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.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

An equation, suitable for computer use, based on the ARC feeding system to determine the energy requirements of growing and fattening cattle

1972 ◽  
Vol 14 (1) ◽  
pp. 17-23 ◽  
Author(s):  
C. A. Zulberti ◽  
J. T. Reid
Keyword(s):  
Weight Gain ◽  
Computer Use ◽  
Agricultural Research ◽  
Energy Requirement ◽  
Metabolizable Energy ◽  
Energy Requirements ◽  
Energy Concentration ◽  
Feeding System ◽  
Agricultural Research Council ◽  
Forward Calculation

SUMMARYBased on the Agricultural Research Council's feeding system, equations were developed that allow the calculation of the metabolizable energy requirements for maintenance and weight gain by cattle, separately or combined. A general equation was developed for the straight-forward calculation of the total metabolizable energy requirements of growing and fattening cattle for any combination of body weight, rate of weight gain, age, level of muscular work, and metabolizable energy concentration of the diet. The estimates of energy requirement made by the use of this equation are in excellent agreement with those made by the Agricultural Research Council using an iterative method.In addition to avoiding the awkward iterative process, the equations proposed are readily adaptable to computer use.

scholarly journals Spallation of thin films driven by pockets of energy concentration

2017 ◽  
Vol 92 ◽  
pp. 1-12 ◽  
Author(s):  
Christopher M. Harvey ◽  
Bin Wang ◽  
Simon Wang
Keyword(s):  
Thin Films ◽  
Energy Concentration

On the irreversibility of internal-wave dynamics due to wave trapping by mean flow inhomogeneities. Part 1. Local analysis

1993 ◽  
Vol 251 ◽  
pp. 21-53 ◽  
Author(s):  
Sergei I. Badulin ◽  
Victor I. Shrira
Keyword(s):  
Shear Flow ◽  
Internal Wave ◽  
Wave Field ◽  
Large Scale ◽  
Spatial Scales ◽  
Energy Concentration ◽  
Local Analysis ◽  
Mean Flow ◽  
Wave Trapping ◽  
Wave Dynamics

The propagation of guided internal waves on non-uniform large-scale flows of arbitrary geometry is studied within the framework of linear inviscid theory in the WKB-approximation. Our study is based on a set of Hamiltonian ray equations, with the Hamiltonian being determined from the Taylor-Goldstein boundary-value problem for a stratified shear flow. Attention is focused on the fundamental fact that the generic smooth non-uniformities of the large-scale flow result in specific singularities of the Hamiltonian. Interpreting wave packets as particles with momenta equal to their wave vectors moving in a certain force field, one can consider these singularities as infinitely deep potential holes acting quite similarly to the ‘black holes’ of astrophysics. It is shown that the particles fall for infinitely long time, each into its own ‘black hole‘. In terms of a particular wave packet this falling implies infinite growth with time of the wavenumber and the amplitude, as well as wave motion focusing at a certain depth. For internal-wave-field dynamics this provides a robust mechanism of a very specific conservative and moreover Hamiltonian irreversibility.This phenomenon was previously studied for the simplest model of the flow non-uniformity, parallel shear flow (Badulin, Shrira & Tsimring 1985), where the term ‘trapping’ for it was introduced and the basic features were established. In the present paper we study the case of arbitrary flow geometry. Our main conclusion is that although the wave dynamics in the general case is incomparably more complicated, the phenomenon persists and retains its most fundamental features. Qualitatively new features appear as well, namely, the possibility of three-dimensional wave focusing and of ‘non-dispersive’ focusing. In terms of the particle analogy, the latter means that a certain group of particles fall into the same hole.These results indicate a robust tendency of the wave field towards an irreversible transformation into small spatial scales, due to the presence of large-scale flows and towards considerable wave energy concentration in narrow spatial zones.

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