scholarly journals Acoustics of Fractal Porous Material and Fractional Calculus

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1774
Author(s):  
Zine El Abiddine Fellah ◽  
Mohamed Fellah ◽  
Nicholas O. Ongwen ◽  
Erick Ogam ◽  
Claude Depollier
Keyword(s):  
Porous Medium ◽  
Fractal Dimension ◽  
Porous Material ◽  
Time Domain ◽  
Spatial Dimension ◽  
Acoustic Properties ◽  
Solid Matrix ◽  
Equivalent Thickness ◽  
Reflection And Transmission ◽  
The Time Domain

In this paper, we present a fractal (self-similar) model of acoustic propagation in a porous material with a rigid structure. The fractal medium is modeled as a continuous medium of non-integer spatial dimension. The basic equations of acoustics in a fractal porous material are written. In this model, the fluid space is considered as fractal while the solid matrix is non-fractal. The fluid–structure interactions are described by fractional operators in the time domain. The resulting propagation equation contains fractional derivative terms and space-dependent coefficients. The fractional wave equation is solved analytically in the time domain, and the reflection and transmission operators are calculated for a slab of fractal porous material. Expressions for the responses of the fractal porous medium (reflection and transmission) to an acoustic excitation show that it is possible to deduce these responses from those obtained for a non-fractal porous medium, only by replacing the thickness of the non-fractal material by an effective thickness depending on the fractal dimension of the material. This result shows us that, thanks to the fractal dimension, we can increase (sometimes by a ratio of 50) and decrease the equivalent thickness of the fractal material. The wavefront speed of the fractal porous material depends on the fractal dimension and admits several supersonic values. These results open a scientific challenge for the creation of new acoustic fractal materials, such as metamaterials with very specific acoustic properties.

scholarly journals Analysis of Longitudinal Guided Wave Propagation in a Liquid-Filled Pipe Embedded in Porous Medium

2021 ◽  
Vol 11 (5) ◽  
pp. 2281
Author(s):  
Nana Su ◽  
Qingbang Han ◽  
Yu Yang ◽  
Minglei Shan ◽  
Jian Jiang
Keyword(s):  
Porous Medium ◽  
Time Domain ◽  
Saturated Porous Medium ◽  
Guided Wave ◽  
Guided Wave Propagation ◽  
Partial Mode ◽  
The Media ◽  
The Time Domain ◽  
Good Agreement

To study the leakage situation of a liquid-filled pipe in long-term service, a model of a liquid-filled pipe embedded in an infinite porous medium as well as in a finite porous medium is designed. The principal motivation is to perform detailed quantitative analysis of the longitudinal guided wave propagating in a liquid-filled pipe embedded in a saturated porous medium. The problems of pipeline leakage and porosity as well as the media outside the pipe are solved to identify the characteristics of the guided wave in a more practical model. The characteristics of the guided wave are investigated theoretically and numerically, with special emphasis on the influence of porous medium parameters on the dispersion properties. Assuming the pipe is a cylindrical shell buried in an isotropic, homogeneous, and porous medium, the dispersion equations are established based on the elastic-dynamic equations and the modified Biot liquid-saturated porous theory. The characteristics of dispersion, time-domain waveform and attenuation curves varying with porous medium parameters, wrapping layer material, and thickness, are all analyzed. The increase in porosity decreases the partial mode phase velocity in the liquid-filled pipe embedded in the finite porous medium. The characteristics of attenuation are in good agreement with the dispersion curves and the time-domain waveform results.

scholarly journals Free-Space Materials Characterization by Reflection and Transmission Measurements using Frequency-by-Frequency and Multi-Frequency Algorithms

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 260 ◽  
Author(s):  
Fábio Gonçalves ◽  
Alfred Pinto ◽  
Renato Mesquita ◽  
Elson Silva ◽  
Adriana Brancaccio
Keyword(s):  
Time Domain ◽  
Free Space ◽  
Dielectric Materials ◽  
Weighting Factor ◽  
Reflection And Transmission ◽  
Favorable Configuration ◽  
The Time Domain ◽  
Transmission And Reflection

The knowledge of the electromagnetic constitutive properties of materials is crucial in many applications. Free-space methods are widely used for this purpose, despite their inherent practical difficulties. This paper describes an affordable free-space experimental setup for the characterization of flat samples in 1–6 GHz in a non-anechoic environment. The extracted properties are obtained from the calibrated Scattering Parameters, using a frequency-by-frequency solution or a multi-frequency reconstruction. For the first, we describe how the Time-Domain Gating can be implemented and used for filtering the signals. For the latter, a weighting factor is introduced to balance the reflection and transmission data, allowing one to have a more favorable configuration. The different role of transmission and reflection measurements on the achievable results is analyzed with regard to experimental uncertainties and different noise scenarios. Results from the two strategies are analyzed and compared. Good agreement between simulation, measurement and literature is obtained. According to the reported results for dielectric materials, there is no need of filtering the data by a Time-Domain Gating in case of the multi-frequency approach. Experimental results for Polymethylmethacrylate (PMMA) and Polytetrafluorethylene (PTFE) samples validate both the setup and the processing.

Characteristic Exponent Extraction of Experimental Nonlinear Time Series

2014 ◽  
Vol 556-562 ◽  
pp. 3835-3838
Author(s):  
Shu Yong Liu ◽  
Xiu Lei Wei
Keyword(s):  
Fractal Dimension ◽  
Time Domain ◽  
Characteristic Exponent ◽  
Measured Data ◽  
Vibration System ◽  
Fast Search ◽  
Extraction Algorithm ◽  
Inquiry Method ◽  
The Time Domain ◽  
Nonlinear Vibration System

The experiment of chaotic exponent extraction is carried out on the basis of nonlinear vibration system, and the responses under different conditions are processed with the improved algorithm. Firstly, the weighted wavelet denoise method is applied to filter the contaminated noise. Then, on the basis of fast search technology i.e. space grid hiberarchy inquiry method, the chaos characteristic exponent extraction algorithm is modified and applied to LE and fractal dimension calculation. Finally the piece-wise vibration system is designed, and the nonlinear dynamics under different harmonic frequencies excitation are analyzed. The comprehensive chaos judgment program is developed, in which the time domain diagram, phase space reconstruction attractor, Lyapunov exponent, fractal dimension curve of the measured data are obtained. The interesting phenomena such as AM modulation, limited cycle, and strange attractor are observed.

ESTIMATION OF THERMAL CONDUCTIVITY OF POROUS MATERIAL WITH FEM AND FRACTAL GEOMETRY

2009 ◽  
Vol 20 (04) ◽  
pp. 513-526 ◽  
Author(s):  
SHOUJU LI ◽  
YUEFANG WANG ◽  
YINGXI LIU ◽  
WEI SUN
Keyword(s):  
Thermal Conductivity ◽  
Fractal Dimension ◽  
Porous Material ◽  
Effective Thermal Conductivity ◽  
Pore Space ◽  
Thermal Flux ◽  
Solid Matrix ◽  
The Finite Element Method ◽  
Heat Transform ◽  
The Relationship

The relationship between thermal conductivity of porous material and fractal dimension is numerically simulated by using the finite element method. The solid matrix and pore space are generated randomly according to material porosity. Material parameters and element properties are changed by using ANSYS parameter design language. The effective thermal conductivity is derived according to thermal flux through some sections computed by FEM and Fourier heat transform law. The investigation shows that the effective thermal conductivity decreases with increasing porosity. The effective thermal conductivity will decrease exponentially with increasing fractal dimension of porosity space and increase exponentially with increasing fractal dimension of solid matrix.

scholarly journals Frequency domain and time domain analysis of thermoacoustic oscillations with wave-based acoustics

2015 ◽  
Vol 775 ◽  
pp. 387-414 ◽  
Author(s):  
A. Orchini ◽  
S. J. Illingworth ◽  
M. P. Juniper
Keyword(s):  
State Space ◽  
Frequency Domain ◽  
Time Domain ◽  
Space Form ◽  
Laminar Flame ◽  
Kinematic Model ◽  
Time Domain Analysis ◽  
Acoustic Properties ◽  
Nonlinear Behaviour ◽  
The Time Domain

Many thermoacoustic systems exhibit rich nonlinear behaviour. Recent studies show that this nonlinear dynamics can be well captured by low-order time domain models that couple a level set kinematic model for a laminar flame, the $G$-equation, with a state-space realization of the linearized acoustic equations. However, so far the $G$-equation has been coupled only with straight ducts with uniform mean acoustic properties, which is a simplistic configuration. In this study, we incorporate a wave-based model of the acoustic network, containing area and temperature variations and frequency-dependent boundary conditions. We cast the linear acoustics into state-space form using a different approach from that in the existing literature. We then use this state-space form to investigate the stability of the thermoacoustic system, both in the frequency and time domains, using the flame position as a control parameter. We observe frequency-locked, quasiperiodic and chaotic oscillations. We identify the location of Neimark–Sacker bifurcations with Floquet theory. We also find the Ruelle–Takens–Newhouse route to chaos with nonlinear time series analysis techniques. We highlight important differences between the nonlinear response predicted by the frequency domain and the time domain methods. This reveals deficiencies with the frequency domain technique, which is commonly used in academic and industrial studies of thermoacoustic systems. We then demonstrate a more accurate approach based on continuation analysis applied to time domain techniques.

Apodisation in the time domain

1992 ◽  
Vol 2 (4) ◽  
pp. 615-620
Author(s):  
G. W. Series
Keyword(s):  
Time Domain ◽  
The Time Domain

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

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