scholarly journals Chladni Figures Simulation on a Rectangular Plate

2021 ◽  
Vol 26 (3) ◽  
Author(s):  
Pavlo Ihorovych Krysenko ◽  
Maksym Olehovych Zoziuk ◽  
Oleksandr Ivanovych Yurikov ◽  
Dmytro Volodymyrovych Koroliuk ◽  
Yurii Ivanovych Yakymenko
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Standing Waves ◽  
Physical Nature ◽  
Practical Significance ◽  
The Fourier Transform ◽  
Further Development ◽  
Top View ◽  
Chladni Figures

An analytical model for creating flat Chladni figures is presented. The equation of a standing wave in the simplest boundary conditions and the Fourier transform are used. Top view images are shown at different frequencies. The practical significance of the results obtained for the further development of the field of creating Chladni figures based on standing waves of different physical nature has been determined.

A Central Crack in a Finite Rectangular Plate With Four Hinged Edges Under the Opening Mode

1990 ◽  
Vol 57 (4) ◽  
pp. 1079-1081
Author(s):  
S. W. Ma ◽  
Y. G. Tsuei
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Fourier Transform ◽  
Fourier Series ◽  
Rectangular Plate ◽  
Uniform Loading ◽  
Central Crack ◽  
Opening Mode ◽  
Loading Case ◽  
The Fourier Transform

By combining linearly the Fourier transform and Fourier series, the stress intensity factor of a central crack in a finite rectangular plate with four hinged edges under the opening mode is expressed as the Fredholm integral equation of the second kind. The uniform loading case is considered in detail. The numerical results include the predictions by Koiter and Fichter as limiting cases.

Optimising the Efficiency of Storm Water Settling Basins by Means of Bypassing

1993 ◽  
Vol 27 (5-6) ◽  
pp. 105-110 ◽  
Author(s):  
F. H. L. R. Clemens ◽  
H. J. van Mameren ◽  
J. Kollen
Keyword(s):  
Boundary Conditions ◽  
Dynamic Behaviour ◽  
Storm Water ◽  
Mixed System ◽  
Research Needs ◽  
Settling Basin ◽  
Potential Increase ◽  
Overall Efficiency ◽  
Further Development

The reduction in pollutional load realised by storm water settling basins is potentially reduced due to the occurrence of a partially mixed situation in the basin or due to resuspension of settled material. The decrease in efficiency can theoretically be avoided by means of partially bypassing the basin. In order to quantify the potential increase in efficiency a settling basin in Amersfoort is taken as an example. This basin seems to behave like an almost completely mixed system, bypassing would increase the overall efficiency from ca. 34 % to ca 39 % for three overflows. The dynamic behaviour of settling basins, scouring conditions and the boundary conditions for which settling basins are to be designed are the research needs for further development in the field of storm water settling basins.

Study of Rheological Properties of Modified Concrete Mixtures at Vibration

2019 ◽  
Vol 968 ◽  
pp. 96-106
Author(s):  
Oleksandr Pshinko ◽  
Olena Hromova ◽  
Dmytro Rudenko
Keyword(s):  
Mechanical Properties ◽  
Rheological Properties ◽  
Physical Nature ◽  
Concrete Mixture ◽  
Practical Significance ◽  
Vibration Displacement ◽  
Concrete Mixtures ◽  
Variable Quantity ◽  
Vibration Compaction ◽  
Mechanism Of Interaction

Study of rheological properties of concrete mixtures based on modified cement systems in order to determine process parameters. Methodology. To study structural-mechanical properties of modified concrete mixtures of different consistency at their horizontal vibrating displacement an oscillatory viscometer was designed. Results. The optimization of the process of vibration displacement of concrete mixtures with the specification of parameters of vibration impacts taking into account structural-mechanical properties of the mixture is performed. It has been established that the viscosity of the modified cement system of the concrete mixture is a variable quantity, which depends on the parameters of the vibration impacts. Scientific novelty. The mechanism of interaction of the modified concrete mixture with the form and the table vibrator during its vibration compaction is determined. On the basis of this, a model of concrete laying process control is proposed, that allows to predict the ability to form a dense concrete structure. Practical significance. Disclosed physical nature of the process of vibrating displacement of modified concrete mixtures using the principles of physical-chemical mechanics of concrete allows reasonably choose the best options for vibration impacts.

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.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

scholarly journals Convolutors on $${\mathcal S}_{\omega }({\mathbb R}^N)$$

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
Angela A. Albanese ◽  
Claudio Mele
Keyword(s):  
Fourier Transform ◽  
Dual Space ◽  
Strong Operator ◽  
Dual Spaces ◽  
Structure Theorems ◽  
The Fourier Transform ◽  
Decreasing Functions

AbstractIn this paper we continue the study of the spaces $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) and $${\mathcal O}_{C,\omega }({\mathbb R}^N)$$ O C , ω ( R N ) undertaken in Albanese and Mele (J Pseudo-Differ Oper Appl, 2021). We determine new representations of such spaces and we give some structure theorems for their dual spaces. Furthermore, we show that $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$ O C , ω ′ ( R N ) is the space of convolutors of the space $${\mathcal S}_\omega ({\mathbb R}^N)$$ S ω ( R N ) of the $$\omega $$ ω -ultradifferentiable rapidly decreasing functions of Beurling type (in the sense of Braun, Meise and Taylor) and of its dual space $${\mathcal S}'_\omega ({\mathbb R}^N)$$ S ω ′ ( R N ) . We also establish that the Fourier transform is an isomorphism from $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$ O C , ω ′ ( R N ) onto $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) . In particular, we prove that this isomorphism is topological when the former space is endowed with the strong operator lc-topology induced by $${\mathcal L}_b({\mathcal S}_\omega ({\mathbb R}^N))$$ L b ( S ω ( R N ) ) and the last space is endowed with its natural lc-topology.

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