces ◽  
Multiply Connected ◽  
Multiply Connected Regions ◽  
Internal Function

The notion of internal function enters naturally in the study of factorization of function in Lumer’s Hardy spaces—see [RUB], where this aspect is developed in some detail.

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