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1

Application of Fractional Calculus in the Theory of Viscoelasticity

Soczkiewicz E.

Molecular and Quantum Acoustics

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2002

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Vol. 23

397-404

EN

The fractional derivate method has been used in studies of the complex moduli and impedances for various models of viscoelastic substances. Calculations vave been performed for MAxwell and Barlow-Erginsav-Lamb models. Influence of the values of the fractional parameters on the frequency dependances of the complex moduli and impedances has been studied.

2

Rozpraszanie wstecz fal akustycznych w ośrodkach przypadkowo niejednorodnych

Soczkiewicz E.

Prace Naukowe Instytutu Telekomunikacji i Akustyki Politechniki Wrocławskiej. Konferencje

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2001

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Vol. 83, nr 27

57-62

EN

Backscattering coefficient for acoustic waves propagating in randomly inhomogeneous media has been estimated by means of Chernov formula. Calculations have been performed for media with spatially continuous fluctuations in the acoustic refractive index as well as for those ones with discontinuous changes of the refractive index. The formulae for backscattering coefficients depend on the following statistical characteristics of a medium: mean square fluctuations of the medium acoustic refractive index, form of the correlation function of these fluctuations, and ratio of the mean dimension of medium inhomogeneities in comparison to the wavelength of acoustic radiation. The derived formulae have been used to estimation limits of application of the method of parabolic equation in studies of waves propagation in randomly inhomogeneous media.

3

Studies of Acoustic Waves Scattering in Randomly Studies of Acoustic Waves Scattering in Randomly Inhomogeneous Media by Means of the Differential Equation of Parabolic Type

Soczkiewicz E.

Molecular and Quantum Acoustics

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2000

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Vol. 21

261-266

EN

Influence of the form of medium inhomogeneities correlation function on the limitation of using the approximation of parabolic differential equation in studies of acoustic waves propagation in randomly inhomogeneous media has been investigated. The approximation of parabolic equation can be used if backscattering coefficient of waves is smali in companson with the forwardscattering one. Backscattering coefficients of waves in randomly inhomogeneous media with the Gaussian inhomogeneities correlation function and the simple exponential one, have been calculated in function of ka

4

Fraktale w procesach falowych i w nieinwazyjnych badaniach materiałów

Soczkiewicz E.

Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska

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1999

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z. 87

125-132

PL

Rozpatrzono wpływ fraktalnej struktury na własności sprężyste materiałów fraktalnych, gęstość rozkładu zlokalizowanych drgań, tzw. fraktonów, oraz ich wpływ na przewodnictwo cieplne ośrodka. Opisano zastosowanie geometrii fraktalnej w badaniach nieniszczących oraz w badaniach ultradźwiękowych materiałów polikrystalicznych. Scharakteryzowano emisję i rozpraszanie fal przez struktury fraktalne oraz fraktalne własności pól falowych.

EN

Elastic properties of fractal materials as well as the dispersion and density of distribution of localized elastic vibrations, so called fractons, have been considered. Nonlinear interactions of phonons and fractons influences heat conduction of amorphous materials. Application of fractal geometry in nondestructive testing and evaluation of materials and in ultrasonic studies of polycrystalline materials have been described. Emission and scattering of waves by fractal structures as well as description of fractal properties of wave fields have been presented.

5

Propagation and Scattering of Acoustic Waves in Randomly Inhomogeneous Media, A Comparison of Methods and Results

Soczkiewicz E.

Molecular and Quantum Acoustics

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1999

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Vol. 20

231-240

EN

Scattering coefficients of acoustic waves in randomly inhomogeneous media have been calculated for various forms of the medium inhomogeneities correlation function. The results obtained by the methods of smali perturbattons, the parabolic equation and the Green function method have been discussed.