Numerical Solution to an Energy Concentration Problem Associated with the Special Affine Fourier Transformation

2017 ◽  
pp. 161-184
Author(s):  
Amara Ammari ◽  
Tahar Moumni ◽  
Ahmed Zayed
Keyword(s):  
Numerical Solution ◽  
Fourier Transformation ◽  
Energy Concentration ◽  
Concentration Problem

ANALYTICAL AND EXPERIMENTAL INVESTIGATION ON THE FREE VIBRATION OF SUBMERGED STIFFENED STEEL PLATE

2021 ◽  
Vol 160 (A2) ◽  
Author(s):  
S S Rezvani ◽  
M S Kiasat
Keyword(s):  
Numerical Solution ◽  
Fourier Transformation ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Steel Plate ◽  
Added Mass ◽  
Fast Fourier Transformation ◽  
Stiffened Plate ◽  
Transformation Functions ◽  
Stiffened Steel

The approach developed in this paper applies to vibration analysis of rectangular stiffened plate coupled with fluid. It is obvious that the natural frequencies of a submerged structure are less than those of in vacuum and these are due to the effect of added mass of water to the structure. This paper focuses on the experimental, analytical and numerical solution of natural frequencies of submerged stiffened plate. The analytical solution based on the deflection equation of submerged orthotropic plate, Laplace’s equation and Rayleigh's method in vibration analysis. By used the FEM software the numerical results for natural frequencies are derived. The natural frequencies of the stiffened plate are obtained practically by using Fast Fourier Transformation functions (FFT) in experimental analysis. Experimental results demonstrate the validity of analytical and numerical solution and results.

Analytical and Experimental Investigation on the Free Vibration of Submerged Stiffened Steel Plate

2018 ◽  
Vol Vol 160 (A2) ◽  
Author(s):  
S S Rezvani ◽  
M S Kiasat
Keyword(s):  
Numerical Solution ◽  
Fourier Transformation ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Steel Plate ◽  
Added Mass ◽  
Fast Fourier Transformation ◽  
Stiffened Plate ◽  
Transformation Functions ◽  
Stiffened Steel

The approach developed in this paper applies to vibration analysis of rectangular stiffened plate coupled with fluid. It is obvious that the natural frequencies of a submerged structure are less than those of in vacuum and these are due to the effect of added mass of water to the structure. This paper focuses on the experimental, analytical and numerical solution of natural frequencies of submerged stiffened plate. The analytical solution based on the deflection equation of submerged orthotropic plate, Laplace’s equation and Rayleigh's method in vibration analysis. By used the FEM software the numerical results for natural frequencies are derived. The natural frequencies of the stiffened plate are obtained practically by using Fast Fourier Transformation functions (FFT) in experimental analysis. Experimental results demonstrate the validity of analytical and numerical solution and results.

Solution of the energy concentration problem and application

2018 ◽  
Vol 29 (5-6) ◽  
pp. 929-938
Author(s):  
Tahar Moumni
Keyword(s):  
Energy Concentration ◽  
Concentration Problem

Analytic solutions of the radiation modes problem and the active control of sound power

2005 ◽  
Vol 461 (2053) ◽  
pp. 55-78 ◽  
Author(s):  
Cedric Maury ◽  
Stephen J. Elliott
Keyword(s):  
Active Control ◽  
Acoustic Radiation ◽  
Special Functions ◽  
Spectral Estimation ◽  
Analytic Solutions ◽  
Energy Concentration ◽  
Spheroidal Wave Functions ◽  
Prolate Spheroidal Wave Functions ◽  
Concentration Problem ◽  
Band Limited

This paper explores the common mathematical foundation of two different problems: the first one arises in electrical engineering for the detection and the spectral estimation of signals in noise and the second one appears in acoustics for the calculation of the acoustic radiation modes of rectangular structures. Although apparently unrelated, it is found that both applications draw on the so–called concentration problem: of determining which functions that are band–limited in one domain have maximal energy concentration within a region of the transform domain. The analytic solutions to problems of this form are seen to involve prolate spheroidal wave functions. In particular, exact expressions are given for the radiation efficiencies and shapes of the radiation modes of a baffled beam as well as their asymptotics. It is shown that a generalization of the concentration problem to the two–dimensional case provides analytic solutions that solve with a good accuracy, although approximately, the radiation problem. The properties of these special functions provide a rigorous basis of understanding some previously observed features of these applications, namely the grouping property of the radiation modes of a baffled panel and the physical limitations for the active control of sound from a panel.

Simulations of high-resolution images of amorphous silicon films

1986 ◽  
Vol 44 ◽  
pp. 544-545
Author(s):  
G. Y. Fan ◽  
J. M. Cowley
Keyword(s):  
Electron Microscope ◽  
High Frequency ◽  
Fourier Transformation ◽  
Amorphous Materials ◽  
Low Frequency ◽  
Chromatic Aberration ◽  
Structure Information ◽  
Frequency Components ◽  
High Resolution Images ◽  
Spatial Frequency Spectrum

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.

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