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1

Magneto-thermo-piezo-elastic wave in an initially stressed rotating monoclinic crystal in a two-temperature theory

Yadav Anand Kumar

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 3

127--158

EN

This research problem is an investigation of wave propagation in a rotating initially stressed monoclinic piezoelectric thermo-elastic medium under with the effect of a magnetic field. A two-temperature generalized theory of thermo-elasticity in the context of Lord-Shulman’s theory is applied to study the waves under the magnetic field. The governing equations of a rotating initially stressed monoclinic piezoelectric thermo-elastic medium with a magnetic field are formulated. This research problem is solved analytically, for a two-dimensional model of the piezo-electric monoclinic solid, and concluded that there must be four piezo-thermoelastic waves, three coupled quasi waves (qP (quasi-P), qT (quasi-thermal), and qSV (quasi-SV)) and one piezoelectric potential (PE) wave propagating at different speeds. It is found that at least one of these waves is evanescent (an evanescent wave is a non-propagating wave that exists) and that there are therefore no more than three bulk waves. The speeds of different waves are calculated and the influence of the piezoelectric effect, two-temperature parameter, frequency, rotation, and magnetic field on phase velocity, attenuation coefficient, and specific loss is shown graphically. This model may be used in various fields, e.g. wireless communications, signal processing, and military defense equipment are all pertinent to this study.

2

Study on acoustic velocity dispersion of carbonate rock and extrapolation of the velocity

Duan Xi, Zheng Haoyue, Liu Xiangjun, Liang Lixi, Xiong Jian

Acta Geophysica

|

2023

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Vol. 71, no. 2

723--733

EN

At present, a series of petrophysical experimental studies have been carried out on the velocity dispersion and attenuation caused by wave induced fluid flow. So as many valuable theoretical models have been proposed or developed. But these studies fail to reflect the influence of different pore structure types on velocity dispersion and attenuation. Carbonate rocks have complex pore structure and strong heterogeneity. The study of the influence of pore structure on acoustic propagation characteristics at different frequencies is of great significance for further refinement of reservoir prediction. Through computed tomography scan and digital image processing, the pore structure distribution of longitudinal section of carbonate rock is obtained. On this basis, the finite difference numerical simulation of acoustic wave field is carried out, and the variation law of acoustic velocity with frequency and the relationship between acoustic velocity dispersion and attenuation coefficient are analyzed. The acoustic velocity extrapolation model based on frequency dispersion is established and compared with the experimental results to verify the effectiveness. The research results provide a theoretical basis for the prediction of carbonate reservoir parameters.

3

A comprehensive Monte Carlo study to design a novel multi-nanoparticle loaded nanocomposites for augmentation of attenuation coefficient in the energy range of diagnostic X-rays

Sayyadi Elahe, Mesbahi Asghar, Zamiri Reza Eghdam, Nejad Farshad Seyyed

Polish Journal of Medical Physics and Engineering

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2021

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Vol. 27, Iss. 4

279--289

EN

Introduction: The present study aimed to investigate the radiation protection properties of silicon-based composites doped with nano-sized Bi2O3, PbO, Sm2O3, Gd2O3, WO3, and IrO2 particles. Radiation shielding properties of Sm2O3 and IrO2 nanoparticles were investigated for the first time in the current study. Material and methods: The MCNPX (2.7.0) Monte Carlo code was utilized to calculate the linear attenuation coefficients of single and multi-nano structured composites over the X-ray energy range of 10–140 keV. Homogenous distribution of spherical nanoparticles with a diameter of 100 nm in a silicon rubber matrix was simulated. The narrow beam geometry was used to calculate the photon flux after attenuation by designed nanocomposites. Results: Based on results obtained for single nanoparticle composites, three combinations of different nano-sized fillers Sm2O3+WO3+Bi2O3, Gd2O3+WO3+Bi2O3, and Sm2O3+WO3+PbO were selected, and their shielding properties were estimated. In the energy range of 20-60 keV Sm2O3 and Gd2O3 nanoparticles, in 70-100 keV energy range WO3 and for photons energy higher than 90 keV, PbO and Bi2O3 nanoparticles showed higher attenuation. Despite its higher density, IrO2 had lower attenuation compared to other nanocomposites. The results showed that the nanocomposite containing Sm2O3, WO3, and Bi2O3 nanoparticles provided better shielding among the studied samples. Conclusions: All studied multi-nanoparticle nanocomposites provided optimum shielding properties and almost 8% higher attenuation relative to single nano-based composites over a wide range of photon energy used in diagnostic radiology. Application of these new composites is recommended in radiation protection. Further experimental studies are suggested to validate our findings.

4

Mathematical study of Rayleigh waves in piezoelectric microstretch thermoelastic medium

Kumar Arvind, Abo-Dahab S. M., Ailawalia Praveen

Mechanics and Mechanical Engineering

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2019

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Vol. 23, nr 1

86--93

EN

This paper is concerned with the study of propagation of Rayleigh waves in a homogeneous isotropic piezo-electric microstretch-thermoelastic solid half-space. The medium is subjected to stress-free, isothermal boundary. After developing a mathematical model, the dispersion curve in the form of polynomial equation is obtained. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. Some special cases have also been derived from the present investigation.

5

Propagation in dielectric rectangular waveguides

Yeap K. H., Teh K. H., Yeong K. C., Lai K. C., Loh M. C.

Optica Applicata

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2016

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Vol. 46, nr 2

317--330

EN

We present a fundamental and accurate approach to compute the attenuation of electromagnetic waves propagating in dielectric rectangular waveguides. The transverse wave numbers are first obtained as roots of a set of transcendental equations developed by matching the fields with the surface impedance of the wall. The propagation constant is found by substituting the values of transverse wave numbers into the dispersion relation. We have examined the validity of our model by comparing the computed results with those obtained from Marcatili’s equations and the finite element method. In our results, it is shown that the fundamental mode is identical with that found in a perfectly conducting waveguide. Our analysis also shows that a hollow waveguide is found to have much lower attenuation than its dielectric counterparts. Since the cutoff frequency is usually affected by the constitutive properties of the dielectric medium, for a waveguide designed for wave with the same cutoff frequency, hollow waveguides turn out to be relatively larger in size.

6

The Effect of Grain-refinement on Zn-10Al Alloy Damping Properties

Piwowarski G., Krajewski P. K., Buraś J., Krajewski W. K.

Archives of Foundry Engineering

|

2014

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Vol. 14, iss. 4

91--94

EN

The paper is devoted to grain-refinement of the medium-aluminium zinc based alloys (MAl-Zn). The system examined was sand cast Zn-10 wt. %. Al binary alloy (Zn-10Al) doped with commercial Al-3 wt. % Ti – 0.15 wt. % C grain refiner (Al-3Ti-0.15C GR). Basing on the measured attenuation coefficient of ultrasonic wave it was stated that together with significantly increased structure fineness damping decreases only by about 10 – 20%. The following examinations should establish the influence of the mentioned grain-refinement on strength and ductility of MAl-Zn cast alloys.

7

Wyznaczanie kruchości skał na podstawie analizy składu mineralnego i chemicznego skał oraz fotoelektrycznego współczynnika absorpcji promieniowania gamma Pe

Kowalska S.

Prace Naukowe Instytutu Nafty i Gazu

|

2012

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nr 182 wyd. konferencyjne

567--571

PL

Parametr kruchości jest podstawowym wskaźnikiem określającym podatność skał na szczelinowanie hydrauliczne wykorzystywane przy udostępnianiu złóż gazu łupkowego. Kruchość skał jest pochodną kilku czynników — składu mineralnego, stopnia kompakcji oraz struktury wewnętrznej skał. Ze względu na zróżnicowanie wykształcenia litologicznego skał istnieje konieczność kalibracji tego parametru indywidualnie dla każdego kompleksu skalnego, biorąc pod uwagę ich charakterystykę mineralogiczną. Obecnie w celu określenia kruchości skał mułowcowo-ilastych wykorzystuje się albo analizę ich składu mineralnego albo chemicznego. Na przykładzie skał mioceńskich wykazano dobrą korelację obu powyższych parametrów po- między sobą oraz z fotoelektrycznym współczynnikiem absorpcji promieniowania gamma Pe pomierzonym w warunkach laboratoryjnych. Fotoelektryczny współczynnik absorpcji promieniowania gamma Pe jest wielkością określającą zdolność ośrodka do pochłaniania promieniowania gamma, zależną wprost od jego składu chemicznego. Promieniowanie gamma pokrywa się w pewnym zakresie z promieniowaniem rentgenowskim. Dzięki temu współczynnik Pe jest proporcjonalny do współczynnika absorpcji masowej µ*, który może być wyznaczony doświadczalnie. Po kalibracji na podstawie szczegółowej analizy mineralogicznej możliwe będzie odczytywanie poziomu kruchości skał na podstawie profilowania efektu fotoelektrycznego (PEF).

EN

Brittleness is the fundamental indicator of the rock susceptibility for hydraulic fracturing which is applied during the shale gas production. The brittleness of rocks depends on several factors — the mineralogical composition, the degree of compaction and the structure of rock. Because of the lithological differences that parameter needs to be calibrated individually for the specific geological formation. At present, the analysis of the chemical or mineralogical composition is used in order to determine the brittleness of clastic rocks. On the example of the Miocene rocks the good correlation of both types of parameters and the photoelectric mass attenuation coefficient Pe was demonstrated. The photoelectric mass attenuation coefficient Pe could be measured in the laboratory. It is the parameter which defines the ability of the medium to absorb the gamma rays, depending on its chemical composition. The gamma radiation coincide in some range with the X-rays. Therefore the photoelectric mass attenuation coefficient Pe is proportional to the mass absorption coefficient µ*, which could be measured directly in the laboratory. After the calibration of the method it will be possible to estimate the brittleness of rocks on the basis of the geophysical logs PEF.

8

Stoneley waves at swelling porous elastic media

Kumar R., Taneja D., Kumar K.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 4

1177-1192

EN

A frequency equation for Stoneley waves at a bonded interface between two swelling porous elastic half spaces [SP/SP] is derived. It is found that Stoneley waves in a swelling porous elastic medium are dispersive in nature. Numerical computations are performed to study the variation of phase velocity and attenuation coefficient with respect to the wave number. Amplitude ratios are obtained and also represented graphically. Some particular cases are also discussed.

9

Quantitative Ultrasound of Cancellous Bone. Modeling and Experiment

Pakuła M.

Image Processing & Communications

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2012

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Vol. 17, no. 4

23--30

EN

The paper present theoretical and experimental issues related to application of Quantitative Ultrasound (QUS) for assessment of cancellous bone quality and prediction of bone fractures. Commonly used for modeling of ultrasonic wave propagation in cancellous bone, the macroscopic Biot’s theory is discussed in context of its potential applicability for theoretical prediction of wave parameters: phase velocity and attenuation coefficient as functions of frequency. The analysis of the model is focused on the absorption mechanisms responsible for attenuation of ultrasonic waves in cancellous bone, which based on the ultrasonic experiments presumably play a predominant role in the total attenuation. The suitability of the model is discussed and verified by comparison of results of sensitivity analysis of the model with ex vivo experimental ultrasonic data obtained for cancellous bones filled with different fluids.

10

Wave propagation in swelling porous elastic layer

Kumar R., Taneja D., Kumar K.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 2

379-398

EN

The present investigation deals with the propagation of straight and circularly crested Lamb waves in a swelling porous elastic layer subjected to stress free boundary. A Helmholtz decomposition technique has been used to simplify the mathematical model. The secular equations for different mechanical situations are obtained. Numerical computations are performed to compute the symmetric and skew-symmetric phase velocity and attenuation coefficient in Swelling Porous (SP) and without Swelling Porous (elastic) (WSP) media. At short wavelength limits, the secular equations for symmetric and skew-symmetric waves in the stress free swelling porous and without swelling porous elastic layer reduce to the Rayleigh surface wave frequency equation. The amplitudes of displacements and stresses are obtained and are presented graphically. Some special cases have been deduced from the present investigation. The present study has immense applications to geophysical problems and structure problems.

11

Wave propagation at the boundary surface of orthotropic porous material with rotation and isotropic elastic half-space

Kumar R., Kumar R.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 3

683-708

EN

The purpose of this research is to study the surface wave propagation in a layer of an orthotropic porous material with rotation lying over an isotropic elastic half-space. The frequency equation is derived after developing the mathematical model. The dispersion curves giving the phase velocity and attenuation coefficient versus wave number are plotted graphically to depict the effects of rotation and anisotropy for (I) welded contact and (II) smooth contact boundary conditions. The amplitudes of normal displacement, normal stress, volume fraction field and gradient of volume fraction field for the welded contact are obtained and are shown graphically for a particular model to depict the rotation and anisotropy effects. Some special cases are also deduced from the present investigation.

12

Effect of rotation on surface wave propagation in a elastic layer lying over a thermodiffusive elastic half-space having imperfect boundary

Kumar R., Chawla V.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 1

37-55

EN

The present investigation deals with the propagation of surface waves at an imperfect boundary between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half- space with rotation in the context of generalized theory of thermoelastic diffusion. Lord and Shulman (L-S) theory in which thermal and thermo-mechanical relaxation time is governed by time constant and diffusion relaxation time is governed by other different time constants is selected for the study. The secular equation for surface waves in a compact form is derivied after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness and then deduced for normal stiffness, tangential stiffness and welded contact. The dispersion curves for these quantities are illustrated to depict the effect of stiffness and thermal relaxation times. The amplitudes of displacements, temperature and concentration are computed at the free plane boundary and depicted graphically. Specific loss of energy is obtained and presented graphically. The effects of rotation are shown for phase velocity, attenuation coefficient and amplitudes of displacements, temperature change and concentration. Some special cases of interest are also deduced and compared with known results.

13

Study of circular crested waves in a micropolar porous medium possessing cubic symmetry

Kumar R., Panchal M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2011

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Vol. 59, nr 1

103-110

EN

The paper is concerned with the propagation of circular crested Lamb waves in a homogeneous micpropolar porous medium possessing cubic symmetry. The frequency equations, connecting the phase velocity with wave number and other material parameters, for symmetric as well as antisymmetric modes of wave propagation are derived. The amplitudes of displacement components, microrotation and volume fraction field are computed numerically. The numerical results obtained have been illustrated graphically to understand the behavior of phase velocity and attenuation coefficient versus wave number of a wave.

14

Wave propagation at the imperfect boundary between transversely isotropic thermoelastic diffusive half-space and an isotropic elastic layer

Kumar R., Chawla V.

Journal of Technical Physics

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2009

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Vol. 50, no 2

121-146

EN

The present investigation is devoted to a study of the surface wave propagation at imperfect boundary between a homogenous, transversely isotropic thermoelastic diffusive half-space and an isotropic elastic layer of finite thickness. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness, and then deduced for normal stiffness, tangential stiffness and welded contact. The dispersion curves for these quantities are illustrated to depict the effect of stiffness and thermal relaxation times. The amplitudes of displacements, temperature and concentration are computed numerically at the free plane boundary. Specific loss of energy is obtained and depicted graphically. Special cases of interest are also deduced and compared with known results.

15

Analysis of wave motion in transversely isotropic generalized thermoelastic diffusive plate

Kumar R., Kansal T.

Journal of Technical Physics

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2009

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Vol. 50, no 1

17-40

EN

The present investigation deals with the propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, thin elastic plate of finite width, in the context of generalized theory of thermoelastic diffusion. Lord and Shulman(L-S) theory, in which thermal and thermo-mechanical relaxation is governed by a time constant and diffusion relaxation is governed by other different time constant, is selected for the study. According to the characteristic equation, three quasi-longitudinal waves, namely: quasi-elastodiffusive(QED-mode), quasi-massdiffusive(QMD-mode) and quasi-thermodiffusive(QTD-mode), can propagate in addition to quasi-transverse waves(QSV-mode), and the purely quasi-transverse motion(QSH-mode), which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew-symmetric modes of the plate are derived. The amplitudes of displacements, temperature change and concentration for symmetric and skew-symmetric modes of vibration of plate are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient and amplitudes of wave propagation, are presented graphically in order to illustrate and compare the analytical results. Some special cases of frequency equation are also deduced from the present investigation.

16

Axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate

Kumar R., Partap G.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 1

211-237

EN

The propagation of axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of the conventional coupled thermoelasticity (CT) and Lord and Shulman (L-S) theories of thermoelasticity. The generalized theory of elasticity developed by Lord and Shulman is employed by assuming the mechanical behaviour as dynamic to study the problem. Mathematical modeling of the problem of obtaining dispersion curves for microstretch isotropic thermally conducting elastic plates leads to coupled differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations have been solved by using the variable separable method to obtain the secular equations in isolated mathematical conditions for the plates with a stress free thermally insulated and isothermal boundary surface. The secular equations for both the symmetric and skew-symmetric wave mode propagation have been obtained. Thin plate results have also been deduced. These vibration modes are found to be dispersive and dissipated in character. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to the Rayleigh surface wave frequency equation. The dispersion curves, attenuation coefficients and amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew-symmetric wave modes are computed analytically and presented graphically for the Lord and Shulman theory of elasticity. The theoretical and numerical computations are found to be in close aggrement.

17

Structure and properties of grain-refined Al-20wt% Zn sand cast alloy

Krajewski W. K., Buraś J., Żurakowski M., Greer A. I.

Archives of Metallurgy and Materials

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2009

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Vol. 54, iss. 2

329-334

EN

Recent foundry industry requires a development of cast alloys whose melting is both energy saving and environmentally friendly; these are two important priorities of the EC programme. The Al – based cast alloys with increased Zn content could response to these demands because of their good mechanical properties, especially the strength and damping ones, and also relatively low melting temperatures. However, the AlZn – based alloys require grain refining to improve their plastic properties. The presented work is devoted to structural characteristics of the grain - refined high - zinc aluminium alloy Al - 20 wt% Zn. The system studied was Al - 20 wt% Zn alloy (AlZn20), Zn - 4.6 wt% Ti master alloy (ZnTi4 MA), ZnAl - 4 wt% Ti (ZnAl -Ti4 MA) as well as the traditional refiners Al - 5 wt% Ti - 1 wt% B (AlTi5B1 MA) and Al - 3 wt% Ti - 0.15 wt% C (AlTi3C0.15 MA). SEM (scanning electron microscopy), LM (light microscopy) and TA (thermal analysis) investigations showed high effectiveness of the used master alloys as grain refiners of the inoculated with them AlZn20 alloy. The initial examinations of the damping properties were performed using an ultrasonic pulse - echo method. The obtained results showed, that attenuation coefficient of the grain refined AlZn20 alloy, naturally aged before casting during 1 year, decreases by about 10 - 30 % together with increased structural fineness. It was stated that the higher grain refinement of the examined AlZn20 sand cast alloy, the higher decrease of its attenuation coefficient.

PL

Współczesny przemysł wymaga rozwoju stopów odlewniczych, których przetapianie jest energooszczedne oraz przyjazne środowiskowo – są to dwa ważne priorytety programów Unii Europejskiej. Odlewnicze stopy na osnowie Al o podwyższonej zawartości Zn powinny odpowiadać powyższym wymaganiom, ponieważ cechują się one dobrymi właściwościami mechanicznymi, szczególnie wytrzymałościowymi i tłumiacymi, i równocześnie stosunkowo niska wartością temperatury przetapiania. Jednak stopy na osnowie AlZn wymagają zabiegu rozdrobnienia struktury w celu polepszenia ich właściwości plastycznych. Niniejsza praca jest poświęcona charakterystyce zmodyfikowanych, wysoko-cynkowych stopów Al. Badaniom poddano stop Al - 20 wag% Zn (AlZn20), zmodyfikowany przed odlaniem do formy piaskowej dodatkiem nowych zapraw modyfikujacych typu Zn - 4.6 wag. % Ti (ZnTi4 MA), ZnAl - 4 wag. % Ti (ZnAl -Ti4 MA) oraz zapraw tradycyjnych Al - 5 wag. % Ti - 1 wag. % B (AlTi5B1 MA) i Al - 3 wag. % Ti - 0.15 wag. % C (AlTi3C0.15 MA). Badania SEM (scanning electron microscopy), LM (light microscopy) i TA (thermal analysis) wykazały wysoka efektywność rozdrabniania ziaren stopu AlZn20 przez zastosowane zaprawy modyfikujące. Wstępne badania własciwości tłumiacych, wykonane przy pomocy ultradźwiękowej metody wykazały, iż współczynnik tłumienia zmodyfikowanego stopu AlZn20, naturalnie starzonego po odlaniu przez okres 1. roku, zmniejsza się o około 10 - 30 % wraz ze wzrostem stopnia rozdrobnienia struktury. Zmniejszenie to jest tym większe, im większy jest stopień rozdrobnienia ziaren badanego stopu AlZn20.

18

Use of Quantitative Ultrasound to Measure Acoustic Properties of Human Skin

Piotrzkowska H., Litniewski J., Lewandowski M., Szymańska E., Nowicki A.

Archives of Acoustics

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2009

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Vol. 34, No. 4

471-480

EN

The scattering of ultrasonic waves depends on the size, shape, acoustical properties and concentration of scatterers in the tissue. The spectrum of the ultrasonic backscatter can be used to characterize non-invasively the structural and mechanical properties of tissue. We intend to apply the custom-designed high-frequency ultrasonic scanner for the skin and cutaneous lesions characterization by evaluating their attenuating and scattering properties. In this pilot study, we have explored the possibility of extracting the human skin backscattering coefficient (BC) from the ultrasonic B-scans obtained in vivo at 20–30 MHz. The measured BC values of normal skin (dermis) agree well with the published data. We have found also that the spatial resolution of the BC determination using our scanner is sufficient (aprox. 1 mm2) to characterize small skin lesions and assess their penetration depth.

19

Effect of rotation on Rayleigh waves in an isotropic generalized thermoelastic diffusive half-space

Kumar R., Kansal T.

Archives of Mechanics

|

2008

|

Vol. 60, nr 5

421-443

EN

he present investigation is a study of the effect of rotation on the characteristics of Rayleigh waves propagation in a homogeneous, isotropic, thermoelastic diffusive half-space in the framework of different theories of thermoelastic diffusion, including the Coriolis and Centrifugal forces. The medium is subjected to stress-free, thermally insulated/isothermal and chemical potential boundary conditions and is rotating about an axis perpendicular to its plane. Secular equations of surface wave propagation in the considered media are derived. The phase velocities and attenuation coefficients of surface wave propagation have been computed by using the irreducible case of Cardano's method, with the help of DeMoivre's theorem known from the secular equations. The amplitudes of surface displacements, temperature change, concentration and the specific loss of energy are computed numerically. Rotation effect on the phase velocity, attenuation coefficient, amplitudes of surface wave propagation and specific loss of energy are presented graphically in order to illustrate and compare the analytically obtained results. Some special cases of frequency equation are also deduced from the present investigation.

20

Ultrasonic waves in densified suspensions

Kowalski S., Sikorski M.

Archives of Acoustics

|

2004

|

Vol. 29, no. 4

633-646

EN

A theory of propagation of ultrasonic waves in sediments is developed. The formulae for the phase velocity and the attenuation coefficient are determined as functions of wave frequency and the mass fraction of the solid phase. These formulae can be used, after suitable calibration, for determination of the solid mass fraction or the water content in densified suspensions. These structure parameters can be determined by measuring the transition time of ultrasonic wave through a given distance of sediment. The phase velocity dispersion curves and the attenuation coefficients determined theoretically and experimentally are plotted as functions of the solid mass fraction for sediment.